A variable sampling interval one-sided CUSUM control chart for monitoring the multivariate coefficient of variation

Abstract

Monitoring techniques based on the multivariate coefficients of variation (MCV) have received a great deal of attention in quality control. Numerous studies have shown that adaptively changing the charting parameters based on the past sample information can improve the performance of a chart in detecting process changes. In view of the performance benefits of adaptive strategies, two one-sided cumulative sum (CUSUM) charts are proposed to monitor the MCV and a variable sampling interval (VSI) strategy is incorporated into these charts. By using the Markov chain method, the formulas for calculating the average and standard deviation of time to signal measures of the VSI CUSUM MCV control charts are derived. Then for the known and unknown shift sizes, the optimization algorithms for obtaining the charting parameters are presented. The superiority of the proposed control charts is confirmed by comparing their performance with two existing MCV charts. Finally, an example using real investment data demonstrates the practical application of the proposed charts.

Keywords

• Multivariate Coefficient of Variation
• CUSUM
• Average Time to Signal
• Markov Chain