A Study on the S^2-EWMA Chart for Monitoring the Process Variance based on the MRL Performance

The existing optimal design of the fixed sampling interval S^2-EWMA control chart to monitor the sample variance of a process is based on the average run length (ARL) criterion. Since the shape of the run length distribution changes with the magnitude of the shift in the variance, the median run length (MRL) gives a more meaningful explanation about the in-control and out-of-control performances of a control chart. This paper proposes the optimal design of the S^2-EWMA chart, based on the MRL. The Markov chain technique is employed to compute the MRLs. The performances of the S2-EWMA chart, double sampling (DS) S^2 chart and S chart are evaluated and compared. The MRL results indicated that the S^2-EWMA chart gives better performance for detecting small and moderate variance shifts, while maintaining almost the same sensitivity as the DS S^2 and S charts toward large variance shifts, especially when the sample size increases.