Optimal design of the modified group runs (MGR) chart when process parameters are estimated

The performance of variable charts is commonly investigated based on the assumption of known process parameters. However, the process parameters are usually unknown and have to be estimated from a limited number of Phase-I samples, leading to a deterioration of a control chart’s performance. To overcome this problem, we examine the performance of the modified group runs (MGR) (Formula presented.) chart with estimated process parameters. A table containing the optimal parameters of the proposed chart when the process parameters are estimated is also given. These optimal parameters will enable practitioners to obtain a similar in-control performance as the known process parameters case.