Optimum degradation test sampling plan for the Wiener process

Abstract

In this paper, we propose degradation test sampling plans (DTSPs) used to determine the acceptability of a product in a Wiener process model. A test statistic and the acceptance criterion based on Wiener process parameter estimates are proposed. The design of a degradation test is investigated using a model incorporating test cost constraint to minimize the asymptotic variance of the proposed test statistic. Some important variables, including the sample size, measurement frequency, and the total test time, are chosen as decision variables in a degradation test plan. The asymptotic variance of the test statistic and the approximate functional forms of the optimal solutions are derived. A search algorithm is also represented in a flow chart for the purpose of finding the optimal DTSPs. In addition, we assess the minimum cost requirement for the result of the test procedure to satisfy the minimum requirements for the producer's risk and the consumer's risk. When the given test budget is not large enough, we suggest some methods to find appropriate solutions. Finally, a numerical example is used to illustrate the proposed methodology. Optimum DTSPs are obtained and tabulated for some combinations of commonly used producer and consumer risk requirements. A sensitivity analysis is also conducted to investigate the sensitivity of the obtained DTSPs to the cost parameters used.