Conditional and marginal performance of the Poisson CUSUM control chart with parameter estimation

Cumulative Sum (CUSUM) type control charts are widely used in industry because of their effectiveness for process control. The Poisson CUSUM is a powerful and easy-to-implement control chart, which is appropriate for monitoring the counts of nonconformities in a unit from a repetitive production process. In the literature, control chart performances are generally evaluated under the assumption of known in-control process parameters. However, in-control process parameters are rarely known in practice and often parameter estimates from a reference sample are used instead. As a consequence of the additional variability introduced by parameter estimation, operational performance of a control chart might differ from the expected performance when the parameters are known. In this paper, effect of estimated process mean on the conditional and marginal performance of the Poisson CUSUM chart are quantified. The Markov Chain approach is used for calculating the aspects of the run length distribution. The effect of estimation on the in-control average run length performance is shown to be significant. Sample-size recommendations are provided.