Optimal Design of Modified Group Runs Scheme with Estimated Process Parameters Based on Expected Average Number of Observations to Signal

Abstract

The modified group runs (MGR) scheme has a superior performance to the Shewhart and synthetic control schemes, particularly in identifying small and moderate mean shifts in a process. Recently, the MGR scheme was studied using the average number of observations to signal (ANOS) criterion, under the scenario where the process parameters are unknown (Case-U). However, a setback of this study is that the exact shift size must be specified prior to the implementation of this scheme as this is required by the ANOS criterion. In most of the scenarios, practitioners do not have a good knowledge of the exact shift size. To tackle this issue, we propose the use of the expected average number of observations to signal (EANOS) criterion in evaluating the performance of the Case-U MGR scheme. We also proposed the optimal design of the MGR scheme with Case-U based on minimizing out-of-control (OOC) EANOS. Finally, we present an example of application and demonstrate that the proposed procedure eases the implementation of the MGR scheme with Case-U as it minimizes the risk of misspecifying the shift size.