Designing a Degradation Test by Minimizing the Variance of Estimating a Product's Mean-Time-To-Failure

Degradation tests are widely use to assess the reliability of highly reliable products. The experimental cost and the precision of the estimate of a product's lifetime in conducting a degradation test heavily depend on some decision variables such as the inspection frequency, sample size and termination time. An inappropriate choice of these decision variables not only wastes experimental resources but also reduces the precision of estimating the product's reliability. This paper deals with the optimal design of a degradation test. Given the constraint that the total cost of the experiment should not exceed a pre-determined budget, the optimal combination of sample size, inspection frequency, and measurement times is determined by minimizing the variance of the estimator of the product's mean-time-to-failure. The optimization problem is formulated as a nonlinear integer programming. An illustrative example demonstrates the effectiveness of the proposed method.