Optimal design of multiple stress constant accelerated life test plan on non-rectangle test region

For optimal design of constant stress accelerated life test(CSALT) with two-stress, if the stresses could not reach the highest levels simultaneously, the test region becomes non-rectangular. For optimal CSALT design on non-rectangle test region, the present method is only focused on non-rectangle test region with simple boundary, and the optimization algorithm is based on experience which can not ensure to obtain the optimal plan. In this paper, considering the linear-extreme value model and the optimization goal to minimize the variance of lifetime estimate under normal stress, the optimal design method of two-stress type-Ⅰ censored CSALT plan on general non-rectangular test region is proposed. First, two properties of optimal test plans are proved and the relationship of all the optimal test plans is determined analytically. Then, on the basis of the two properties, the optimal problem is simplified and the optimal design method of two-stress CSALT plan on general non-rectangular test region is proposed. Finally, a numerical example is used to illustrate the feasibility and effectiveness of the method. The result shows that the proposed method could obtain the optimal test plan on non-rectangular test regions with arbitrary boundaries. This research provides the theory and method for two-stress optimal CSALT planning on non-rectangular test regions.