Economically Optimal Design of a Multivariate Synthetic T² Chart

Abstract

Economic and economic-statistical models are developed for the synthetic T ² chart. The input parameters that result in larger cost and affect the optimal parameters are identified. The optimal parameters are quite robust toward changes in input parameters, except the number of variables and the Mahalanobis distance. Alternative choices of parameters, which result in minimal cost increase, can be chosen if it is infeasible to operate the chart optimally. The results are based on numerical examples and verified through simulation. The synthetic T ² chart has better economic and economic-statistical performances than the Hotelling's T ² and MEWMA charts under most conditions.

Keywords:

• Comparison of economic performance
• Cost minimization, Misspecification
• Multivariate synthetic T ² chart
• Optimal parameters
• Sensitivity analyses

Mathematical Subject Classification:

• 62P30
• 90C31

Acknowledgments

This work is supported by the Universiti Sains Malaysia, Fundamental Research Grant Scheme (FRGS), no. 203/PMATHS/6711232.