Designing of tightened-normal-tightened sampling scheme under Weibull and gamma distributions for mean life assurance

Abstract

A number of sampling plans and sampling systems (or schemes) have been designed in the literature with the intention of improving the discriminating power of operating characteristic curve of zero acceptance number single sampling plans. In this article, we propose one of such sampling schemes namely, tightened-normal-tightened scheme to assure the mean life of the products where the lifetime follows the Weibull or gamma distribution. In order to execute the sampling scheme, we determine the optimal parameters on the basis of two points on the operating characteristic curve approach and for such determination we consider different values of consumer’s risk, shape parameters with predetermined producer’s risk. The implementation of the proposed scheme is explained with real life data. The performance of the proposed scheme is compared with some other existing sampling plans in terms of average sample number. The operating characteristic curve is investigated to show the better performance of the proposed scheme. The average sample number obtained under both distributions is compared with each other. In addition, the economic aspect designing of the proposed scheme is investigated under both distributions and the comparative study is done on the cost of inspection of the proposed scheme with other existing plans.