Optimal design of the side-sensitive modified group runs (SSMGR) x̄ chart when process parameters are estimated

A side-sensitive modified group runs (SSMGR) X chart is commonly examined under the assumption of known process parameters (denoted as Case-K). However, in practical situations, the process parameters are seldom known, and it is essential to estimate them from in-control (IC) phase I samples. From the study of the minimum amount of phase I samples, m that is required by the SSMGR X chart when the process parameters are estimated (represented as Case-U), to achieve practically the same performance as that of the Case-K, it was found that a huge number of IC phase I samples are needed. Due to time and cost factors, accumulating a substantial amount of IC phase I samples is difficult. To circumvent this problem, we study the optimal designs of the Case-U SSMGR X chart, based on both the zero and steady states' average number of observations to signal (ANOS) and expected ANOS (EANOS). Tables containing optimal charting parameters are provided to ease the implementation of the Case-U SSMGR X chart. By using these optimal parameters specifically designed for the Case-U SSMGR X chart, we can obtain similar zero and steady states' ANOS and EANOS performances to that of the Case-K. The use of the optimal Case-U SSMGR X chart is demonstrated with real data taken from a hard-bake process in a manufacturing company.