CUSUM-based process capability control chart for detecting small shift during Phase-II monitoring

Control chart technique and process capability analysis are two of the most important measures of process control. A fusion of these two, viz. process capability control chart is also no-new to the literature. The process capability control charts, that have been designed till date, are mostly of Shewhart type. However, these charts are primarily used at the Phase-II quality control, where one can expect only small shifts in process parameter values, as the larger shifts should already have been taken care of in the Phase-I. Interestingly, cumulative sum (CUSUM) control charts have been seen to outperform Shewhart-type control charts in detecting small shifts. In the present article, a fusion of CUSUM chart and Cpk, one of the most famous process capability index, is proposed to address this problem. An extensive study has been carried out to compare the performance of the newly developed chart with the existing ones based on average run length. Two numerical examples have been discussed demonstrating the efficacy of the proposed method. The necessary R codes are also documented in the article to facilitate prospective future applications.