Statistical 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.

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Phase I is crucial for the success of the overall statistical process control (SPC) and monitoring regime. Shewhart‐type charts are recommended in this phase because of their broader shift detection ability. In this paper, a Phase I Shewhart‐type trueX¯ chart is considered for the balanced random effects (also called a variance components) model. The proposed methodology takes proper account of the effects of parameter estimation and uses the false alarm probability (FAP) metric to design the chart. In the sequel, the corrected (adjusted) charting constants are calculated and tabulated. The constant can be found, on demand, from an accompanying R package. Motivations and illustrations with some real data are provided. Performance of the chart is examined in terms of in‐control robustness and detection of nonhomogeneity (out‐of‐control). The proposed chart is shown to be easily adaptable to more general models, with more variance components and nested factors, and can accommodate various estimators of variance. Thus, it enables a broader Phase I process monitoring strategy, under normality, which can be applied within the ANOVA framework applicable for many DOE models. A summary and some recommendations are provided.

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