Optimal design of variable acceptance sampling plans for mixture distribution

ABSTRACT

The paper investigates the design of single and sequential variable acceptance sampling plans for a mixture distribution. Mixture distributions are seen in many practical problems such as life testing experiments of electronic components and clinical trials. The sampling plans for this kind of situations are not well addressed in the literature. We first propose a single sampling plan for a distribution which is a mixture of two exponential distributions. An optimization problem which minimizes the total cost of testing at given producer's and consumer's risks is solved to obtain the plan parameters. Two different sequential sampling plans are also defined and plan parameters are obtained by solving corresponding optimization problems. Finally, a case study, a simulation study and a sensitivity analysis are presented to illustrate our sampling plans.

KEYWORDS:

• Acceptance sampling plan
• exponential distribution
• Ttype I censoring
• Type-II censoring
• optimization

MATHEMATICS SUBJECT CLASSIFICATION CODE 2010:

• 62N02
• 62N05

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 associate editor for helpful comments.

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

The research of the second author was supported by DST (Department of Science and Technology, INDIA) (SERB) [grant number EMR/2017/000775].