Economic design of variable sampling interval sign control chart

Abstract

In this article, we have proposed an economic design of variable sampling interval (VSI) control chart based on sign statistic. An expression for expected loss per unit time is obtained and minimized with respect to design parameters. The performance of this economic design is compared with economic design of fixed sampling interval (FSI) sign chart to control location of process characteristic. Though the power of VSI sign chart is slightly lower than that of FSI sign chart design, it appears to be dominant over FSI sign chart design for moderate shifts. The effect of change in input parameters on loss cost is observed for different out of control probabilities of quality characteristic under VSI sign chart scheme. Change in shift parameter, penalty cost parameter, and time to detect the shift have considerable effect on loss cost from the design. The design is fairly robust to the changes in other parameters.

Keywords:

• Economic design
• nonparametric control chart
• sign control chart
• variable sampling interval design

Acknowledgment

The authors are grateful to the editor and both the referees for their valuable suggestions and comments. The first author would like to acknowledge the support from the University Grants Commission, New Delhi, for providing Teacher Fellowship under Faculty Development Programme. The second author would like to acknowledge the financial support received from University Grants Commission under Major Research Project (F. No.43-542/2014(SR)) to carry out the research work.