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Abstract:A system reliability is often evaluated by individual tests of components that constitute the system. These component test plans have advantages over complete system based tests in terms of time and cost. In this paper, we consider the series system with n components, where the lifetime of the i-th component follows exponential distribution with parameter λi. Assuming test costs for the components are different, we develop an efficient algorithm to design a two-stage component test plan that satisfies the usual probability requirements on the system reliability and in addition minimizes the maximum expected cost. For the case of prior information in the form of upper bounds on λi's, we use the genetic algorithm to solve the associated optimization problems which are otherwise difficult to solve using mathematical programming techniques. The two-stage component test plans are cost effective compared to single-stage plans developed by Rajgopal and Mazumdar. We demonstrate through several numerical examples that our approach has the potential to reduce the overall testing costs significantly.

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Acceptance sampling plans are used to assess the quality of an ongoing production process, in addition to the lot acceptance. In this paper, we consider sampling inspection plans for monitoring the Markov-dependent production process. We construct sequential plans that satisfy the usual probability requirements at acceptable quality level and rejectable quality level and, in addition, possess the minimum average sample number under semicurtailed inspection. As these plans result in large sample sizes, especially when the serial correlation is high, we suggest new plans called ''systematic sampling plans.'' The minimum average sample number systematic plans that satisfy the probability requirements are constructed. Our algorithm uses some simple recurrence relations to compute the required acceptance probabilities. The optimal systematic plans require much smaller sample sizes and acceptance numbers, compared to the sequential plans. However, they need larger production runs to make a decision. Tables for choosing appropriate sequential and systematic plans are provided. The problem of selecting the best systematic sampling plan is also addressed. The operating characteristic curves of some of the sequential and the systematic plans are compared, and are observed to be almost identical.