Optimal statistical design of variable sample size multivariate exponentially weighted moving average control chart based on median run-length

Abstract

Conventionally, a standard control chart implements fixed sample size in process monitoring. In this study, we propose an optimal statistical design for the variable sample size (VSS) multivariate exponentially weighted moving average (MEWMA) chart based on the median run-length (MRL). The proposal is based on the fact that the percentiles of the run-length distribution, especially the MRL, are more reflective and reliable for performance evaluation with respect to a skewed run-length distribution. The MRL for the VSS MEWMA chart computed using the Markov chain approach is verified with Monte Carlo simulation. For benchmarking purposes, the performance of the VSS MEWMA chart is compared against the standard MEWMA chart and the synthetic T² chart, in terms of the MRL. The numerical results show that the VSS MEWMA chart performs better than the standard MEWMA chart and the synthetic T² chart, in detecting shifts in the process mean vector. Finally, an application is provided as an illustration for the implementation of the VSS MEWMA chart based on the MRL.

Keywords:

• Markov chain approach
• median run-length
• multivariate exponentially weighted moving average chart
• variable sample size