Optimal estimated process parameters side sensitive group runs chart based on expected average run length

The side sensitive group runs (SSGR) chart is better than both the Shewhart and synthetic charts in detecting small and moderate process mean shifts. In practical circumstances, the process parameters are seldom known, so it is necessary to estimate them from in-control Phase-I samples. Research has discovered that a large number of in-control Phase-I samples are needed for the SSGR chart with estimated process parameters to behave similarly to a chart with known process parameters. The common metric to evaluate the performance of the control chart is average run length (ARL). An assumption for the computation of the ARL is that the shift size is assumed to be known. In reality however, the practitioners may not know the following shift size in advance. In light of this, the expected average run length (EARL) will be considered to measure the performance of the SSGR chart. Moreover, the standard deviation of the ARL (SDARL) will be studied, which is used to quantify the between-practitioner variability in the SSGR chart with estimated process parameters. This paper proposes the optimal design of the estimated process parameters SSGR chart based on the EARL criterion. The application of the optimal SSGR chart with estimated process parameters is demonstrated with actual data taken from a manufacturing company.