Effect of phase I applications on the phase II performance of Poisson-exponentially weighted moving average (PEWMA) control charts

By offering quality products or services to the customers with low costs, organizations are trying to ensure sustainability and development in the national/international domains, which are becoming more and more competitive, through the use of various Statistical Process Control tools. Control charts, which are considered to be the most effective of these tools, are widely used today. The use of control charts is considered to be a two-stage application that consists of a retrospective analysis stage named Phase I and monitoring stage named Phase II. The choice and design of an appropriate control chart has significant effects for the performance of the control chart in practice. In this thesis, effects of Phase I application on the Phase II performance of the Poisson-Exponentially Weighted Moving Average (PEWMA) and Shewhart c control charts are investigated. In cases where process parameters are known and not known, implementation of Phase I for parameter estimation and not implementing Phase I are compared. It the study best design parameters for control charts are determined by using different parameters and variables in Phase I and Phase II applications. In this context, shift and contaminated data cases in the process are examined in order to simulate the out-of-control behaviour of the process. Phase I stage of the control charts is simulated for various parameter combinations and Average Run Length (ARL) values that indicates Phase II performance of control charts are calculated by Markov chain approach for PEWMA control charts and by determining probability values for c control chart. The performance of the control charts is compared and evaluated by different metrics such as Average of the ARL (AARL), Median of the ARL (MARL), Standard Deviation of the ARL (SDARL), Coefficient of Variation of the ARL (CVARL) and percentiles of ARL, which are calculated from ARL values that are results of simulation of different parameter combinations. Based on the AARL results obtained in the thesis study, a method for determining the best control limit widths used in Phase I analysis is determined. The recommended control limit widths are determined according to the number of best results in cases with and without contaminated data. Practical suggestions are provided for industrial applications.