Experimental design in environments with low repeatability error.

Abstract

This dissertation addresses the problem of which arrays should be used for experimentation in environments with low repeatability error. This problem is relevant because engineers increasingly are using rapid prototyping, repeated simulations, finite element analysis, computational fluid methods, and other highly repeatable methods. Many engineers incorrectly believe that two-level or sometimes three-level orthogonal arrays are their only economical option. This dissertation concludes that a new class of search arrays is the most appropriate choice in environments with low repeatability error. In general, the recommended arrays offer a substantial reduction in the number of runs needed to permit interactions and other non-linear effects to be modeled. For example, with less than one-third the number of runs, the methods achieved greater accuracy than modeling based on the 3$\sp3$ factorial array (L$\sb{27}$) when applied to the design of a plastic seal (Chapter 1V), as measured in integrated squared error. We demonstrate in Chapters I and II that, if the repeatability error is low and the appropriate arrays are used, then runs beyond the number required to estimate all coefficients are useful for two purposes only: (1) to select the best candidate model and (2) to detect whether none of the candidate models is acceptable. Further, we show that only limited numbers of runs are required for these purposes. Chapter III presents search arrays that exploit a common cost structure to permit a substantial reduction in the engineering time required for experimenting using finite element analysis. The array is applied to the design of D-shaped shafts. The resulting engineering design is expected to be useful for automotive heating, ventilating, and cooling (HVAC) applications. Chapter IV provides a case study of the development of a tongue and groove design for an HVAC application. The chapter also compares the application of one of the arrays and procedures from Chapters I and II with alternative approaches. In Chapter V, we explain how the problems formulated in Chapter I are sometimes so small that they can be solved by complete enumeration and discuss symmetry operations of the type used in the case study in Chapter IV.