An empirical study of two classes of estimators for process variation transmission

Abstract

Manufacturing processes often consist of a number of sequential stages. Of interest is to control the variation in one or more quality characteristics of a production unit at the final stage. By understanding how variation is transmitted and added across the stages, remedial actions in reducing variation at the final stage can be properly planned. With one quality characteristic measured at each stage, a set of naive estimators is previously proposed and shown to perform indistinguishably well with maximum likelihood estimators. Thus naive estimators are more convenient than maximum likelihood estimators as the former exist in closed form while the latter do not. This article considers situations when more than one quality characteristic is measured throughout the stages. Methods of analyzing variation transmission are briefly reviewed and the finite sample properties of naive and maximum likelihood estimators for multivariate measurements are further examined. A broad conclusion is that for moderate number of production units, naive estimators have smaller bias and variability. Furthermore, "proper" naive estimates provide more accurate interval estimates at a given confidence level. Finally, a set of piston-machining data is used for illustration. © World Scientific Publishing Company.