The multivariate exponentially weighted moving average chart for monitoring short production runs

Abstract

This study investigates the performance of the multivariate exponentially weighted moving average (MEWMA) chart for monitoring a process with a finite horizon and this control chart is termed as the SR MEWMA chart. The statistical performance of the SR MEWMA chart is evaluated in terms of the truncated run length properties when the shift in the process mean is known a priori. The optimal statistical design of the SR MEWMA chart is to find the optimal design parameters such as the smoothing parameter and the control limit through the minimization of the out-of-control truncated average run length. The study of the truncated run length performance of the SR MEWMA chart is also extended to the case when the shift in the process mean is unknown, by selecting a range of the process mean shifts that can be modeled by means of a uniform distribution. The numerical comparisons show that the SR MEWMA chart outperforms the variable sample size Hotelling’s T² chart, in terms of the truncated average run length and expectation of the truncated average run length criteria. An example is provided to illustrate the implementation of the SR MEWMA chart.

Keywords:

• Markov chain
• MEWMA chart
• Short production runs
• Truncated average run length
• Truncated standard deviation of run length