Phase II process monitoring for the balanced one‐way random effects model

Abstract

AbstractStatistical process control (SPC) and monitoring techniques are useful in a variety of applications. In this paper, we consider prospective (Phase II) process monitoring for the balanced random effects (variance components) model with Shewhart‐type charts when parameters are estimated from a Phase I study. Such a model is a nonstandard application of control charts and arises in a number of situations in practice. Effects of parameter estimation need to be accounted for or there maybe too many false alarms that will disrupt the monitoring regime. To this end, two types of corrected (adjusted) control limits are proposed, based on two perspectives, namely the unconditional and the conditional, as recommended in the recent literature. Results and derivations are provided along with tabulations and illustrations with real data. Robustness of the charts is examined and a summary and recommendations are given. An accompanying R package is provided for deploying the methodology. Other Phase II charts such as the EWMA and the CUSUM can be considered along similar lines and will be presented elsewhere.