Determination of multiple dependent state repetitive group sampling plan based on the process capability index

Abstract

In this article, we propose a sampling plan called a multiple dependent state repetitive group sampling plan for variable inspection based on the process capability index C_pk. The proposed sampling plan is applicable for the inspection of normally distributed quality characteristics when both mean and variance are assumed to be unknown. This new plan under variable inspection will be very useful particularly in compliance testing. Tables are also constructed for the determination of optimal parameters for easy selection and implementation of the plan. The optimal parameters can be determined by using the approach of two points on the operating characteristic curve. Symmetric and asymmetric cases based on the fraction nonconforming by the lower and the upper specification limits are also considered. Advantages of the proposed plan are also discussed. It is also shown that the proposed plan outperforms other existing sampling plans under variable inspection.

Keywords:

• Conditional sampling by variables
• decision making
• nonlinear programming
• process capability index
• quality control

MATHEMATICS SUBJECT CLASSIFICATIONS:

• 62D05
• 62P30
• 78M50

Acknowledgments

The authors thank the Editor and the reviewers for their constructive comments and valuable suggestions that significantly improved the presentation of this article.