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Optimum time-censored simple ramp-stress accelerated life test sampling plan for the log-logistic distribution

Preeti Wanti Srivastava (Department of Operational Research, Delhi University, Delhi, India)
Deepmala Sharma (Department of Operational Research, University of Delhi, Delhi, India)

Journal of Quality in Maintenance Engineering

ISSN: 1355-2511

Article publication date: 9 March 2015




Acceptance sampling plans are designed to decide about acceptance or rejection of a lot of products on the basis of sample drawn from it. Accelerating the life test helps in obtaining information about the lifetimes of high reliability products quickly. The purpose of this paper is to formulate an optimum time censored acceptance sampling plan based on ramp-stress accelerated life test (ALT) for items having log-logistic life distribution. The log-logistic life distribution has been found appropriate for highly reliable components such as power system components and insulating materials.


The inverse power relationship has been used to model stress-life relationship. It is meant for analyzing data for which the accelerated stress is nonthermal in nature, and frequently used as an accelerating stress for products such as capacitors, transformers, and insulators. The method of maximum likelihood is used for estimating design parameters. The optimal test plan is obtained by minimizing variance of test-statistic that decides on acceptability or rejectibility of lot. The optimal test plan finds optimal sample size, stress rates, sample proportion allocated to each stress and lot acceptability constant such that producer’s risk and consumer’s risk is satisfied.


Asymptotic variance plays a pivotal role in determining the sample size required for a sampling plan for deciding the acceptance/rejection of a lot. The sample size is minimized by optimally designing a ramp-stress ALT so that the asymptotic variance is minimized.


The model suggested is of use to quality control and reliability engineers dealing with highly reliable items.



This research is supported by R & D grant received from University of Delhi. The authors are grateful to the referees for their valuable comments on an earlier version of the paper.


Srivastava, P.W. and Sharma, D. (2015), "Optimum time-censored simple ramp-stress accelerated life test sampling plan for the log-logistic distribution", Journal of Quality in Maintenance Engineering, Vol. 21 No. 1, pp. 112-132.



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