Design of EWMA and CUSUM control charts subject to random shift sizes and quality impacts

Statistical process control charts are important tools for detecting process shifts. To ensure accurate, responsive fault detection, control chart design is critical. In the literature, control charts are typically designed by minimizing the control chart's responding time, i.e., average run length (ARL), to an anticipated shift size under a tolerable false alarm rate. However, process shifts, originating from various variation sources, often come with different sizes and result in different degrees of quality impacts. In this paper, we propose a new performance measure for EWMA and CUSUM control chart design to take into consideration the variable shift sizes and corresponding quality impacts. Unlike economic designs of control charts that suffer from a complex cost structure and intensive numerical computation, the proposed design methodology does not involve any cost estimation and the design procedure is as simple as looking up tables. Given the Gaussian random shifts and quadratic quality loss function, we show that the proposed design has a significant reduction in the quality impact as compared to converitional ARL-based designs. Guidelines and useful worksheets for practical implementation of the proposed designs are then suggested to practitioners with different knowledge levels of the process excursions.