Adjustment strategies and estimation for short-run processes with run-to-run variation.

摘要

A primary task of the industrial statistician is to identify, monitor, and mitigate the effects of variability in manufacturing processes. An important source of variability for many manufacturing operations, such as short run job shop machining and batch chemical processing, is run-to-run set-up variability. The presence of set-up variability is especially critical in the short run manufacturing environment since the ability to detect and correct an imprecise set-up is limited. Existing methods for such set-up assessment are inadequate. Some methods, like the heuristic Pre-Control, fail to consider how the process is to be corrected. Other procedures assume an infinite production horizon. This research addresses these deficiencies and focuses on adjustment strategies that permit a single adjustment to correct for a perceived set-up error. Under our single adjustment process model, an adjustment is made only if an estimate of the set-up error exceeds an adjustment threshold. By incorporating fixed costs of sampling and adjustment, a decision theoretic treatment of the problem is used to find fixed sample size and sequential single adjustment procedures. Procedures for both 0-1 and quadratic quality loss functions are developed and compared for a set of standard parameter cases. These procedures are operationally simple to implement and offer cost advantages over ad hoc procedures often used in practice.;Estimates of process parameters are required inputs for the aforementioned set-up assessment procedures. As a second part of this research, a parameter estimation protocol for the single adjustment process model is described. There are three parameters of interest: within run process variance, between-run set-up error variance, and adjustment error variance. Two estimation procedures are described. The first relies on direct maximization on the entire likelihood function. The second is based on a conditional maximization of multiplicative factors of the likelihood. Simulation indicates that the conditional procedure performs nearly as well as the global procedure. In addition, it has important operational advantages: it provides closed form point estimates and confidence intervals for some parameters. Also, two hypothesis tests useful for formulating a quality improvement strategy are derived.