An Integrated Approach for Designing a Phase I c-Control Chart Based on the Phase II Performance of Poisson Exponentially Weighted Moving Average Control Chart

A control chart implementation in practice generally consists of two stages: Phase I for control chart design and Phase II for process monitoring. It is well known that the choice and design of a control chart have significant effects on its performance. In this study, a Shewhart c-control chart is considered for the Phase I study. The effects of parameter estimation in Phase I on the Phase-II performance of the Poisson exponentially weighted moving average (PEWMA) control chart are investigated. Chart designs are evaluated by taking a holistic approach for Phase I and Phase II. In this context, the out-of-control behavior of the process in Phase I is simulated for various shift and contamination scenarios, together with the c chart implementation for parameter estimation. For each simulation replication, the Markov chain approach is used to calculate the average run length (ARL) performance in Phase II. Obtaining the ARL distributions for different design parameter and simulation variable combinations, the performances of different designs are evaluated. Using a scheme based on the average of ARL performances in Phase II, control limit widths are determined for Phase-I analysis. Practical suggestions are provided for real-world implementations.