Optimal classification of highly-reliable products whose degradation paths satisfy Wiener processes

At the research and development stage of a product, the manufacturer usually faces the problem of classifying the better and worse designs among several competing designs for each of these parts (or components). It is a great challenge for the manufacturer if these competing designs are highly reliable, since there are a few (or even no) failures that would 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 classification problem where the products' degradation paths satisfy Wiener processes. First, an intuitively appealing classification 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 the termination time needed by the classification rule for each of competing designs are computed by solving a nonlinear integer programming with a minimum probability of correct classification and a maximum probability of misclassification. Finally, an example is provided to illustrate the proposed method.