The (a,b)-Precision Theory for Production System Monitoring and Improvement

Abstract

In the eld of production system engineering, machine parameters, such as Mean Time Between Failures (MTBF), Mean Time To Repair (MTTR), machine quality parameter (q), and machine cycle time (tau), are widely used in quantitative methods for production system performance analysis, continuous improvement, and design. Unfortunately, the literature offers no methods for evaluating the smallest number of measurements necessary and sufficient to calculate reliable estimates of these parameters and the induced estimates of system performance metrics, such as machine efficiency (e), throughput (TP), quality parts throughput (TPq), production lead time (LT), and work-in-process (WIP). This dissertation is intended to provide such a method. The approach is based on introducing the notation of (alpha, beta)-precise estimates, where alpha characterizes the estimate's accuracy and its probability.

Using this notion, the smallest number, n*T(alpha, beta), of up- and downtime measurements necessary and sufficient to ensure (alpha, beta)-precise estimates of MTBF and MTTR is calculated, and a probabilistic upper bound of the observation time required to collect n*T(alpha, beta) measurements is derived.

The MTBF and MTTR are used to calculate production systems performance metrics e, TP, LT, WIP, which are necessary for managing production systems and for evaluating effectiveness of potential continuous improvement projects. This dissertation evaluates the induced precision of these performance metrics estimates, based on (alpha, beta)-precise estimates of MTBF and MTTR. An inverse problem, i.e., calculating the smallest number of machines' up- and downtime measurements to ensure these performance metrics estimates with a desired precision, is also solved.

Along with MTBF and MTTR, the machine quality parameter q, which represents the probability that a part produced is non-defective and 1-q the probability that it is defective, is used to evaluate quality parts throughput TPq. This dissertation calculates the smallest number of parts quality measurements to ensure (alpha_q, beta_q)-precise estimate of q, evaluates the induced precision of TPq estimates, and presents solution to the inverse problem concerning q and TPq, i.e., calculating the smallest number of parts quality measurements to ensure estimates of TPq with a desired precision.

The (alpha, beta)-Precision Theory is also compared with other probabilistic method, which can be used for evaluating the critical numbers. Specically, we consider the Markov inequality, Chebyshev inequality and the simulation approach. It is shown in this work that these classical probability inequalities can only give estimates of the critical numbers that are much larger than their real values, which are too conservative and unrealistic to be implemented in practice. The simulation method also has several disadvantages compared with the theory, for example, large computation time complexity and the necessity to repeat these calculations if the parameters of the systems are changed.

In addition, this dissertation applies the (alpha, beta)-Precision Theory to the study of production systems with cycle overrun. The cycle overrun takes place, for instance, in automated machines with a constant part processing time, tau , and manual loading/unloading operations, which may have a random overrun in their duration. In this dissertation, the methods to obtain reliable estimates of cycle overrun, and the modeling, analysis, improvability and bottleneck identification of such systems are presented as well. Finally, the dissertation presents a case study motivated by an automotive transmission machining line.