Optimal design for reliability improvement experiments with a non-constant scale parameter

Traditionally, when planning reliability improvement experiments, the orthogonal design with equal sample allocation has been the typical choice. However, it is often found that both the scale parameter and the shape parameter of lifetime distributions vary across experimental factors, rendering the conventional approach unsuitable for such scenarios. In this article, we introduce a new approach named the ‘optimal design’ for planning such experiments. The D-optimality criterion is adopted to reduce the censoring issue as much as possible and thus to improve accuracy in estimating product lifetime. Our design strategy breaks down the problem into two essential subprocesses: sample allocation and determination of treatment combinations. To arrive at the best possible solution, we have devised an iterative algorithm that efficiently identifies the optimal solution. Through a case study on a real-world example, we demonstrate that the proposed methodology is highly effective in improving both the accuracy of estimations and the efficiency of experiments.