The geometric-Poisson exponentially weighted moving control chart with estimated parameters

In many count data sets, an item may have more than one defect that causes the item to be defective. The Poisson EWMA scheme cannot be used to monitor such defects. The geometric-Poisson exponentially weighted moving average (EWMA) chart has been shown to be an effective scheme to monitor the number of defects over time. In these applications, it is assumed that the process parameters are known or has been accurately estimated. However, in practice, the process parameters are rarely known and must be estimated from reference sample to construct the geometric-Poisson EWMA chart. The performance of the given chart, due to variability in the parameter estimation, might differ from known parameters case. This article explored the effect of estimated parameters on the conditional and marginal performance of the geometric-Poisson EWMA chart. Recommendations about the proper choice of sample-size, smoothing constant and dispersion parameter are made. Results of this study highlight the practical implications of estimation error, and to offer advice to practioners when constructing a phase-I sample.