Phase I monitoring of individual normal data: Design and implementation

Abstract

Control charts play an important role in Phase I or retrospective studies, which are essential to establish stability and generate reference data necessary for calculation of prospective (Phase II) control limits for process monitoring. The Shewhart-type Phase I chart for individual normally distributed data is one of the most popular monitoring methods. However, the control limits (charting constants) available in the literature do not account for either the effect of parameter estimation or use an appropriate chart performance metric. This can increase the rate of false alarms to an unacceptable level. In this paper, we consider the Shewhart-type Phase I chart for individual data for two common estimators of standard deviation and a suitable chart performance metric. We derive the formulas and tabulate the corrected (or adjusted) charting constants. Effects of violations of assumptions are examined in terms of in-control (IC) robustness to normality and presence of autocorrelation, via simulations. Some out-of-control (OOC) performance analysis is also presented. An illustration using some data is provided along with a summary and some recommendations. The accompanying R program may be used to calculate the corrected charting constants in practice on demand.