A phase II EWMA chart for the balanced one‐way random effects model

Abstract

Statistical process control (SPC) techniques are used in applications where more than one sources of variation are present, for example, in a one‐way random effects (variance components) model. The Shewhart X¯$\bar{X}$ control charts for this situation have been studied by several researchers. However, exponentially weighted moving average (EWMA) charts are generally recommended in Phase II, as they are more sensitive to detecting smaller process mean shifts. We consider EWMA charts for the one‐way random effects model in the balanced case, properly accounting for the effects of parameter estimation while designing and implementing the control charts. In the sequel we derive and calculate the corrected (adjusted) control limits for Phase II applications. Following the recent literature, the limits are formulated under two perspectives, the unconditional and the conditional. Tabulations of the charting constants are provided under both perspectives along with an illustration with some actual data. A simulation study examining in‐control (IC) robustness performance is conducted under both perspectives. Finally, some conclusions are given. An R package is provided to support deployment of the proposed control chart in practice.