Effect of measurement errors on double sampling S² control chart

Abstract

Product quality can be understood as inversely proportional to the variability in its production process. The control chart is a well-established statistical tool for quantifying and analyzing this process' variability based on observed information about some of its measurable characteristics. To simplify the control chart application, some researchers and users assume that the data used to evaluate the process is accurate. However, since the construction and use of control charts are based on measurement and no measurement system is perfect, errors in the measured data are inevitable. Recent studies indicate that the Double Sampling control chart can be an alternative for process monitoring. However, there is still a lack of studies that investigate the impact of measurement errors on Double Sampling control chart to monitor process variability. Based on the preceding, the present work aims to study how the performance of the Double Sampling S² control chart is affected by the presence of measurement errors. Initially, a systematic review of the literature is proposed in order to explore studies on the subject. The main methodology of the research is mathematical modeling and simulation. A design modeling for considering measurement errors in the Double Sampling S² control chart is proposed. The impact on the average run length (ARL) for different measurement error values is verified through simulation. Using a genetic algorithm, we propose an optimization study of the Double Sampling S² control chart for operation with measurement errors. Finally, a simulation example is presented to verify using the Double Sampling S² chart with the optimized parameters. The results indicate that measurement error deteriorates the performance of the Double Sampling S² chart, and the impact rises as measurement error increases. The simulation analysis showed the advantage of using the optimized Double Sampling S² chart, particularly for larger measurement errors. The present study contributes to the practical application knowledge of the Double Sampling S² control chart, providing parameters for its use in the presence of measurement errors.