Abstract
Minimum-cost reliability test durations based on gamma failure count data are found by solving mixed integer nonlinear programming problems. The optimal numbers of test units and failures allowed are also determined. A linear combination of test time and sample size is minimized assuming that producer and consumer risks are controlled. A quite accurate approximation of the smallest feasible acceptance number is deduced in closed-form. Moreover, a fast and efficient iterative algorithm is presented in order to obtain the optimal reliability demonstration test plan, which provides the best criterion to decide the acceptability of submitted lots and production processes. Furthermore, some descriptive analyses of the proposed inspection schemes, as well as applications of the developed methodology to the manufacturing of deep groove ball bearings, semiconductor lasers, and water pumps, are provided for illustrative and comparative purposes.
Highlights
T HE development of reliability test plans to decide the acceptability of production processes and lots is a relevant topic in industrial quality control
Optimal sample sizes and decision criteria are usually found by solving constrained optimization problems, whereas test durations are often prefixed
The design of minimum-cost gamma test plans with controlled producer and consumer risks is developed in Section III, whereas Section IV deals with the determination of feasible reliability inspection schemes, which adequately protect both manufacturers and customers
Summary
T HE development of reliability test plans to decide the acceptability of production processes and lots is a relevant topic in industrial quality control. Assuming that the lifetime variable follows a gamma distribution, Fernández [34] and Fernández et al [35] determine sampling plans (n, a) with fixed test times and minimal sample sizes using diverse perspectives. The goal of this article is to find the optimal reliability test duration, in addition to the best sample size and acceptance number. The design of minimum-cost gamma test plans with controlled producer and consumer risks is developed, whereas Section IV deals with the determination of feasible reliability inspection schemes, which adequately protect both manufacturers and customers.
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