Optimal designing of variables quick switching system based on the process capability index C_pk

Abstract

The process capability indices (PCI) are useful management tools, particularly in the production industry, which provide common quantitative measures on the production quality and capability. So sampling plans based on PCI will have wide applications in the production industries. This article proposes a variables quick switching system based on the PCI C_pk, where the quality characteristic of interest follows the normal distribution with unknown mean and variance. The proposed sampling system will be effective when testing is costly and destructive. The advantages of this system are also discussed. To determine the optimal parameters, tables are also constructed. The problem is formulated as a nonlinear programming where the objective function to be minimized is the average sample number and the constraints are related to lot acceptance probabilities at acceptable quality level and limiting quality level under the operating characteristic curve.

Keywords:

• application
• decision-making
• nonlinear programming
• process capability index
• quadratic programming
• sampling system
• sampling by variables

Acknowledgments

The authors would like to thank the reviewers and the editor for their valuable comments which led to improve the manuscript.