Construction of minimum cost reliability acceptance sampling plans for multistage process

ABSTRACT

In this paper an attempt is made to derive lot acceptance sampling plans based on failure censored data.  The items in the lot having multiple quality charecteristics are processed through multistage production process. We assume that quality charecteristics of the units follow exponential distribution with different parameters.  The acceptance criterion for the given lot is obtained based on the average-life of units in the sample at every stage. Two nonlinear optimiztion problems which minimize the  expected total testing costs at the acceptable quality level are solved.  Further, a sensitivity analysis study is conducted to assess the behaviour of testing costs with respect to changes in producer's risk, consumer's risk, and sample sizes. The plan parameters are obtained by solving nonlinear mixed integer programming problem by using genetic algorithm solver in MATLAB. Some numerical exapmles and two case studies are discussed to illustrate our sampling plans.

KEYWORDS:

• Quality control and sampling plan
• multiple quality characteristics
• type-II censoring
• optimization

Acknowledgments

The authors are deeply grateful to the referees for their extremely careful reading and valuable comments, which enhanced the quality and presentation of the paper. The authors are thankful to the senior editor for helpful comments.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Correction Statement

This article has been republished with minor changes. These changes do not impact the academic content of the article.

Additional information

Funding

This work was supported by the Science and Engineering Research Board [EMR/2017/000775].

Notes on contributors

M. Kumar

Dr Mahesh Kumar (M. Kumar) received his Ph.D. in applied statistics from Indian Institute of Technology (IIT) Bombay, India, in the year 2006. His research interests are reliability theory, acceptance sampling plans,  fuzzy reliability estimation,  and optimal reliability test plans. Presently he is working as a full time faculty in the Department of Mathematics,  National  Institute of Technology (NIT) Calicut, India.

P. C. Ramyamol

Dr. Ramyamol P. C. received her Ph.D in Mathematics, from NIT Calicut, India. Her research interests are reliability estimation and reliability acceptance sampling plans. Presently, she is a faculty in Govt Polytecnic in Kerala state, India.