Designing an accelerated degradation experiment with a reciprocal Weibull degradation rate

Accelerated degradation tests (ADTs) are usually used to assess the lifetime distribution of highly reliable products which are not likely to fail under the traditional life tests or accelerated life tests. Several factors, such as the inspection frequency, the sample size and the termination time, are closely related to the experimental cost and the estimation precision. Obviously, an inappropriate setting of these decision variables not only wastes the experimental resources, but also reduces the precision of data analysis. Recently, some studies (e.g., Yu (Qual. Reliab. Eng. Internat. 19(3) (2003) 197)) addressed the problem of how to determine the optimal setting of these decision variables for a linearized degradation model, where the degradation rate follows a lognormal distribution. In practical applications, Weibull and lognormal distributions may fit the lifetime data well. However, their predictions may lead to a significant difference. In this paper, we will deal with the optimal design of an ADT where the degradation rate follows a reciprocal Weibull distribution. Under the constraint that the total experimental cost does not exceed a pre-determined budget, the optimal decision variables are solved by minimizing the mean-squared error of the estimated 100p100pth percentile of the lifetime distribution of the product at use condition. An example is provided to illustrate the proposed method.