Evaluation of Phase I analysis scenarios on Phase II performance of control charts for autocorrelated observations

Phase I analysis of a control chart implementation comprises parameter estimation, chart design, and outlier filtering, which are performed iteratively until reliable control limits are obtained. These control limits are then used in Phase II for online monitoring and prospective analyses of the process to detect out-of-control states. Although a Phase I study is required only when the true values of the parameters of a process are unknown, this is the case in many practical applications. In the literature, research on the effects of parameter estimation (a component of Phase I analysis) on the control chart performance has gained importance recently. However, these studies consider availability of complete and clean data sets, without outliers and missing observations, for estimation. In this article, we consider AutoRegressive models of order 1 and study the effects of two extreme cases for Phase I analysis; the case where all outliers are filtered from the data set (parameter estimation from incomplete but clean data) and the case where all outliers remain in the data set during estimation. Performance of the maximum likelihood and conditional sum of squares estimators are evaluated and effects on the Phase II use are investigated. Results indicate that the effect of not detecting outliers in Phase I can be severe on the Phase II application of a control chart. A real-world example is provided to illustrate the importance of an appropriate Phase I analysis.