Optimal selection of the most reliable design whose degradation path satisfies a Wiener process

At the research and development stage of a product, the manufacturer usually faces the problem of selecting the most reliable design among several competing ones for some parts (or components) of the product in order to enhance the product's quality. It is a great challenge for the manufacturer if these completing designs are highly reliable, since there are few (or even no) failures can be obtained by using traditional life tests or accelerated life tests. In such cases, if there exist product characteristics whose degradation over time can be related to reliability, then collecting “degradation data” can provide information about product reliability. This paper proposes a systematic approach to the selection problem where the products' degradation paths satisfy Wiener processes. First, an intuitively appealing selection rule is proposed and, then, the optimal test plan is derived by using the criterion of minimizing the total experimental cost. The sample size, inspection frequency, and termination time needed by the selection rule for each of competing designs are computed by solving a nonlinear integer programming problem with a minimum probability of correct selection. Finally, an example is provided to illustrate the proposed method.