The Effect of Estimated Parameters on Poisson EWMA Control Charts

Performance of control charts is generally evaluated with the assumption that the process parameters are known. In many control chart applications, however, the process parameters are rarely known and their estimates from an in-control reference sample are used instead. In such cases, the moments of the run length distribution depend on the values of the estimated parameters. The Poisson exponentially weighted moving average (EWMA) is an effective control chart in situations where the number of nonconformities per unit from a repetitive production process is monitored. The objective of this paper is to study the effect of estimating the mean on the performance of the Poisson EWMA control chart. We make use of the Markov Chain approach. Sample-size recommendations and some concluding comments are provided.