Likelihood Ratio Methods for Monitoring Parameters of a Nested Random Effect Model

Abstract

In many practical situations the variance of a set of measurements can be attributed to several known sources of variability. For example, if several measurements of each item of a lot are taken, then one may need to deal not only with the within-item variability, but also with item-to-item within-lot and lot-to-lot components of variability. In such cases conventional control charts tend to produce an unacceptably high rate of false alarms and in general represent a rather weak diagnostic tool. This article shows how to build a control system based on likelihood ratio tests capable of monitoring the mean and variance components of a nested random effect model. The strong points and weaknesses of this approach are compared to those of competing methods, and some examples related to manufacturing of integrated circuits are discussed.

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