THE UNIVERSITY OF MICHIGAN The Industry Program of the College of Engineering The Institute of Science and Technology The Department of Mechanical Engineering jointly present a conference on ENGINEERING FOR RELIABILITY under the direction of DR. CHARLES LIPSON Professor, Mechanical Engineering March 14, 1962 RACKHAM AMPHITHEATER ANN ARBOR

"....If the University has any unique contribution to make, it has to do with knowledge: with its discovery and with its transmission..." Roger W. Heyns Vice-President and Dean of Faculties The University of Michigan "....It is because we recognize the economic implications of reliability that most of us are here..." Herbert L. Misch Vice-President, Engineering and Research Ford Motor Company iii

TABLE OF CONTENTS Page PARTICIPANTS............................................. vii OPENING OF TEE CONFERENCE............................. 1 Charles Lipson Professor, Mechanical Engineering The University of Michigan WELCOMING ADDRESS........................................... 5 Roger W. Heyns Vice-President and Dean of Faculties The University of Michigan INTRODUCTION TO RELIABILITY.................................. 9 SESSION NUMBER ONE.................................... 19 SESSION NUMBER TWO................................................. 35 LUNCHEON ADDRESS............................................. 47 Herbert L. Misch Vice-President, Engineering and Research Ford Motor Company SESSION NUMBER TREE..........................................3 SESSION NUMBER FOUR....................................... 67 BIBLIOGRAPHY.................................................. 87

PARTICIPANTS Alexanderson, H.A. Director Engineering Bendix Corp. Utica Division Utica, New York Appelblatt, Irving Chief U.S. Army Ordnance Engineering Division Tank-Auto. Command Center Line, Michigan Aronson, 0. R. President The Govro-Nelson Co. 1931 Antoinette Street Detroit 8, Michigan Atkin, R. L. Chief Engineer Kelsey-Hayes Company Automotive Division Romulus, Michigan Attwood, S. S. Dean The Univ. of Mich. College of Engineering Ann Arbor, Michigan Bancroft, C. 0. Manager Thompson Ramo Wooldridge Quality Prod. Valve Div. Cleveland, Ohio Bauer, C. G. Director Chrysler Corporation Quality Control Office P.O. Box 1919 Detroit 31, Michigan Beal R. W. Director U. S. Army Engineering Research and Dev. Lab. Fort Belvoir, Virginia Bender, D. C. Vice President Hayes Industries Ltd. Engineering Jackson, Michigan Benson, Irving General Motors Corp. 2860 Clark Detroit 32, Michigan Black, S. A., Dr. Research Associate U.S. Rubber Company Research Center Wayne, New Jersey Bluhm, Richard Assistant Chief Engrg. Bendix Corporation Reliability Engrg. Dept. Eclipse-Pioneer Div. Teterboro, New Jersey vii

Bonow, Eric Assistant Chief Engr. Wisconsin Motor Corp. 1910 S. 53rd Street Milwaukee 46, Wisconsin Boswinkle, George Senior Advisor Whirlpool Corporation Design Engineer St. Joseph, Michigan Braun, A. Chief Engineer General Motors Corp. Rochester Prod. Div. Rochester, New York Brede, A. Director Motor Wheel Corp. Research and Dev. 1600 N. Larch Lansing, Michigan Brock, HE. L. Director Deere and Company Engineering Research Waterloo, Iowa Broughton, D. C. A. 0. Smith Corp. Milwaukee, Wisconsin Brumbough, E. M. Manager J. I. Case Company Engineering 700 State Street Racine, Wisconsin Burks, G. E. Vice President Caterpillar Tractor Co. Engrg. and Research Peoria, Illinois Carlson, G. A.,Jr. Acme Mfg. Company 1400 East Nine Mile Detroit, Michigan Carlson, J. A. Sealed Power Corp. 2001 Sanford Street Muskegon, Michigan Carmichael, Colin Editor Penton Building Machine Design Cleveland, Ohio Carpenter, W. F. Sundstrand Aviation 2421 11th Street Rockford, Illinois Carson, R. C. Vice President Shuler Axle Company Engineering Louisville, Kentucky viii

Chapin, Gordon Director Kelsey-Hayes Company Quality Control Automotive Div. Romulus, Michigan Cheal, N. L. General Motors Corp. 895 Joslyn Road Pontiac, Michigan Christenson, C. Dana Corporation Toledo, Ohio Clark, H. M. Assistant Thompson Ramo Wooldridge Chief Engineer 34201 Van Dyke Avenue Warren, Michigan Coleman, W. W. Executive Engineer Ford Motor Company Product Development Engine and Foundry Div. Dearborn, Michigan Conover, W. C. Director Outboard Marine Corp. Marine Engineering Waukegan, Illinois Cornish, Roy R. Director General Motors Corp. Reliability Saginaw Steering Gear 3900 Holland Road Saginaw, Michigan Cutler, G. Research Director Whirlpool Corporation Research Laborabory St. Joseph, Michigan Danford, D. L. Assistant to Director The University of Mich. Industry Program Ann Arbor, Michigan Dean, M. M. Manager, Dev. Dept. Ford Motor Company Truck Engineering Dearborn, Michigan Deileth, R. J. Chief Engineer Motor Wheel Corporation 1600 North Larch Lansing, Michigan Dick, Wesley M. Clutch Engineer Dana Corporation Toledo, Ohio Dickenshied, R. H. Manager Ford Motor Company Technical Service Dearborn, Michigan Donley, C. O. Chief Engineer General Motors Corp. Diesel Equipment Div. Grand Rapids, Michigan Dorsey, R. S. General Electric Co. Evendale, Ohio ix

Dorton, G. A. Assistant Chief Engr. The Cooper-Bessemer Corp. Development Division. Mit. Vernon, Ohio Dullabaun, P. W. Project Engineer The Mather Spring Co. Box 6695 W. Toledo Station Toledo 12, Ohio Dunn, G. E. Chief Engineer Chrysler Corporation Detroit Universal Div. Detroit, Michigan Eaton, W. C. Chief Production Engr. Midland-Ross Owosso Division Owosso, Michigan Edmonson, G. V. Associate Dean The University of Mich. College of Engineering Ann Arbor, Michigan Erwin, R. L. Manager Ford Motor Company Admin. Engr. & Service 2500 Maple Road Tractor and Impl. Div. Birmingham, Michigan Evaldson, R. L. Associate Director The University of Mich. Instit. Sci. and Tech. Ann Arbor, Michigan Farley, N. E. Dir., Proving Grounds General Motors Corp. Chevrolet Division Milford, Michigan Farley, R. A. Senior Project Engr. General Motors Corp. Harrison Rad. Div. Lockport, New York Flagan, R. G. Director Fruehauf Trailer Co. Engr. and Research Detroit, Michigan Ford, C. B. General Motors Corp. Cadillac Motor Car Div. Fox, M. L. Chief Engineer Dana Corporation Parish Pressed Steel Toledo, Ohio Division Gadd, Charles General Motors Tech. Cent. Research Laboratories 12 Mile and Mound Roads Warren, Michigan x

Gajda, Vice President Snyder Corporation Engineering 3400 E. Lafayette Ave. Detroit 7, Michigan Gale, Cutler Whirlpool Corporation St. Joseph, Michigan Gately, T. J. Koppers Co., Inc. 200 Scott Street Baltimore 3, Maryland Gayley, Harry Metallurgical Engineer Ingersoll-Rand Co. Research and Dev. Dept. Phillipsburg, New Jersey Gregory, E. M. Nat. Aero. and Space Adm. Langley Research Center Langley AFB3, Virginia Green, D. C. Chief Engineer Rockwell-Standard Corp. Spring Division Logansport, Indiana Halberg, R. W. Associate Director Borg-Warner, Corp. Automotive Department Des Plains, Illinois Hall, J. M. Chief Engineer Vickers Corporation Technical Services Detroit} Michigan Hanslip, R. E. Engineer Manager The Mather Spring Co. Toledo, Ohio Happe, M. J. Production Test Manager New Holland Machine Co. Div. of Sperry Rand New Holland, Penn. Hart, J A. Head, Nordberg Mfg. Co. Analytical Design Sect. Milwaukee, Wisconsin Harty, J. C. Reliability Manager Lear Inc. Grand Rapids, Michigan Held, L. F. Chief Design Engineer General Motors Corp. Euclid Division Hauling Equipment Cleveland, Ohio Hellenberg, C. E. Manager Mobile Division Racine Hydraulics Racine, Wisconsin xi

Henkin, Alexander Instructor The University of Mich. Mechanical Engrg. Dept. Ann Arbor, Michigan Herr, F. Principal Staff Engr. Lear, Incorporated 110 Ionia Ave. N.W. Grand Rapids, Michigan Hesling, D. M. Vice President Sealed Power Corporation Research and Development Muskegon, Michigan Heyl, R. G. Chief Engineer American Metal Products 5959 Linsdale Detroit 4, Michigan Heyns, R. W. Dean of Faculties The University of Mich. Ann Arb-orl Michigan Hill, J. F. Manager Engineering Midland-Ross Corporation Janitrol Aero Division Columbus, Ohio Hillring, L. A. Design Reliability Engr. Bendix Product Auto. Div. 401 Bendix Dr. South Bend, Indiana Hinkel, L. Whirlpool Corporation Research Laboratory 300 Broad Street St. Joseph, Michigan Horan, R. P. Chief Engineer-Design Eaton Mfg. Company Eaton Research Center 26201 Northwestern Hgwy. Southfield, Michigan Horn, N. W. Chief Application Engr. Borg-Warner Corporation Wooster Division Wooster, Ohio Howard, Wayne Midland-Ross Corporation Owosso, Michigan Hull, G. A. Test Engineer Lear, Inc. Instrument Division Grand Rapids, Michigan Hummel, P. J. Chief Engineer U.S. Armny Regional Maintn. Office Schenectady, Gen. Depot Schenectady, New York xii

Huseby, R. A. Associate Director A. 0. Smith Corporation Metallurgical Research Milwaukee 1, Wisconsin Hyler, J. If. Chief Engineer LeTourneau-Westinghouse Product Res. and Dev. Peoria, Illinois Jandasek, V. J. Executive Engineer Ford Motor Company Transmissions and 36200 Plymouth Road Chassis Division Livonia Michigan Jass, John Director Caterpillar Tractor Co. Engineering Peoria, Illinois Jester, Ralph Walker Mfg. Company Jackson, Michigan Johnson, H. W. Executive Engineer Ford Motor Company Product Engr. Office Dearborn, Michigan Johnson, Leonard Reliability Scientist General Motors Corp. Research Laboratories Gen. Mtrs. Tech. Center Warren, Michigan Jones, L., Jr. Chief Bearing Engineer Kaydon Engineering Co. Muskegon, Michigan Jones, M. H. Bohn Alum. & Brass Corp. Piston Engineering Center South Haven, Michigan Jordan, E. R. Chief Engineer Clinton Engine Co. Chainsaw and OutboardDiv. Clinton, Michigan Jorgenson, J. G. Chief Engineer Kearney and Tractor Corp. Res. and Dev. Division 6800 W. National Ave. Milwaukee 14, Wisconsin Jung, R. R. Chief Engineer Clark Equipment Company Development Division Battle Creek, Michigan Junker, A. J. Chief Quality Engineer American Motors Corp. 14250 Plymouth Detroit 32, Michigan xiii

Juvinall, R. C. Associate Professor The University of Mich. Mechanical Engr. Dept. Ann Arbor, Michigan Kadis, George Manager Quality Control General Motors Corp. Euclid Division Hudson, Ohio Kallenbach, Ralph Chief Engineer Internatl Harvester Co. 10400 W. North Avenue Melrose Park, Illinois Kaplan, A. L. Starr-Kap Engineering Co 13727 Plymouth Road Detroit 27, Michigan Kauppila, Raymond Teaching Fellow The University of Mich. Mechanical Engr. Dept. Ann Arbor, Michigan Kelley, A. HE., Jr. Head, General Motors Corp. Engineering Test Dept. General Motors Prvg. Gd. Milford, Michigan Kerawalla, J. N. Teaching Fellow The University of Mich. Mechanical Engr. Dept. Ann Arbor, Michigan Kimberly, A. E. Chief Engineer Chrysler Corporation Vehicle Reliability Detroit, Michigan Klinge, E. R. Executive Engineer Ford Motor Company Truck Division Dearborn, Michigan Knox, D. R. Director of Engineering Bundy Tubing Company 8109 E. Jefferson Detroit, Michigan Koch, K. M. Director Rockwell-Standard Corp. Engineering Detroit, Michigan Kohltmann, S. J. Whirlpool Corporation St. Joseph, Michigan Kreuze, Floyd Chief Reliability Engr. Lear, Incorp. Instrument Division Grand Rapids, Michigan Kuchera, G. Jo Executive Engineer A. O. Smith Corporation Milwaukee, Wisconsin xiv

Lambeck, R. P. Chief Engineer Vickers, Inc. Aero Space Division Detroit, Michigan Lambertine. J. A. Chairman The Bendix Corporation Reliability Commission 1104 Fisher Building Detroit 2, Michigan Lee, R. E. Firestone Steel Product Akron 1, Ohio Leist, Robert Product Engineer Bohn Alum. & Brass Corp. Detroit, Michigan Lemke, L. L. Chief Engineer Internatl Harvester Co. Design Analysis Section 10400 W. North Avenue Melrose Park, Illinois Limberg, A. A. Chief Body Engineer General Mtrs. Tech. Cent. 12 Mile and Mound Roads Warren, Michigan Little, Robert Teaching Fellow The University of Mich. Mechanical Engrg. Dept. Ann Arbor, Michigan Lipson, Charles Professor The University of Mich. Mechanical Engrg. Dept. Ann Arbor, Michigan Logue, R. L. Chief Engineer Ford Motor Company Metal Stamping Division 20000 Rotunda Drive Product Engrg. Office Dearborn, Michigan Maugh, L. C. Acting Chairman The University of Mich. Civil Engrg. Dept. Ann Arbor, Michigan Mazur, J, C. Assistant Professor The University of Mich. Mechanical Engrg. Dept. Ann Arbor, Michigan Mazziotti, Phillip Director Dana Corporation Engineering Toledo, Ohio Milde, E. D. Vickers Company Marine & Ordnance Div. 172 E. Aurona Street Waterbury, Conn. xv

Misch, t. L. Vice President Ford Motor Company Executive Director Dearborn, Michigan Mitchell, Larry Teaching Fellow The University of Mich. Mechanical Engrg. Dept. Ann Arbor, Michigan Moncher, F. Director - Engineering Vickers Inc. Aero Space Detroit, Michigan MacKay, R. W. Chief Engineer The Electric Autolite Co. Toledo 2, Ohio MacKusich, M. H. Manager Firestone Steel Products Research and Dev. Akron, Ohio McCormick, Harold Project Engineer Ramsey Corporation P. 0. Box 513 St. Louis 66, Missouri McKee, R. E. Sales Manager R.K. LeBlend Mach. Tool Co. Cincinnati 8, Ohio McNitt, L. F. Manager Midland-Ross Corporation Management Sales Cleveland, Ohio Ordorica, M. Chief Engineer Willys Motors Chassis Design Toledo, Ohio Orr, Palmer Chief Engineer Borg Warner Corporation Warner Gear Division Muncie, Indiana Park, D. M. Mfg. Engineering Manager Associated Spring Corp. B.M.R. Division Plymouth, Michigan Passon, P. J. Liaison Engineering General Motors Corp. Reliability Engrg. Supv. Engineering Center Chevrolet Motor Division 30003 VanDyke Warren, Michigan Perry, W. J. McGraw-Hill New Yor!k, New York Pettis, G. H. Chief Fruehauf Trailer Company Liaison Engineer P. 0. Box 238 Detroit 32, Michigan xvi

Pierce, W. G. Chief Product Engineer A. O. Smith Corporation Automotive Division Milwaukee, Wisconsin Plante, Robert Director Whirlpool Corporation Laboratory Services St. Joseph, Michigan Prince, Thomas Reliability Engineer The Bendix Corporation Scintilla Division Sidney, New York Quackenbush, L. J. Associate Professor The University of Mich. Mechanical Engrg. Dept. Ann Arbors Michigan Quintilian, B. F. Manager Koppers Co. Inc. Engineering Services Baltimore, Maryland Raymond, C. C. Quality Manager Eaton Manufacturing Co. Marshall Division Detroit, Michigan Richards, J. W. Director Ford Motor Company Tech. Analysis Office 20000 Rotunda Drive Engineering Staff Dearborn, Michigan Ridler, C. G. Supervising Engineer Harrison Radiator Div. General Motors Corp. Lockport, New York Rumpf, R. J. Product Study Office Ford Motor Company P. 0. Box 2053 Dearborny Michigan Rupert, S. J. General Manager Cimco Engineering Co. 2465 Industrial Hgwy. Ann Arbor, Michigan Schafer, Vernon Staff Engineer General Motors Detroit Diesel Eng. Div 13400 W. Outer Drive Detroit, Michigan Schultz, F. Midland-Ross Corp. Owosso, Michigan Schultz, Richard Whirlpool Corporation St. Joseph, Michigan xvii

Shields, J. J. Chief Design Engineer Cont. Avia. & Engrg.Corp. Turbine Division 12700 Kercheval Avenue Detroit 15, Michigan Shigley, J. E. Professor University of Michigan Mechanical Engrg. Dept. Ann Arbor, Michigan Smalley, R. D. Head, Nordberg Mfg. Company Advanced Design Section Milwaukee, Wisconsin Smiley, F. Chief Engineer McGill Mfg. Co. Inc. Bearing Division Valparaiso, Indiana Smith, R. J. Chief Engineer McGill Mfg. Co. Inc. Bearing Division Valparaiso, Indiana Spinner, R. W. Director Reliability General Motors Corp. Buick Motor Division Flint, Michigan Staples, C. F. President Staple Engrg. Co. Inc. 1315 S. Woodward Birmingham, Michigan Taylor, Joseph Assistant to Director The University of Mich. Engrg. Summer Confer. Ann Arbor, Michigan Taylor, R. E. Chief Engineer Murphy Diesel Company Milwaukee, Wisconsin Tobin, L. W.,SJr Director Ford Motor Company Product Quality Dearborn, Michigan Trost, N. F. Assistant Dir. of Rel. General Motors Corp. Truck and Coach Div. Pontiac, Michigan Van Auker, D. Superv. of Publications Vickers Corporation Detroit, Michigan Vanator, G. M. Head, Tech. Data Dept. General Motors Corp. Gen. Mtrs. Proving Gd. Milford, Michigan VanderbiltV.Jr. Chief Research Engr. Perfect Circle Company Hagerstown, Indiana Van Wylen, G. J. Chairman The University of Mich. Dept. of Mech. Engrg. Ann Arbor, Michigan xv i i

Wallin, R. E. Senior Production Engr. New Holland Machine Co. Div. of Sperry Rand New Holland, Penn. Wasielewskil E. W. Associate Director Goddard Space Flight Cent. Greenbelt, Maryland Watt, V. S. U.S. Naval Exp. Station Annapolis, Maryland West, George Associate Professor The University of Mich. Naval Arch. & Marine Ann Arbor, Michigan Westra, Dan Chief Engineer Challenge Machinery Co. Grand Haven, Michigan Widman, J. C. Executive Engineer Ford Motor Company Adv. Prod. Design,M.S.P. Dearborn, Michigan Williams, C. W. Bower Roller Bearing Co. Detroit, Michigan Wilson, John Project Engineer Cincinnati Milling Mach. Marburg Avenue Cincinnati 9, Ohio Woodward, S. G. Chief Engineer Bendix Corporation Eclipse Machine Div. Elmira, New York Wright, L. W. General Motors Corp. Buick Motors Div. Flint, Michigan Wynne, T. N. Supervisor - Quality Cummins Engine Company Control Engineer 1000 Fifth Street Columbus, Indiana Zweier, W. C. Administrative Engr. The White Motor Company Cleveland 1, Ohio xix

TRANSCRIPT OF THE CONFERENCE December, 1962

OPENING OF THE CONFERENCE Charles Lipson Professor, Mechanical Engineering The University of Michigan

A few days ago there appeared in the Wall Street Journal a letter to the editor raising some questions as to the general usefulness of seminars. This letter specifically referred to business and management seminars, but the message it carried can just as well apply to today's seminar on engineering. Here's what the letter essentially said: Such seminars have not lived up to their expectation because middle-aged executives, instead of young, receptive, and trainable men, have been dispatched to the college campus for retreading. Harvey Lehman has shown in his book "Age and Achievement" that scientists, authors, athletes and others make their peak contribution in the middle thirties. Perhaps seminars would continue to serve a useful purpose if the upper age limit for admission was set at thirty-five. Well, unfortunately at the time this article appeared it was much too late to do anything about it, too late to separate the young, the vigorous, the receptive - I am, of course, referring to those under thirty-five - from those in need of retreading, who are over thirty-five. So we have asked Mr. Roger Heynes, Vice-President and Dean of Faculties, to come here and to re-assure you on behalf of the University that you are all welcome. Mr. Heynes. -'3

WELCOMING ADDRESS Roger W. Heyns Vice-President and Dean of Faculties The University of Michigan

Thank you, Professor Lipson. I seem to feel I am well qualified as a middle-aged man to assure you that if you are over thirty-five you are indeed welcome, because I certainly am not going to join in any movement to make that group underprivileged. I often wonder when I get these invitations to extend a word of welcome to people coming to important educational activities,just exactly what the motivation is behind these invitations. Sometimes I feel it is something parallel to the mother who brings her offspring into the room where there are lots of adults and says, "Say hello to the nice people." On other occasions, I think that perhaps kind and gentle professors feel a little bit sorry for the administration and want to use an occasion like this to have them feel that they are involved, in some even minor way, in the educational process. I am grateful for that. I enjoy these moments and I enjoy thinking about them in advance. It gives one a chance to speculate and to think, and we need occasions like this to think about the basic purposes of a university. And, indeed, one of the major purposes of a university is represented in a meeting such as this. If the university has any unique contribution to make, it has to do with knowledge: with its discovery and with its transmission. Now, typically, we think about this at the undergraduate level and sometimes at the graduate level, but there comes a moment in the discovery of knowledge when it is just terribly important that professors, who are agents of society engaged in investigations at the frontiers of knowledge, interact with people who have the responsibility for tackling important problems in the world. It is important that these people be brought together. Indeed, out of this interaction of the investigator (who has been permitted by our society and by an institution, such as this, to devote himself to discovery) with people, who are engaged in the struggle with important problems, comes in the most creative possible way, new knowledge - effective new knowledge. It is at the moments like this that we recognize the false dichotomy between pure and applied knowledge. Indeed, pure knowledge is interesting to us because of what we can do with it. And nowhere does this come into clearer focus than at a seminar like this. What I am saying is that, not only is Professor Lipson playing an important role in this meeting, but you with your reactions are playing an important role too. Out of this process comes real discovery and real advancement. I hope that you won't mind if I spend one moment paying tribute to your host, Professor Lipson, who in a very undramatic way comes to a point in his thinking where he would like to communicate it, without a lot of ostentation and, I might add, without a lot of overhead. He asks his colleagues and yourselves to come and discuss with him some of the things he has on his mind. I think this is in the finest tradition of -7

-8the world of academicians and I compliment him for it, and I am sure I do it also on your behalf. Let me close then by saying that I think this is an exciting moment and an important moment for these sponsoring agencies: The Industry Program, The College of Engineering, The Institute of Science and Technology and The Department of Mechanical Engineering. Finally then, for all age groups, on behalf of the University, I want you to feel very welcome. Thank you.

INTRODUCTION TO RELIABILITY Charles Lipson g-9

In the way of introducing myself and justifying my appearance on this platform I would like to compare our work in Reliability to an inverted pyramid, with a broad base at the top and a sharp point at the bottom. The broad base corresponds to five years of work we have done in this field, some of it here at the University and some in industry. Subsequently we condensed all this information into a three-month course called "Reliability Considerations in Design" which we offered to our students last fall. This July we are running an intensive summer course on this subject to last for five days. Today we are meeting at a seminar for one day. Next month or so we are going to England to deliver a paper to the Institution of Mechanical Engineers on Reliability, the time of presentation to be precisely thirty-five minutes. If we were to extend this unmistakable trend.to its logical conclusion I suspect that the time will arrive when we could condense this whole wealth of information into a single sentence. And this sentence might read: "Reliability is just an Organized, Common Sense." And in this spirit of common sense let us proceed with today's seminar. What is reliability? In the true sense of the word it is just what I said: an organized, formalized common sense. A more formal definition may read like this: "Reliability is an ability or, in the language of a mathematician, a probability that a product will perform its function to specific standards, under specified conditions, for a specified period of time, without failure." Thus, reliability is a hope, a belief, an expectation that the product you make will behave satisfactorily in the hands of the customer. Now we all know that for a product to be satisfactory in service it is the responsibility of not one but of three departments: engineering, manufacturing, and service. Today we will be principally concerned with the engineering phase of reliability. The reason is two-fold: first, because I feel we are really qualified principally in that field; and second, because the engineering phase is really the only new function of reliability. The reliability in production and in service, in one form or another, exists in practically every organization. So let us discuss today the engineering aspect of reliability. First, why all this interest in reliability? Why almost anywhere you turn do you see a new article on this subject? Why are ten colleges already offering courses in reliability (although admittedly only the mathematical or the management phases of it) and ten more colleges scheduled to offer courses in reliability next fall, with one institution listing a Master's degree program in this field? Why does practically everybody establish or plan to establish Departments of Reliability, in one form or another and under one name or another? Why, in short, has Mr. Cole of General Motors called reliability the "Number one phase of our busine ss'"? -11

-12I believe that all this interest in reliability is due to the heavy cost of unreliability. Warranties, field campaigns, parts replacements, gratis payments, all are manifestations of management's concern with unreliability. It is not uncommon for an organization to spend, say, twenty million dollars a year on engineering, but another twenty million dollars on keeping the customers happy. This is no longer good enough. We can no longer afford three years to produce a product and six additional years to make it work. Instead, we require a high level of confidence that in the hands of the customer the product will work the first time out. Now how to achieve it? This is precisely the subject of our seminar and we propose to discuss with you how to predict reliability, and what are the limitations of this prediction; how to verify reliability by undertaking a suitable test program; and what are some of the tools of reliability, such as Failure Analysis, Statistical Tolerances, Accelerated Tests, Stress and Strength Considerations, Variance Analysis, etc. Let me give at this time a very brief preview of some of these topics: Figure 1 - Here is a graph showing one of the most important causes of unreliability: the scatter in the properties of manufactured parts. We shall show this figure and others in detail later on. Figure 2 - We shall attempt to show you how to predict reliability with the aid of diagrams such as this, where you relate the design life with percent reliability and percent failures. Figure 3 - We shall indicate how many samples to use in a test in order to obtain results in which you have a certain level of confidence. Figure 4 - This will indicate how much overload is to be put on a part, in this case an engine part, so that the test can be terminated in 100 hours instead of 1000 hours. Figure 5 - We shall attempt to show how by studying progressive stages of pitting we can interpret more effectively data coming from the field.

-13Figure 6 - Fractures can be classified and analyzed to get a better insight into the causes of failure. Figure 7 - Through a method known as Multi-Variant Analysis some of the causes of failure may be traced. Figure 8 - We shall discuss Statistical Tolerances as an important tool in any Reliability Program. But this is probably enough of a preview and let us proceed with our Discussion. Let us start with causes of unreliability.

-14200.080 Oo 0 a co 0 00 I00 cn 5 0_ _ _ _ _ _ 3 70 200 ~-~~ ~.L -C YCE'"o 7 0'~..~..% 1 ~,,Im,.~~. -. 0._ Figure 1. Scater in thePopete o Hyoi\ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~~~~ ~ ~ ~ I~~ ~ 98 ~me ~ cn50 -~ ul PROPOSED DESIGN LIMIT CD,U. (NOT OVER 5 PER CENT FAILURES)I ____ ~ ~ ~ ~ a 0.9 30 l~~~~~~~~~~~~o 2O I~~~~~~~~~~~~~0. LIFE - CYCLES Figure 1. Scatter in the Properties of Hypoid and Bevel Gears. PERCENT RELIABILITY 99.99 99.9 99.8 99.5 99 98 96 90 80 70 60 501.0 0.9 J.~.~ 7 0.8 0.7 0.6 WHEELS p —-t, C-' —— L-f_ 0.4 < ILEAF IL FANS I IiI o 4 GEARS 02 i-1. C'SHCAFT A~ Y /II/ w UC'SHAFT BI I 0.1 WHEEL 0.09 i1I o s SPID 0. 08 0.07 0.06 -_J m 0.05 Ix z 0.04 W ENGINE 0_0. SALVES.o 4 ILI 0.02 L - ~ ~ ~ ~ ~ ~~~~~~~~~~~0.09 I 0.01 01 0.2 0.5 I2 5 10 20 30 40 50 PERCENT FAILURES Figure 2. Reliability of Automotive Parts.

-1.5I 2 a I 90 % CONFIDENCE 95 % LEVEL 99 % 10 100 10. 0 100 999% 104 50 3 20I00 = 50 0 I \1010 10 2010 0 i 0 10 E, 9 9.9% I\0 1 0[ D I 14 Figure 3. Number of Samples Required for a Significant Test. 2780 HOURS 2000 1000o 0 I 00 0 I 1, 1O123 OVERLOAD Figure 4. Amount of Overload Required for a Significant Test.

-16TRANSMISSION I ST GEAR ~ 72,300 psi 2.7 DESIGN A 2ND GEAR (B 66,100 psi 2.1 TRANSMISSION IST GEAR () 82,000 psi 1.9 DESIGN B 2ND GEAR (G 59,600 psi 2.1 REAR AXLE PINION 2.9 TAPERED ROLLER BEARING 2.7 Figure 5. Pitting Conversion Factors. S|rs~s No Stress Concentrotion Mild Stress Concentrotion HOigh Stress Cniofr2sotio. Low Overstress High Overstress Low Overtress High Overstress Low Oversitres High Ovaltll, e ~. Ca s b.. d# ~ One-way banding load Tw-way bonding load e Revenrd beading ond rotration load

POSSIBLE CAUSES LETTER VALUE OF FAILURE ASS IGNED GOOD Al FIT BAD A2 GOOD B1 ENVIROMENT BAD B32 GOOD C1 ALIGNMENT BAD C2 Figure 7. Multivariant Analysis of a Journal Bearing. 14 16 TOLERANCE FOR OTHER PART IL LL Ir0 2 4 6 8 8.6 10 12 14 Algebraic to Statistical.

SESSION NUMBER ONE Charles Lipson -19

I feel that one of the most important causes of unreliability is the scatter in the properties of manufactured parts. No two parts produced are exactly the same, no matter how carefully they are made. Although the differences may be small they nevertheless exist, and, in turn, they have an important bearing on reliability. Figure 9 (which is a repeat of Figure 1 shown before) gives the life of bevel and hypoid gears. The stress is plotted on the ordinate in 1000 pounds per square inch, and the life is plotted on the abscissa in cycles,on a logarithmic scale. You will note that at any stress level imposed on the gears by the fatigue load, the number of cycles to failure varies widely, by a factor of the order of 50:1. You will also notice a line, which reads "Proposed Design Limit (not over 5% failures). We have done some work on the Design Limits, and we will have more to say about it later. Now this scatter in life is not confined only to gears but it is characteristic of every manufactured part, some parts exhibiting a wide scatter, and some a narrow scatter. Here, for example (Figure 10), are engine exhaust valves. Several engines were installed in fleet operation, the various groups representing various engine designs. In the first engine of the first group the first valve failure was recorded at about 15,000 miles. The second engine when examined at 65,000 miles had no failure. The next engine showed also no failure. But the fourth engine had a failure at 30,000 miles, and the fifth engine of the group at about 25,000 miles. The same degree of scatter was more or less characteristic of all the other engine groups shown in Figure 10. One might say that this large scatter in the life is not surprising because,after all,this was a fleet operation, and everybody knows that the speed may not have been the same, the load was not the same and, in general, the engines were not subjected to identical operating conditions. And, so, a test was run, this time on the dynamometer, under controlled conditions, with the results as shown in Figure 11. You will note that the degree of scatter is approximately the same. This strongly suggests that although the operating conditions are important there is something inherent in the properties of manufactured parts so that even under controlled conditions we may still get considerable scatter. One more graph on the subject of scatter. Figure 12 refers to front wheel bearings of a truck. The data are plotted in a form of a standard Cumulative Life Curve (I say "standard" because the Weibull method of plotting will be shown later). Bearing Life in thousand miles is shown on the ordinate and Percent of Bearings Failed on the abscissa. -21

-22200 goo o a co o oo 10z: I.... a —- - 750 (/) PROPOSED DESIGN LIMIT * OC (NOT OVER S PER CENT FAILURES) 30 20 10. 0 LIFE - CYCLES Figure 9. Scatter in the Properties of Hypoid and Bevel Gears. 70 60 50 _40o u) LJ -J i 30 GROUP I GROUP 2 GROUP 3 GROUP 4 GROUP 5 ENGINE Y ENGINE Y ENGINE Y ENGINE G ENGINE G Figul-e 10. Life of Engine Exhaust Valves, Fleet Test. GROU I GOUP GROP 3 ROUP4 GRUP

-231000 900 800 700 - 0 z 600 W 500 - 400 300 200 100 GROUP I GROUP 2 GROUP 3 GROUP 4 GROUP 5 ENGINE A ENGINE B ENGINE B ENGINE B ENGINE B Figure 11. Life of Engine Exhaust Valves, Dynamometer Test. 350. 300 250 0 0 200 w U__ J w Lu b, IS 15o z w m 100 50 20o — 0 10 20 40 60 80 90 100 PERCENT OF BEARINGS FAILED Figure 12. Life of Front hieel Bearings in a Truck.

-24You will note that although the Average Life, corresponding to approximately 50% failures is about 100,000 miles, fully 10% of all bearings will have a life under 20,000 miles and another 10% bearings will have a life in excess of 250,000 miles. You obviously cannot design to the average life because 50% of the parts will end up as failure. The reason that we still design to the average life and somewhat get by is that we reinforce the design with empirical factors which, depending on the mood we are in,we call Factors of Safety or Factors of Futility. Figure 13 provides some more data on this problem of the average. It refers to the perennial problem of making a prediction on the basis of laboratory tests and finding a year later that the reports from the field say exactly the opposite. Here we have two gear designs, A and B, and the problem is to compare them for life. Ten gears of design A were tested on the dynamometer and the number of hours to failure recorded. These lives are arranged here in an increasing order of life. The same is true of gear design B. Now, judging the qualities of these gears by comparing their averages one would conclude that design A is better than design B. This, however, is entirely misleading, because although the average of A is greater than the average of B, if the criterion of satisfactory service life is 400 laboratory hours design A has 6 out of 10, or 60% of gears under 400 hours, while design B has only 3 out of 10, or 30% low life gears. Since it is the low life parts which exhibit themselves as service failures B gear design will be found the better of the two, contrary to what laboratory has predicted. All this means is that in Reliability we must go to statistical methods. In describing statistics as a tool of reliability we might begin with Figure 14 in which 450 consecutive measurements were recorded of gas explosions in a combustion chamber. The data are plotted with number of explosions or the frequency of occurrence on the ordinate and gas pressure in psi on an abscissa. If we connect the peak points with a smooth curve we should obtain an approximation to what is known as the Normal Distribution Curve. The conditions leading to a Normal Distribution Curve should be such that the event represented by this curve (in this case, gas pressure) must occur by chance alone. Not all distributions give a Normal Curve because not all events are due to chance alone. Figure 15 is a histogram of television commercials, where the number of occurrences is plotted on the ordinate and the

THE MEANING OF THE AVERAGE Number of Hours to Failure GEAR DESIGN A GEAR DESIGN B 120 f t I10 150 30% 160 210 I 350 250 60% 400 360 410 370 430 5 10 500 870 520 980 530 1140 570 496 AVERAGE HOURS 398 Figure 13. The Meaning of the Average. DISTRIBUTION OF GAS PRESSURE 100 z o0 -j: 50 - z 1100 1150 1200 PSi GAS PRESSURF Figure 14. Distribution of Gas Pressure in a Combustion Chamber.

o 6 z i.U 5 0 4 0 0 4 w 2 z 0 20 40 60 80 100 120 140 160 TIME - SECONDS Figure 15. Histogram of TV Commercials /Jue1. NomlDsrbuinCre

-27TEST DATA: 28 56 52 35 61 48 46 39 31 X=44 C=i 0'=y n-i = (28 - 44)1(56 - 44)2+... 0 =11.5 I o =11.5 44 + 11.5 32.5-55.5 68. 27% 2a =23.0 44 +23 21.0- 67 95.45% 3a =34.5 44+34.5 9.5-78.5 99.73% Figure 17. Standard Deviation'4 4 0 10 10T 10e LIFE - CYCLES Figure 18. Scatter of' Fatigue Life.

-28time of each commercial is on the abscissa. This graph will never give a Normal Distribution Curve because, I suspect, commercials do not occur by chance. The Normal Distribution Curve is of great importance in Reliability because of its useful characteristics. As you recall, on the abscissa we plot the variable under study, which may be gas pressure, stress, electrical resistance, etc. On the ordinate is plotted percent of occurrence. If we plot la, which stands for standard deviation, each side of the average value (as in Figure 16), then 68.27% of all the items will occur within + la. Similarly, 95.45% of the events will occur within + 2a and 99.73% within + 3a. (The numbers at the bottom of Figure 16 refer to an example worked out in Figure 17.) In view of the fact that a, standard deviation, is one of the most important factors in the study of Reliability, it might be worthwhile to refresh our memory of how it is computed. Consider the test data in Figure 17, which shows a certain degree of scatter. First we determine the average value x, which comes out to be 44. We then determine a as shown by the equation, where xi stands for each of the individual values, x is the average, n the number of items in the sample and Z stands for the summation of (xi _ X)2. Substituting the individual values in the expression we obtain a = 11.5. With the aid of the average x and of standard deviation a we can describe the product: the average (44) represents the quality of the product and standard deviation (11.5) its uniformity, that is, the degree of scatter. Now it will be noted that if we take one standard deviation and add and subtract it from the average, giving us the range shown in Figure 17 then 68.27% of all the items will lie within this range. Similarly, for two standard deviations 95.45% of the items will lie within its range and with three standard deviations 99.73% will lie within the range shown. Now what is the significance of all this? The significance is that here, for the first time, we are beginning to make Reliability Predictions. Thus, suppose you are to produce say 100,000 gears and you want to determine how good they are, how they compare with last years production, or with some competitive design. You cannot test all 100,000 gears because after you are through there is nothing left for the customer. You test, therefore, only a few gears, in this case nine, and from the test data you thus obtain you predict how the whole lot of 100,000, or as the statistician calls it the whole population, will behave.

-29Say, these data represent wear or pitting in gears and suppose that the maximum amount of wear you can tolerate is 80 units. This test on the nine gears tells you that 99.73% of all your gears will have a wear lying somewhere between 9.5 and about 80 units. Therefore,. 27%, that is the difference from a 1004, of the gears will have a wear lying outside these limits. In view of the fact that you are interested only in what happens at the low end you take half of the.27%, that is,.135%, and conclude that 135 gears out of the lot of 100,000 (that is.135% out of 100,000) will be defective, that is, they will have excessive wear. You thus made your first Reliability Prediction. I hasten to add that this is a prediction in its simplest form and we are going to say more about it later in the seminar. Making a prediction is not an easy task and probably it represents the single most difficult problem in Engineering Reliability. I would like, at this time, to suggest to you a method that you may find useful. Let us first start with fatigue curves, essentially like the one we showed you on the scatter of hypoid and bevel gears (Figure 1), except that here we describe the scatter by bands instead of by points (Figure 18). This particular band refers to Aluminum but, of course, the method applies to any material. Again, to refresh your memory, on the ordinate we plot a stress imposed on the tested part,in psi,and on the abscissa the corresponding number of cycles to failure. Now if at any stress level we took the scatter of the test points, which represent life, and plotted this as a distribution curve, we would obtain a graph as shown in Figure 19. Here we plot the number of test parts having a given life, or occurrence in percent, against the life itself. The resultant curve is not a Normal Distribution, being skewed very much to the right. There are several explanations for this skewness. One of the most logical ones is that you cannot have a negative life and this sets the limit for the left hand of the scale, while no limit exists at the right hand. Further,one very large value of life will have greater effect on the average life than several small values. Thus, the average life tends to be to the right of the most probable life. (You undoubtedly remember that in a Normal Distribution Curve the mode, the median, and the mean are all the same. In a skewed curve, like this, they are all different.) Now, it is difficult to analyze this skewed curve. Fortunately if we convert lives into logarithms of lives, and use this as a variable we obtain a close approximation to a Normal Distribution Curve, which we do know how to handle.

100 80 z iri 0 o. 60 z iLi 0 Z 40 (D~ o 0 0 20 0 I__ _ _ _ _ 0 10 20 30 40 50 60 70 80 90 100 LIFE - CYCLES/ l0 Figure 19. The Distribution of Fatigue Life.

-31Figure 20 shows a Normal Distribution Curve. You recall from Figure 16 that if we measure off one standard deviation each side of the average life, then 68.27% of the population will lie within + la. This means that 31.73% will lie outside these limits, half to the left and half to the right. Now in Reliability we set a certain design goal, say 5000 hours for an engine or at least 100,000 miles for a truck axle. This means that we are interested principally in those parts which may not meet this limit, to the left of the design value, because these are the ones that are likely to fail. Thus, we take one-half of 31.73%, that is 15.86%, and this then is the percentage of probable failures. The converse of failure is Reliability: Zero Failures are 100% Reliability and 100% Failures are zero Reliability. Thus, by subtracting 15.86% from one hundred we obtain 84.14% as Percent Reliability. To summarize, if we design our part to a value of + la of the average, we can predict a 84.14% reliability, that is, 15.86% failures. With 2a we obtain 97.72% Reliability and with 3a we have 99.865% Reliability. Before we apply these values to the prediction of Reliability let us once more consider a fatigue curve, such as in Figure 21. Suppose we focus our attention on one stress level and consider the scatter of the test points. We can then measure off the average life x one standard deviation, two standard deviations and three standard deviations, as shown. However, we just established in Figure 20 that one standard deviation represents 84.14% Reliability and 15.86% failures and we can obtain similar data for two standard deviations, three standard deviations, or any number or fraction of standard deviations. We can thus relate the design life in cycles, hours, etc. with percent reliability and percent failures. However, instead of expressing the design life as an absolute quantity, such as cycles which then will apply only to a specific problem,we prefer to express it in terms of a dimensionless quantity by dividing each life by the average life. Average, by its definition, corresponds to 50% reliability, and each of the design life points on the abscissa corresponds to some reliability,as we just determined. Thus we obtain a fraction: life at a given reliability divided by a life at 50% reliability. This we call the Design Life Factor. In Figure 22 we plot Percent Reliability on the upper abscissa. The lower abscissa gives the corresponding Percent Failures. Thus, 99% reliability corresponds to lo failures, 90%o reliability to 10% failures and, of course, 50% reliability to 50% failures. On the ordinate we plot the Design Life Factor which was just defined.

-32~ — C — T + I a 68.27 % INSIDE 31.73 % OUTSIDE 15.86 % FAILURES 84.14 % RELIABILITY -2 a + 2 ( 2.28 % FAILURES 97.72 % RELIABILITY -3 CT +3 ('.135 % FAILURES 99.865 % RELIABILITY Figure 20. Normal Distribution Curve. I.,../ —Xy SCATTER UI I BAND 03: I:I *3 Figure 21. Fatigue Data.

-33PERCENT RELIABILITY 99.99 99.9 99 90 50 1.0 I0.4 0.0 0.1 1 00.4 Fig475urSe 22-. - 0.18 07 o. I I ~z II I dw I ILi 0.01 0.01 0.1 I 10 50 PERCENT FAILURES Figure 22. Design Life Factors for a Ball Bearing. LIFE AT GIVEN RELIABILITY = 4 LIFE AT 50% RELIABILITY LIFE AT 90% RELIABILITY 4 100,00 MILES AVERAGE LTIFE AVERAGE LJE AVERAGE LI 100000 250,000 MILES Figure 23. Average Life vs Design Life.

-34If test data are plotted on this chart a straight line results, as shown for a particular part (ball bearings tested at 475,000 psi) in Figure 22. The chart indicates that if you desire a 90% reliability, that is a maximum of 10% failures, you should design these bearings to 0.4 of the average life. If you want fewer failures, say 1% failures, that is 99% reliability, you must design more precisely, to.18 of the average life. Let us illustrate the use of this chart by the following example. Suppose you are a manufacturer of chassis springs and you set a goal of 100,000 miles with not more than 10% failures. This particular chart, if it applied to springs, would state that for 90% reliability the design life must be 0.4 of the average life. Solving the equation in Figure 23 we conclude that the average life must be 250,000 miles. That is, if you want 100,000 miles of failure-free operation, withnot more than 10% failures, your springs must have an average life of 250,000 miles; because if you design to an average life of 100,000 miles and your goal is still 100,000 miles, you will record 50% failures.

SESSION NUMBER TWO Charles Lipson -35

Using the method of design discussed in Session No. 1 we have analyzed a great deal of data accumulated over a period of years and some of these are shown in the next few graphs. In all of these, as in Figure 22, we plotted percent reliability on the upper abscissa, percent failures on the lower abscissa and on the ordinate is Design Life Factor, which as defined before is life at a given reliability divided by life at 50% reliability. Thus, in a case of a wheel (Figure 24) for 90% reliability one must design it to about.7 of the average life while in the case of exhaust valves to 0.3 of the average life. This is because engine valves show considerably more scatter than truck wheels. The lower the value on the ordinate the worse the scatter. Now the degree of scatter and thus the Design Life Factor depends on several things: the complexity of design at the critical section, uniformity of material properties, method of manufacture, quality of the inspection methods, etc., and these will differ among the various manufactured parts. Thus, a shaft whose critical section is a keyway would be expected to show higher variability in life than a shaft whose critical section is a large fillet. The size and the method of grinding a large fillet can be carefully controlled. On the other hand it is more difficult to control the manufacture of a keyway and more scatter can be expected. Thus, you will note that a higher design life factor was obtained for a cast wheel than for the front wheel spindle because this was a wheel where, at the point of maximum bending moment,the section was quite uniform. In the case of the spindle,the fillet near the bearing was smallrand there were considerable production variations between individual spindles. In the same manner data shown in Figure 25, 26 and 27 were analyzed. Figure 25 refers to hypoid and bevel gears tested at several stress levels. The scatter is considerable, which is characteristic of parts subjected to contact loading. Figure 26 refers to axle shafts from farm tractors and automobiles. You will note that two sets of axles, presumably identical but tested at two different stress levels (27 Ksi and 38 Ksi) produce different degrees of scatter. This may be due to the fact that shafts coming out of quenching baths are frequently distorted. To bring the runout within limits axle shafts are cold straightened. This process results in high residual tensile stresses, of the order of 100,000 psi, which in turn decreases the fatigue strength by 20%-30%. Since the distortion is different between different shafts the residual stresses will be different too. As the effect of these stresses is different at different stress levels the degree of scatter will vary too. -37

-38PERCENT RELIABILITY 9m 9e m ths on M U 9 c i0 so 6 ISo 5Ol.o as 08 0.7 04 WHEELS 04 LEAF SPRINGS 0. o3 _ FANS J w GEA RS ]0.2 aI: C'SHAFT A /' 0 Ul C'SHAFT B / w 0.1 U SPINDLES - - - - __ - o -- GoIN VADLVES oo. 0.06 0.0. hi z w IENGINE >oo VALVES 4 002 / Iol ~ oG 02 os i 2 s i 20 30 40 50o o PERCENT FAILURES Figure 24. Design Life Factors. Automotive Components. PERCENT RF'.IABILITY "-.o 999 99B 995 99 9 6!0 8 0 ~ 6 50 i 10 0.7 0.6 05 0.4 P3 co o, <_ / 0.i - 1 \HYPOID GEAR - - U 1093 KSI BEVEL GEAR o,, - 75KSI 0 - -— 0 07 0..I BEVEL GEAR / 006 93 KSI M - ~~~~~~~~~~~~~~~~~oo?, 00 L 001 aa 01 02 05 I 2 5 0) 99 30 40 s PERCENT FAILURES Figure 25. Design Life Factors, Hypoid and Bevel Gear.

-39PERCENT RELIABILITY soW sm ss s s a so so 0 so 01so at lof O s 06 05 o~ FARM TRACTOR0 30 KSI w FARM TRACTO M Y I II Q 54 KSI -- 54 451~~~~~~~~~ 0.2 AUTOMOTIVE 0 38 KSI ~~~~~~~~~~ AUTOMOTIVE W"a (SHOT PEENED) ) 43 KSI a Io AUTOMOTIVE o00 >27 KSI 0.0 _J I z U 004 > 0.03 w ooe PERCENT FAILURES Figure 26. Design Life Factors, Axle Shafts PERCENT RELIABILITY L9 (0 I — LA. -1 06 i ~~~~~~~~~~oz I~~~~~~ ool ol o2 05 I 02 5 I0 00 30 40 30 PERCENT FAILURES Figure 26. Design Lif4e Factors, Axle Shafts PERCENT RELIABILITY 0.4 o8 _ _ I J - Os Ol 06 0.Z/'IMKEN 8-10 LIFE w 04 4 510 KSI - I- 101 388 KSI 0o, alm OD 475 KSI 0L —X+ —----?0w — o.o6 O //~~~~~~~~~~~~~~~~~~~~~a Z 430 KS I ooe I 540 KSI> 004 oo3 w IL 002 388 KI __Iioo, 0 o, o1(5 05, - S io -o so 40 50 PERCENT FAILURES Figure 27. Design Life Factors, Ball Bearings.

-40Figure 27 refers to radial ball bearings tested at five different stresses. This represents a plot of very extensive data from literature which we have analyzed, and in order to indicate that linear relations result some of the test points are indicated. You will also note a point referring to Timken t-10 life, where B-10 stands for 10% failures. It is reported that B-10 corresponds approximately to 20% of the average, which on our scale is 0.2 on the ordinate. In the case of the radial bearings plotted here, 10% failures correspond to 0.4 instead of 0.2 of the average life. Also from literature we gathered some data pertaining to materials (Figure 28). Of particular interest is the band of values pertaining to an annealed steel magnetically presorted. As you would expect, they show a very high Design Life Factor that is, high uniformity. This confirms what we intuitively know: if you want your part to last longer either make it stronger or make it more uniform. The latter can be accomplished either by controlling production through, say, tighter tolerances, or by controlling inspection by truncating the lower end of the Distribution Curve, which thus eliminates the low life parts. By collecting all the data pertaining to materials, which were obtained from carefully prepared laboratory specimens, a band, as shown in Figure 29, is obtained. Similarly, by collecting the actual manufactured parts, such as crankshafts, axle shafts, wheels, fans, etc., all subjected to flexural loading, as the laboratory specimens were, we obtained the lower band. The latter have lower Design Factors than the specimens, that is, more scatter. This is consistent with the fact that manufactured parts have greater variation in surface finish, hardness, etc. than carefully prepared specimens. Figure 30 refers to manufactured parts only,but distinction is made between those parts which were subjected to flexural loading and those subjected to contact loading. By flexural we mean bending, torsion and axial loading (axle shafts, connecting rods, crankshafts, spindles, etc.). Parts subject to contact loading are meshing gears, bearings, cams, tappets, valves, rollers, etc. As you will note, we obtained lower life factor and thus higher scatter for tappets than for connecting rods. This confirms general experience that parts under contact loading such as gears, bearings, etc., show considerable scatter in life, sometimes of the order of 50 or 100 to 1. This is because the life under this condition varies inversely as the ninth power of the unit pressure and therefore even a slight non-uniformity in load or geometry will produce a high variation in life.

-41PERCENT RELIABILITY r1 sm gm w5 9 so 0 so K so DDL ANNEALED 1O STEEL 07 MAGNETICALLY SORTED 2 4340 * "' 81.4 KSI I 4 1050 _o__ -J 02 w? 4 -J - -- - - — " o/~ 0h w U. -02 o01 o0 02 5 1 2 40 - 0 - - 0 -0 PERCENT FAILURES Figure 28. Design Life Fa ctors, Various Steels. s ManfactuERCENT RLIABILIomponents. 911 tll on It I M 0 so lO0 o olo as o. 0.J cure oot -J1

-42PERCENT RELIABILITY no 90 ED ao a W so'MW 50 to 05.. -Os bJ l 0105 05X I 21, $ Io 51o m 1 o U4 2 5 051 PERCENT FAILURES Figure 30. Design Life Factors, Comparison Between Flexural and Contact Loading. Stress Strength UNRELIABLE UNDERDESIGN RELIABLE OVERDESIGN _. V RELIABLE OPTIMUM DESIGN Figure 31. The Optimum Design

-43The foregoing data represent one method for predicting reliability. The second method for predicting Reliability is what is known as the Interference Method and I would like to comment briefly on it. Let me first describe the method schematically. (Figure 31) Suppose the upper left curve represents a stress distribution due to the road loads acting on a truck suspension, that is, the load or stress spectrum. Also, suppose the upper right curve represents the fatigue strength of this suspension. Then whenever the stress exceeds strength failure will result. Judging from the large area of interference there will be many failures. The suspension therefore is unreliable because it is underdesigned. The suspension can be made reliable by increasing the strength or decreasing the stress, so that no failures will occur. The part is now made reliable but it may be grossly overdesigned because if you have no failures whatsoever, you do not really know whether the strength is only 504o better than the stress or 500% better. An ideal or optimum design is one where you have a very small carefully controlled number of failures. This number, of course, will depend on what is economically sound and also what is sound from a safety point of view. Now we shall apply the Interference Theory shown schematically in Figure 31 to a specific case. In Case I (Figure 32) the average stress was 30,000 psi or 30 ksi and the standard deviation 10 ksi. The average strength was 50 ksi and its standard deviation 2 ksi. With a few simple calculations we obtain values shown in Figure 33, which when plotted in Figure 35 indicate that we may expect 3.1% failures. Suppose we decide that this is excessive. We may increase the strength or decrease the stress or make the product more uniform. Suppose we decide to leave everything the same and only decrease the average stress from 30 ksi to 20 ksi. What will happen? Figure 35 shows that this change will result in a ten-fold improvement. The number of failures will decrease from 3.1% down to 0.3% failures. Thus, knowing the stress on the part and the strength of the material, we have some means of predicting what the reliability is likely to be. Or conversely, if at the outset of design we decide that we cannot tolerate more than, say, one,failure in 1000 (99.90 reliability) we

CASE I STRESS STRENGTH 0 10 20 3 0 40 50 so 70 KSI X, = 30 X, = 50 a, = x o m- = 2 Figure 32. Interference Method, Case I. CASE I CASE II STRESS STRENGTH STRESS STRENGT' X, = 30 X2= 50 X, = 20 X2= 50 o;= 1o C2= 2 c,= I 2= 2 CTmax I0 max I 0 CTmin 2'min 2 (X2- X) 50 -30 (X2-X,) 50-20 =10 - -15 amin 2 O'min 2 PERCENT FAILURES 3.1 % PERCENT FAILURES =.3% Figure 33. Interference Method, Case I. Figure 34. Interference Method, Case II.

50 \J1 m (D F 1 _. I — J 9 -' CD L 9i _ 5~~~~~~~~~~ 96.9 ~ ~ 3.1 CD clIa a ~99 3 ~'d U Z Z z z CD (- 99.7 0.3 o a. 99.9 01 a H 9 9'....~ i 0'0 99-,99 0 O 0 2 4 6 8 10 12 14 15 16 18 X2 - XI AVE. STRENGTH AVE. STRESS O'min MIN. STANDARD DEVIATION

-46can determine for a given material what is the maximum load, torque or stress the part can carry. I do not want you to feel that it is easy to make this determination. To do it we must know the stresses and the strength rather precisely. We shall discuss this aspect of Reliability later in the seminar.

LUNCHEON ADDRESS Herbert L. Misch Vice-President, Engineering and Research Ford Motor Company -47

I am most pleased for the opportunity to be here and have found the Seminar to be very informative so far. I am told that the attendance today represents practically a 100% response to the invitations extended. This is a true testimonial to the importance of the subject we are discussing, especially when you take into account the fact that papers on the same subject are also being given today in Detroit at the S.A.E. The statistics of reliability as they apply to the products of most of our industries can be very discouraging unless carefully analyzed. For instance, an automobile with 1,000 critical parts, if it is to meet a 5% failure rate, must contain parts so perfect that there will be only a 0.005% failure rate for each part. We are inclined to say this is impractical and not attainable and have, in the past, relied on designing to industry practice or commercial standards. However, as our products have become more complex, we have had to become more sophisticated. It is important to recognize the depth and scope to which the subject of reliability can be expanded. In the automotive industry, we believe reliability starts with the initial product plans and is given mechanical sense in the engineering department and brought to fruition in the manufacturing process. Therefore, each area has its contribution to make. Since we must be objective and purposeful inour everyday work, reliability must be translated into terms of understandable economics. We most certainly are interested in a scientific and technical foundation for our work, but what does this mean to the public - our customers, who buy the automobiles we make? Reliability to them is not an engineering problem; it is something to which they may apply a very definite meaning - namely preferential purchasing power. We, at Ford Motor Company, have attempted to translate vehicle reliability into sales volume. In so doing, we determined that the number of repeat customers is inversely proportional to "things gone wrong" with the vehicle. To exemplify this, I would like to quote from some market research data which summarizes the answers to two questions asked of new car owners -- they had their new car two - three months: first, from your experience to date, would you repurchase the same make, and, second, how many things have gone wrong with your new car? These data show a surprisingly smooth curve where 87% of those reporting nothing gone wrong would repurchase the same make, and only 39% of those who experienced 10 or more things gone wrong would repurchase. Now to show what this could mean in sales, we have constructed a hypothetical case based upon 1.5 million annual units in which 1,300,000 are excellent and 200,000 rated troublesome. The possibilities of a repeat sale on the excellent units is 70% and on the troublesome units 50%. Let us assume that we improve the reliability so that only 100,000 rather than 200,000 are troublesome. This means that we have improved the probability for repeat sale on 100,000 units from 50% to 70%, or in other words, added 20,000 future sales. This, gentlemen, is quite a carrot and indicates that, even though perfection is impractical, reaching for it and realizing improvement has a big payoff. -49

-50It's because we recognize the economic implications of reliability that most of us are here. I, for one, am not here as an expert but as a student. We are all generally aware of the new field of mathematics that deals with unequals and approximations - the computer techniques and other new tools available since I left school; but their application to a specialized field such as designing for reliability requires the help of an expert. I consider Dr. Lipson such an expert. I am sure that Charlie will forgive me if I reminisce a bit, but I've known him for more than 20 years. I remember back in 1942 when he was an engineer with Chrysler, he made a presentation in which he forecasted reliability of aircraft engine structural members. Of course, in those days the terminology "reliability" was not in our engineering vocabulary and we chose to speak in terms of "design analysis." In any event, Charlie's presentation contained such exotic terms as "photoelasticity," "stresscoat," "electric strain gages;" and you may be sure that during this period this type of analysis was considered to be way out -- real long hair stuff. But you will also recognize in this the substance of reliability forecasting. For in this presentation Charlie had statistically analyzed many types of construction, and, as a result of all available facts, he had drawn conclusions and made decisions. Here we see that this unique study preceded the present day quality control approach, although actually the field of quality control was not exploited until the latter years of World War II. From the quality control concept we emerged into our present sophisticated program of mechanical reliability. I give you this background to indicate the rapidity with which this subject has grown and the initial impetus given to it by such people as Charles Lipson. He has, since that time, maintained a clear knowledge of industry's changing requirements through his extensive consulting activities, and has been a large contributor to the creation and maintenance of a strong curricula in mechanical engineering here at the University. It is this strong background in both the academic and practical aspects of engineering design that make him an obvious leader for this seminar today. We all wish to express our appreciation to Dr. Lipson for the tremendous effort he has put into this, the first major seminar dealing with the engineering aspects of mechanical reliability. I for one have seen and heard enough already today to convince me that such sessions as this are very worthwhile - but of equal, if not greater, importance is the realization that this material is being taught to the undergraduates here at the University. It is the mass education of this practical engineering approach which can help our industries most.

-51When I look at the total engineering job of my own Company and realize that we design approximately 100,000 new parts every year and do this with 4,000 engineers, I recognize the importance of having a source of talent trained in these new concepts so that we can continually update our organization. I would like to congratulate Dr. Lipson and his colleagues for this bold and modern addition to Mechanical Engineering Education. This morning the session dealt with factors adversely affecting reliability -- now we are anticipating a discussion on the tools for improving reliability. THANK YOU

SESSION NUMBER THREE Charles Lipson -53

-55So far we discussed the problem of predicting reliability and designing it into a product. But one would not design a part and release it for production without some kind of a test. Similarly, in Reliability you will not make a Reliability Prediction without some kind of verifical tion. This leads us to tests: laboratory tests and field tests and this is the subject of the present session. Tests have been done before but what I would like to suggest is that the main difference between the traditional approach and the new approach is that now we will design the test for the specific purpose of verifying the predicted reliability value. This may involve some new techniques, largely based on statistics, where we will have to decide how many samples we should use, how long the test should run, how much overload to apply, and how much confidence we have in the final test results. Before we discuss some factual data let us consider a hypothetical example shown in Figure 56, which illustrates one of the most important concepts in testing. Consider 1000 "identical" gears, "identical" in the sense that they were made from the same print and on the same machines. Arbitrarily divide them into two groups of 500 each. To evaluate these gears, say for life, pick up a sample of 10 gears from group A, test and determine the average life to be 51 hours. Repeat this for samples two and three of group A. Naturally you would not expect the averages to be the same because of scatter. Conduct identical tests on group B. Then by comparing the average of 58 from A with the average of 41 from B we arrive at a conclusion that A is 42% better than B. This obviously is absurd because both A gears and B gears came from the same lot of 1000 "identical" gears. Thus there can be no real difference between A and B and the 42% observed difference arose by chance alone. Of course, in this case we had an a priori knowledge that all the gears came from the same population. But suppose now, in the course of your everyday work as an experimental engineer, you are asked to compare your spring design with a competitive design. You run a test and obtain a 30% difference in life. How do you know that this 30% represents a real and valid superiority of one design over the other, rather than that no real difference exists between the two, and the impressive looking 30% difference has not arisen by chance alone. Therefore in testing we must consider the Confidence Levels, the degree of confidence we have in our results.

-56Now let us come to some factual data. Figure 37 illustrates the problem of how many samples or measurements to take and it refers to the engine exhaust valves which were shown as a scatter in Figure 11. The ordinate is the number of valves tested and the abscissa is the difference in the lives of valves, in percent, between two different designs, materials, methods of manufacture and so on. The three lines marked 90%, 95%0,and 99% refer to the Confidence Levels. This means that if we use, for example, the 90% curve we will be reasonably sure that the conclusion we draw from a given test will be correct in 90 cases out of 100. Similar meaning can be attached to the 95% and 99% curves. Notice that if only eight valves are tested, the difference in life between two sets of valves that can be detected is only of the order of 6oo. If you want to detect smaller differences in life, say 15%, you need 82 valves. If you want to detect very small differences, such as 10%', this is practically an impossible task because you need over 100 valves of each kind. Fortunately in engine work, if one is in trouble with exhaust valves, small improvements in life would not do. We need improvements of the order of 5X% and these can be detected with a small number of samples. The general conclusion drawn here, as to the relationship between the differences to be detected and the number of samples needed to detect these differences, applies to all manufactured products. Figure 38 refers to a problem of determining how effective induction hardening is in minimizing wear in engine cylinder bores. The test was run as follows: three out of six cylinder bores in a number of engines were induction hardened, the remaining three bores in each engine remaining standard. These engines were run for 25 hours at 4000 RPM full load with air-cleaner dust fed into intake ports and at the end of the run the amount of wear in each cylinder was noted. The statistical analysis of the test data is shown in Figure 38. On the ordinate is plotted the number of cylinder bores measured and on the abscissa the difference in inches between the wear in the standard bore and the induction hardened bore. You will note that if the number of measurements is small, such as five, the only difference that one can detect with any confidence is large (.002"). If you want to detect finer differences, for example,.001", you must make more measurements, in this case about 11. But, as you will note, this is a law of diminishing returns. If you want to make still more precise measurements and to detect say.0004" differences in wear between standard bore and induction hardened bore the number of necessary measurements is well over 80.

-571000'IDENTICAL GEARS GROUP A/ \GROUP B SAMPLE 1 2 3 4 5 6 NO. AVERAGE 51 58 48 41 46 50 LIFE 58 = 1.42 41 Figure 36. The Significance of Test Results. Figure 37. Statistical Analysis of Valve Life Data. 100_ 82 60 ~(An I~ I \\ Confidence - I Levels L I) W I 95 10 99% 0 8 D N A FI 3 S z z 7 1/5 I60 100 500 %.0005.0010.0014.0020 INCHES DIFFERENCE IN AVERAGES. DIFFERENCE IN AVERAGE WEAR

-58Thus there is a practical limit of how precise and accurate we want our answer. In this particular case about seven measurements is what we may call the most efficient number of measurements. Another test we ran on fuel economy also gave seven as the most efficient number of test runs to make. In reliability,establishing the most efficient number of measurements for each product would be highly desirable. Figures 37 and 38 refer to specific situations, the first to engine valves, the second to cylinder bores. In order to provide a chart of general utility, applicable to all parts, we have constructed a nomogram shown in Figure 39. Notice that this contains all the variables pertinent to a problem: confidence levels, number of samples or measurements, standard deviations and the difference one wants to detect between two designs, two materials or two methods of manufacture. This difference can be a difference in life, in stress, electrical resistance, fuel economy, etc. The right scale extends from very small differences of the order of hundred thousandth or a millionth to very large differences of the order of a million. The first may apply to problems involving wear measurements. The latter refers to problems such as life of rear axles where one design may last 100,000 miles while the other 300,000. This nomogram can be used as follows: say a test was run on two designs, 1 and 2, four test specimens of each design being used. A difference in the averages in some property of these designs, for example, of 5000 units, was measured. Does this really reflect the superiority of one design over the other, or did this 5000 unit difference arose by chance alone? Suppose this is to be established at a 95% confidence level. Locate four on the 95% scale, draw a horizontal line to the intersection with the reference line. By knowing from previous tests or general experience the degree of scatter in each desing locate i1 + 2 on the appropriate scale (in this case 107). Connect the two points and extend the line to the intersection with the x1 - x2 scale to read approximately 8 x 103 or 8000. This represents the minimum difference that must exist between the two designs to be able to say that one is superior to the other. Since in actual test only 5000 difference was noted one concludes that no significant difference exists between the two designs. The diagram can also be used in the reversed direction. That is, suppose one is faced with the problem of failures and a preliminary analysis indicates that in order to get out of trouble an improvement of 8000 units is necessary. This chart indicates that to detect this improvement four pieces must be tested. This is the way one would design the test.

-59a, + O2 X2 - 2 90 % 10'4- - Iol0 CONFIDENCE _ 95 % LEVEL 99% lO 100 10'0 o100,9.9% 10/ 50' 0loo 100 20 - 50 l10I2020 0 20 1020 ~~~1~~~~~~~ ~i0- - 20-0 411640 10 i-f'410-6 Figure 39. Number of Samples Required for a Significant Test.

-60So far we discussed only one aspect of testing: how many samples or measurements to make and how much confidence we can place in the results. Another equally important phase of experimental work is the problem of Accelerated Tests. Here, in view of the fact that it may take a long time to run a test under normal operating conditions, we increase the load, temperature, or some other aspect of environment to obtain the results in a shorter period of time. Now, how valid are such tests? Let me illustrate this with the following example: we know from the study of fatigue that if a member~ made from steel lasts for 10 million cycles and does not fail then it should last, theoretically, forever. This means that an engine running at 4000 rpm will accumulate 10 million gas-and-inertia-load-cycles in about 100 hours. Therefore, if the engine is run on the dynamometer, wide open throttle, for 100 hours and if the crankshaft does not fail, we should have a reasonably good expectation that it will last forever. Once we had such a reasonable expectation in testing a brand new engine design,and after the 100 hour mark was passed, we began a restrained celebration. The disconcerting fact, however, was that seven hours later the crankshaft broke. The answer now is obvious. The 10 million cycle criterion refers to the most probable value of the gas pressure (on the basis of which all calculations are generally made), which was 840 psi. But once every few thousand revolutions there is a turbulence in the combustion chamber which momentarily produces a pressure of 1050 psi. In 100 hours of operation this may occur only 50,000 times. To take these occasional overloads into account, obviously, you must run the engine longer than 100 hours. Calculations show, for example, that if one sets as a criterion 5000 hours of satisfactory engine life, one has to run this engine on the dynamometer for 2780 hours, and if, in this time, the engine does not fail, then and theoretically only then, one can be confident that the service life of this engine will be the required 5000 hours. (Figure 40) Now, nobody can run an engine for 2780 hours, particularly if he wants to incorporate some design changes as he goes along. That is where the accelerated tests come in. In Figure 41,hours on the dynamometer on a logarithmic scale are plotted against the amount of overload, in percent, put on the engine beyond and above the W.O.T. operation. Zero overload refers to W.O.T. operation. The graph shows that if the criterion is 5000 hours one must run the engine, as I said before, for 2780 hours, with no failure, before one can be sure that it will be satisfactory in service.

-611200 cn oo" -) wj4" 1100 w 1000 a: L 900 z 0 800 w a. 700 100 HOUR TEST 2780 HOUR TEST 600 I I I I I I I I 10O 10_ Io 0 I108 LIFE, CYCLES Figure 40. The Meaning of a 100-Hour Dynamometer Test. 2780 HOURS,000LU LUJ 10R 0 I O VERLOA

-62If the engine is overloaded the number of required test hours will obviously decrease. But contrary to expectations 10% of overload will not do very much because it will decrease the number of test hours from 2780 to 2000, which is still too high. The curve shows that if one wishes to run the engine for only 100 hours and on the basis of this run wants to predict how the engine will behave in service, the engine has to be overloaded by 23%. Figure 41 applies only to an engine and specifically only to one part of the engine, in this case the life of a crankshaft. But similar analysis can be made on almost any manufactured part: gears, drive lines, suspension and so on. We have also begun some work on various methods for reducing test time, such as Factorial Design, Sudden Death Testing, 50% Testing, Sequential Analysis, and so on. I am afraid, however, that time is running short and maybe we can only touch upon these methods during the discussion period. However, I would like to present to you one aspect of testing which should be of interest: the problem of field testing and particularly a method of analyzing test data coming from service. Let me illustrate this with some recent experience: the problem involved testing in the field a certain drive line in the hands of some selected customers, prior to a full scale production run. After six months of field operation the vehicles were torn down and the parts examined for pitting and scoring. All the pertinent data were recorded, such as the number of hours that each vehicle ran during this six month period, the absence or presence of pitting, the degree of pitting, and so on. The data were then analyzed. Here, however, was the problem. If all the drive lines, installed in these vehicles, have failed in terms of excessive pitting and scoring, in an identical manner, then the problem of plotting and analyzing these data would be simple and the plot would be as shown in Figure 42. This method of plotting is known as the Weibull Method. On the ordinate is plotted the Percent Failed, on a special log-log scale, and on the abscissa Life, in Hours. The resultant curve is, as you see, a straight line, from which we can read our design value. Thus, for example, if we demand, for our part as a design criterion, 700 hours of failure-free operation we may expect less than 10% failures. As an illustration of this method of plotting note Figure 43 which illustrates the difference in bearing quality between various vendors, as reported by Timken. Going back to our initial problem, the method of plotting shown in Figure 42 is all right if all the parts tested have failed. Sometimes,

-6390 80 7O 60 40 1-30 z w w 10 oI /o 0 100 300 500 700 1000 2000 5000 10,000 DESIGN VALUE LIFE-HOURS Figure 42. The Weibull Method. 90 VENDOR "A", n. 50 VENDOR C <[ VENDOR VENDOR " — CD B-10 z: 20 m 5 CATALOG LIFE 10 50 100 500 1000 5000 ENDURANCE, HOURS Figure 43. Life of Antifriction Bearings.

-64however, both in the laboratory and in the field, the parts are removed before they have failed. That is, the number of hours accumulated up to the time the part was removed undamaged is recorded. These items are called suspended items and they can be statistically analyzed and their effect included, as in Figure 44. The line on the left shows only the data which have failed and the one on the right includes the effect of the suspended items. Sometimes the difference can be quite appreciable, particularly in engineering applications where the number of test items is small. Our problem,and this is true of many field data analyses, was was even more complicated. Not only did we have drive lines which have failed and drive lines which had not failed but, in addition, we had different degrees of failure. Thus, when the vehicles were torn down some of the components had considerable pitting and we called it failure, others had moderate pitting and still others had only incipient pitting or no pitting at all. You can readily see that for the purpose of analysis these were not similar items and, therefore, could not be analyzed by the method shown in Figure 42 and 44 until they were all put on the same basis. This was done with the aid of data accumulated in connection with another program previously run. This involved testing the parts under controlled conditions and inspecting these parts for evidence and progress of pitting and scoring at various intervals of time. Thus, a given part showed only incipient pitting at 75 hours, moderate pitting at 160 hours, and severe pitting and scoring, which we called failure, at 280 hours. By dividing the time at which failure occurred (in this case 280 hours) by the time only an incipient failure was observed (here 75 hours) we obtained what we may term Pitting or Scoring Conversion Factors. Some of the Conversion Factors accumulated are shown in Figure 45 and as you see, they range approximately from a low of about two to a high of about three. Thus, if we receive a gear from the field which shows only incipient pitting, to use the number of hours or miles of this gear (up to the time of removal) in our analysis we multiply that number by one of the above factors to put it on the same basis as the gears which have really failed (that it completely pitted). We are still in the process of making this analysis and hope to arrive at some more significant conclusions.

90 - o / 70 60 50 SUSPENDED ITEMS 40 NOT INCLUDED\. L_ -SUSPENDED ITEMS Iwl INCLUDED 30 z o20.... 20 100 300 500 1000 2000 4000 10o0ooo LIFE - HOURS Figure 44. Effect of Suspended Items. TRANSMISSION I ST GEAR ( 72,300 psi 2.7 DESIGN A 2ND GEAR (a 66,100 psi 2.1 TRANSMISSION I ST GEAR (D 82,000 psi 1.9 DESIGN B 2ND GEAR ( 59,600 psi 2.1 REAR AXLE 2.9 2.9 PINION TAPERED ROLLER BEARING 2.7 Figure 45. Pitting Conversion Factors.

SESSION NUMBER FOUR Charles Lipson -67

-69Next I would like to discuss various tools of reliability such as fracture analysis, failure analysis, statistical tolerances and stress analysis. Let us begin with Fracture Analysis. What can we learn from the examination of a failed part? When one looks at Figure 46 one thing is obvious: the part has failed because of the very sharp corner. But we can learn much more than this by carefully examining the appearance of the face of fracture. Here is an obvious example (Figure 47). Keyway has sharp corners and almost always this is the source of failure. In this particular case, however, the crack did not start from the corner of the keyway but from the inspector's punch work. You can readily see that the crack started at the punch mark and propagated in semi-circles to a complete fracture. This study of the progress of the crack and the location of the final zone of failure may yield interesting information, such as the type of loading which caused failure, whether it was a recent crack or the part ran damaged for a long time, whether the failure was due to underdesign or to overloading, etc. In making such an examination we should distinguish between two zones (Figure 48): smooth, velvety fatigue zone and rough and crystalline instantaneous zone. The crack starts in the fatigue zone and propagates itself until the remaining section cannot withstand even a single application of load and the part breaks. Notice in Figure 49 that we relate the type of operating load which may have caused failure (one-way bending, two-way bending, and reversed bending and rotation); the relative magnitude of this load (low overstress versus high overstress); and the absence or presence of stress concentration (no stress-concentration, mild stress-concentration, high stress concentration). Thus from an examination of a failed part a judgement can frequently be made whether the part has failed due to an abrupt change in section or simply from an insufficient section, or whether the failure was not due at all to a defective design but to an excessively high operating load. As an example, please focus your attention on sketches 3f and 2e (Figure 49) because these will be illustrated with actual photographs. Sketch 3f, with its centrally located instantaneous zone, was due to the fact that the operating load (two-way bending and rotation) was too high; sketch 2e, on the other hand, is typical of front wheel spindle failures, where the load is two-way bending and the operating stress was low. This is illustrated with Figures 50 and 51.

-70-:~~ ~~~ ~ i ~ i.!E..iX~~~~~~~~~~:..V;: r::0l0.:;;::: iff 00 Figure 46. A Superficial Examination of Fracture. a F:i t P - ------- I: Figur~~~~~~~~~~~e 47. -,LFailure OrBig` inaiga h ucak

-71-............... ~......................i Figure 48. Fatigue and Instantaneous Zones. $tre I No Stress Concentration Mild Stress Concentration High Street Ceceetreottee Gem Low QOeratrese NHigh Overltrese L Overetrese High Overltrees Low Overatrege Hi rs/ Two-way bending road Rever1ed banding and rotation load Figure 49. Appear ance of Fatigue Fractures in Bending.

-72~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~:......'.'"...;:....";:''".'.. 0~~~~~~~~~~~ rb: ~ ~ U:iP~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ii Figure 51. Failure Due to a Low Operating Load.

-73All of the above dealt with the analysis of bending failures. Figure 52 represents torsional failures, where we relate the basic pattern with tensile, transverse shear and longitudinal shear fractures and the remaining sketches are variations of these three basic patterns. Figure 53 is clearly a helicoidal torsional failure and as Figure 52 has shown, it is caused by excessive tensile stresses which are maximum at 45~ to the principal axis. But some torsional failures occur transversely, or even longitudinally. Now, what causes these two different types of failure? In Figure 54 we have four steel specimens all subjected to a torsional load. The first and the third were perfectly uniform, with no stress concentration, and as the theory predicted they failed transversely due to excessive shear. The second specimen had a small transverse oil hole and, again as the theory would predict, it failed at 450, in the plane of the maximum tension. The fourth also had an oil hole and it also failed at 450 except that the torsional load was completely reversed. Thus, I believe, we can learn much from the examination of failed parts and it may be worth considering an establishment of a Diagnostic Laboratory as a part of the Reliability Program, whose function would be to analyze and interpret field fractures and to provide information useful to the Design Engineer. Another useful tool of Reliability is the Multi-Variant Analysis. Let me illustrate it with the following example. Suppose we have a problem of bearing failures, characterized by scoring. The first thing to do is to rate the degree of scoring (Figure 55). The next step is to prepare a list of factors that may affect scoring. Suppose after some analysis you decide that bearing fit, dirt due to environment, and misalignment, are potential causes. A list is made of these factors and a letter is assigned as shown in Figure 56. Thus, if a bearing has a good fit, no dirt (good environment) but poor alignment, it will be characterized by AlB1C2 and if this leads to scoring, and the scoring is severe, from the previous chart we will assign to it number four. Thus, this situation is described by the symbol: A1B1C24. Now, suppose we run a series of tests under controlled conditions where we can vary bearing fit making it either good or bad and do the same with the environment, that is, the amount of dirt we introduce) and the alignment. The tests are run under the various combinations of these conditions and at the end of each test we examine each bearing. If the bearing is all right and there is only very little scoring we assign to it

-74FTa ofe Basic Pattern Variations of Basic Pattern ilP__U rea_0b) Sow tooth due to stress Star pattern concentration at fillet Tensile Transverse K Z Small step Large step Longitudinal Shear 3 Figure 52. Appearance of Fatigue Fractures in Torsion. Figure 53. Helicoidal Torsional Failure.

-75Figure 54. Types of Torsional Failure. DEGREE OF NUMBER DAMAGE ASSIGNED VERY SLIGHT I SLIGHT 2 MODERATE 3 HEAVY 4 Figure 55. Multi-Variant Analysis, Classif ication of Damage.

number 1; if it has a slight scoring, number 2; moderate scoring, number 3; and heavy scoring, number 4. We can now tabulate test results, as in Figure 57. Thus suppose that the test we ran with poor fit, a lot of dirt but good alignment, produced slight scoring. We therefore assign number 2 in the space shown. But suppose, on the other hand, the test was run with poor fit, with dirt and poor alignment, and very heavy scoring resulted, we then assign number 4 in the appropriate space. We now tabulate the results (Figure 58) and determine the effect of each variable. Thus the effect of good fit, irrespective of other conditions, is: 1 + 3 + 1 + 2 = 7 and of poor fit: 2 + 3 + 2 + 4 = 11. Similarly: the effect of good alignment is 1 + 2 + 1 + 2 = 6 and of poor alignment: 3 + 3 + 2 + 4 = 12 and so on. As you see, the difference between good fit and poor fit is not particularly high (4). The difference between no dirt and a great deal of dirt is quite unimportant (0). However, alignment seems to make quite a difference, as the difference between good alignment and poor alignment is 6. From this we conclude that in this particular application alignment is by far more important than either bearing fit or dirt. Statistical Tolerances are another useful tool of reliability. Since they are based on statistics they properly fit into today's discussion on Reliability. Now what are Statistical Tolerances? They are realistic tolerances because with proper control they check much more closely with parts as they come out of production than the present algebraic tolerances. Thus, if we have three parts A, B, and C (Figure 59) going into an assermbly, and if the tolerances on each part is as shown we will find that in over 99% of the cases the maximum stack-up will not be.009 +.oo6 +.005 = o020, obtained from the traditional stackup but.012, if treated statistically. To demonstrate that statistical stack-up is real and valid and it conforms to what one would obtain from productions several years ago Westinghouse Electric Company conducted the following test: three parts were chosen, as shown in Figure 60, with the pertinent dimensions for a tolerance stack-up as shown. Fifty pieces of A, fifty of B and fifty of C were chosen at random from sub-lots which had been produced in a single run, each by a single machine. These items were then gaged for these pertinent dimensions, as shown in Figure 61.

-77POSSIBLE CAUSES LETTER VALUE OF FAILURE ASSIGNED GOOD A, FIT BAD A2 GOOD B, ENVIRONMENT BAD B2 GOOD C, ALIGNMENT BAD C2 Figure 56. Multi-Variant Analysis, Causes of Failure. A, A2 CII 1 B2_ C2 4 CFigure 57. Multi-Varia 4

-78EA, I+ 3+1 +2 = 7 A2 = 2 + 3 + 2 +4 =I EB, + 2 + 3+3 9 B2= 1+2+2+4= 9 SC, = I + 2 + I +2 = 6 C2 =3+ 3+2+4 12 Figure 58. Multi-Variant Analysis, Analysis of Test Results. GEAR TOLERANCE A.009 B.006 C =.005 A B C TOLERANCE ON THE TOTAL WIDTH ALGEBRAIC METHOD.009 +.006 +.005:.020 STATISTICAL METHOD 4(.009f) + (.006)2 + (.005)2 012 Figure 59. Algebraic versus Statistical Stack-Up of Tolerances.

-79- fl _ A - k.063 + 004 1/16 -1 - (5: B 3/16 - aj~.250 ~. 005 C.5 00 ~. 005 625 ~.002 Figure 60. Study of Design Tolerances.

-80A w w a:,a..059.065.067 B -I O D.245.250.255 C w w I: a. I:: I I.495.500.505 HEIGHT-IN ASSEMBLIES (A+B+C) _- 1 1 1 I I I I I 8 I I.810.815.820.825 HEIGHT-IN Figure 61. Gaging of the Parts and Assemblies.

-81TOLERANCE ON THE ASSEMBLY DERIVED FROM THE CONVENTIONAL ALGEBRAIC STACK-UP OF THE.0228" INDIVIDUAL TOLERANCES PREDICTED BY THE PROPOSED.,016 STATISTICAL STACK-UP OBTAINED FROM ACTUAL TEST DATA AS A RANGE BETWEEN LOWER.013 AND UPPER LIMITS OBTAINED FROM THE I3aSTATISTICAL.016" QUALITY CONTROL LIMITS Figure 62. Tolerance on the Assembly. 18 ALGEBRAIC 16 w O8 100 z 0 ~- - - -- STT TICAL 4 0~ 0z 2I 8 NUMBE OFCMOETSCMIE Figure 63. Div=ergneBtenAgbacadttsia oeacs

-82Then components AB, and C were selected at random and assembled, and the assemblies A + B + C were gaged as shown. The fifty assemblies fell within the range of.013". as shown in Figure 61. Now how does this check with the predicted stack-up? From the actual test data (Figure 61) all the fifty assemblies fell within.013" (Figure 62). If we added up the individual tolerances of A, B, and C algebraically, by the traditional method, we would get.028", which just does not check with the actual value. If on the other hand the individual tolerances were added statistically.016"would be obtained, which is much closer to the actual test data. One might say that after all we have tested only fifty assemblies but perhaps if we tested 500 or 5000 assemblies we may come much closer to the.028 than to.016. For this reason we computed these data statistically by calculating standard deviation and using + 3a as the probable range. As you recall this would tell us how 99.73% of the assemblies will behave. This gave us.016, which is a satisfactory check with the statistical method. Thus, statistical tolerances are realistic tolerances but let me emphasize that they work only if we have an equal system of checks in the factory, that is, if one employs Statistical Quality Control. Now, what is the advantage of statistical tolerances? 1. First, as we demonstrated with the Westinghouse example, they conform much more closely with the parts as they come out of a factory, than do the algebraic tolerances. The divergence between statistical and algebraic stackup is shown in Figure 63. 2. Second, for a given assembly tolerance, tolerances of individual parts going into the assembly can be made broader than conventional tolerances and therefore more economical. Let me illustrate the advantage of statistical tolerances with Figure 64. This chart was made for an expressed purpose of converting algebraic tolerances into statistical tolerances. After all there is a considerable background of prints expressed in terms of traditional tolerances and this chart illustrates how to convert traditional tolerances into statistical ones. Suppose the tolerance, say on a shaft is eight units and on the bore six units, giving, by the traditional method, a total tolerance

-8314 19 12 a-~~~~~~~~~~~~~~~16 z I 1 1 w 2~~~~~~~~~~~~) 01 2 4\ 6 88. t 1 TOLERANCE FOR OTHER PART Figure 6. Conversion of Algebraic into Statistical Tolerances. z~~~~~~ < 0 4 J~~ 0 2 4 6 8 8.6 10 12 14 TOLERANCE FOR O-THER PART Figure 64. Conversion of Algebraic into Statistical Tolerances.

-84on the assembly of 14. Draw a line through the intersect of 8 and 6 and the origin to the circle marked 14. From this drop horizontal and vertical lines giving 11.6 and 8.6. Now, for the same tolerance on the assembly (14) the statistical tolerance is 11.6 while algebraic was 8, thus, it is over 3C0 broader and therefore cheaper. The same is true of the other part: statistical tolerance is 8.6, the algebraic is 6 and the same advantage results. I would like to summarize everything we have said today with three illustrations. The sight in Figure 65 is familiar. It shows broken axle shafts, but it could have been crankshafts, gears, mufflers, tappets or wheels. In the past we dealt with problems like this with tables such as in Figures 66 and 67. In my judgment Factors of Safety of not less than 1.3 but not more than 2.0 should be an adequate insurance against failure (Figure 68). The days when we designed with data such as in Figures 65 and 66 are over and they should be over. Over the last 10 to 20 years we have made considerable progress, the type of progress that Mr. Misch in his lunch address referred to, by dispelling some of the ignorance which was covered by those large factors of safety. This lead us to smaller factors which being smaller do not mean we are less safe but only less ignorant. But even this is not enough and what we discussed today represents the next step toward more effective engineering. Factors of Safety, no matter how precise they still tell us only how the average behaves. The performance of a product in service is judged by the customer not by what the average does but by the number of failures or time to failure of the low 5 or 10% of the components. This, in turn, depends on scatter, which leads us directly to reliability. Thus, the next step in improving our product lies in Reliability. Somebody recently said: "What this country needs is a lowcost, practical program of Reliability." I hope that today, in some measure, we contributed to such a program. Thank you.

IRON Figure 65. Brokenl Axle Sheft.. KIND OF LOAD | STEEL Sa ROsN. DEAD LOADS 5 6 REPEATED ONE DIRECTION 6 10 GRADUAL (MILD SHOCK) REPEATED REVERSED DIRECTION GRADUAL 8 15 (MILD SHOCK) SHOCK 12 20 Figure 66. Factors of Safety.

-86SHOCK LOADS 10 FLUID TIGHT JOINTS 6 LIVE LOADS 6 VARIABLE LOADS 6 ORDINARY WORK 4 DEAD LOADS 4 Figure 67. Some More Factors of Safety. 1.3 < F.S.( 2.0 Figure 68. Recommended Factors of Safety.

BIBLIOGRAPHY Some References Pertinent to the Conference'"Engineering for Reliability" 1. J. M. Stokely, R. C. Gray, and S. R. Calish, "Automotive Gear Lubricants and Greases," Paper presented at Southern California Section Meeting, Los Angeles, March 15, 1951. 2. K. L. Pfundstein and J. D. Bailie, "Factors Affecting Tractor Valve Performance," SAE Journal, July, 1952. 3. W. Coleman, "An Improved Method for Estimating the Fatigue Life of Bevel Gears and Hypoid Gears," SAE Preprint No. 627, June, 1951. 4. E. Epremian and R. G. Mehl, "Investigation of Statistical Nature of Fatigue Properties," NACA Technical Note 2719, June, 1952. 5 G. E. Dieter and R. F. Mehl, "Investigation of the Statistical Nature of the Fatigue of Metals," NACA Technical Note 3019, September, 1953. 6. H. W. Russell and W. A. Welcker, Jr., "Damage and Overstress in the Fatigue of Ferrous Metals," ASTM Proceedings, Vol. 36, Part II, 1936. 7. A. M. Freudenthal and E. J. Gumbel,'Distribution Functions for the Prediction of Fatigue Life and Fatigue Strength, " The Institution of Mechanical Engineers, International Conference on Fatigue of Metals, September, 1956. 8 M. N. Torrey and G. R. Gohn, "A Study of Statistical Treatment of Fatigue Data", ASTM Preprint No. 70, 1956. 9. W. Weibull, "Statistical Design of Fatigue Experiments," Journal of Applied Mechanics, Vol. 19, No. 1, March, 1952. 10. 0. J. Horger and C. H. Lipson, "Automotive Rear Axles and Means of Improving Their Fatigue Resistance," ASTM Symposium on Testing of Parts and Assemblies, 1946. 11. J. Leiblein and M. Zelen, "Statistical Investigation of the Fatigue Life of Deep-Groove Ball Bearings," National Bureau of Standards, Vol. 57, No. 5, November, 1956, Research Paper No. 2719.

-8812. E. S. Rowland, "Resistance of Materials to Rolling Loads," Handbook of Mechanical Wear, Edited by Charles Lipson and L. V. Colwell, University of Michigan Press, 1961. 13. V. M. Faires, "Design of Machine Elements" The Macmillan Company, 1961. 14. J. 0. Smith, "The Effect of Range of Stress on the Fatigue of Metals," University of Illinois Bulletin, No. 334, 1942. 15. L. G. Johnson, "GMR Reliability Manual," GMR-302, General Motors Research Laboratories, 1960. 16. L. G. Johnson, "The Statistical Treatment of Fatigue Experiment$," GMR-202, General Motors Research Laboratories, 1959. 17. Temco Aircraft Corporation, "Reliability A", Class Training Manual. 18. B. Epstein, "Tolerances on Assemblies, " American Machinist, January, 1946. 19. G. M. Hailes, "Some Statistical Principles of Tolerances, Industrial Quality Control, May, 1951. 20. C. Lipson, "Why Machine Parts Fail," Penton Publishing Company, 1950. 21. C. Lundberg and A. Palmgren, "Dynamic Capacity of Rolling Bearings," Acta Polytech., Mech. Eng. Ser. 1 (3), 1947. 22. K. A. Brooks, "Statistical Dimensioning Program," Machine Design, September, 1961. 23. D. Shainin, "Quality Control Methods - Their Use in Design," Machine Design, July, 1952 and January, 1953. 24. E. T. Fortini, "Dimension Control in Design," Machine Design, April, 1956. 25. L. A. Eckert, "Design Reliability Prediction for Low Failure Rate Mechanical Parts," Allison Division, G.M. Report. 26. M. J. Moroney, "Facts from Figures," Pelican Books, 1960.

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