Designing of a mixed-chain sampling plan based on the process capability index with chain sampling as the attributes plan

ABSTRACT

In this article, we propose a new mixed chain sampling plan based on the process capability index C_pk, where the quality characteristic of interest having double specification limits and follows the normal distribution with unknown mean and variance. In the proposed mixed plan, the chain sampling inspection plan is used for the inspection of attribute quality characteristics. The advantages of this proposed mixed sampling plan are also discussed. Tables are constructed to determine the optimal parameters for practical applications by formulating the problem as a non linear programming in which 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. The practical application of the proposed mixed sampling plan is explained with an illustrative example. Comparison of the proposed sampling plan is also made with other existing sampling plans.

KEYWORDS:

• Application
• chain sampling
• decision-making
• mixed sampling plan
• non linear programming
• process capability index
• quadratic programming

MATHEMATICS SUBJECT CLASSIFICATION:

• 62P30
• 90C30
• 90C90
• 97K80

Acknowledgments

The authors thank the anonymous reviewers and the editor for their insightful comments and valuable suggestions which led to improve the presentation of the manuscript.

Funding

The first author acknowledges the Department of Science and Technology, Government of India, for supporting the research work financially (FIST) (grant number SR/FST/MSI-107/2015).