Design and analysis for monitoring mean of paired quality characteristics: an application to continuous stirred-tank reactor process

In industrial, healthcare, and business processes, numerous quality characteristics are matched pairs. These characteristics help to identify anomalies, trends, and patterns that enable better decisions and process optimization. In process monitoring, the control chart is an effective tool for detecting unusual changes in the process parameters. The cumulative sum (CUSUM) and Shewhart charts are considered efficient, respectively, for detecting small and large shifts in the understudy process. The CUSUM and combined Shewhart-CUSUM (CSC) schemes are developed in this study to monitor the location parameter of the differences of paired processes. For the assessment of the proposed CUSUM and CSC charts, the run-length metric is used, which is produced by developing an algorithm in the R language. The conditional and unconditional run length distributions of the proposals are evaluated. The performance of the proposed charts is compared with some well-known existing schemes, and the comparative study shows that the proposed schemes perform uniformly better than their existing counterparts. Moreover, the estimation effect is also evaluated on the performance of the proposed schemes. A practical application related to the continuous stirred-tank reactor (CSTR) process, along with a hypothetical example of the proposed charts, is also provided to implement the proposed designs for the concerns of practitioners.