LIKELIHOOD RATIO METHODS FOR MONITORING PARAMETERS OF A NESTED RANDOMEFFECT MODEL

In many practical situations the variance of a set of measurements can be attributed to several known sources of variability. For example, i f several measurements of each item of a lot are taken, then one may n eed to deal not only with the within-item variability, but also with i tem-to-item within-lot and lot-to-lot components of variability. In su ch cases conventional control charts tend to produce an unacceptably h igh rate of false alarms and in general represent a rather weak diagno stic tool. This article shows how to build a control system based on l ikelihood ratio tests capable of monitoring the mean and variance comp onents of a nested random effect model. The strong points and weakness es of this approach are compared to those of competing methods, and so me examples related to manufacturing of integrated circuits are discus sed.