Economic-statistical design of synthetic max chart

Abstract

This paper studies the economic-statistical design of a synthetic max chart. The synthetic max chart consists of a combination of a max sub-chart and a conforming run length sub-chart. The design of the chart is developed by considering the minimization of the cost function, subject to constraints on the average run length. A sensitivity analysis is performed to investigate the effects of the cost and process parameters on the solution of the economic-statistical design. Furthermore, the economic-statistical designs of the synthetic max chart and the max chart are compared in this study. The results show that the synthetic max chart outperforms the max chart from an economic-statistical viewpoint. Although the economic-statistical design of the synthetic max chart has the disadvantage of a slight increase in cost over the economic design, the economic-statistical design gives better in-control statistical performance, where the desirable statistical properties are justified. This study is also extended to the multivariate case.

Keywords:

• Average run length
• conforming run length chart
• max chart
• economic-statistical design