Equivalent optimum design for accelerated life test scheme based on D-efficiency

Equivalent optimum design is a new method of designing an optimum accelerated life test scheme. Traditional method is to establish a statistical model based on the corresponding life distribution and acceleration model under the premise of determining the test stress loading mode. The premise of predetermined stress loading mode results in a locally optimal solution, rather than achieving the global optimal requirement of minimizing the test time or cost during the period of actual experimental implementation. The existing equivalent experimental design has already compensated for the above constraints roughly, which provides an equivalent conversion approach between different accelerated life test plans. Thus, an equivalent design scheme can be obtained on the baseline of existing optimal constant stress accelerated life test. However, the current equivalent criterion is a little bit too harsh that is to request the equation of two plans' corresponding quintile life asymptotic variance under normal stress level or fisher matrix determinant. It is difficult to obtain the satisfied solutions. In this paper, a new equivalent optimization method is proposed based on a new equivalent criterion called D-efficiency. With this method, equivalent design scheme can be realized by utilizing the ratio of fisher information matrix determinant to measure the equivalent degree. In this work, it assumes the fisher matrix determinant of optimal constant-stress accelerated life test is the baseline to determine the objective of an optimal model. The constraints can be built with several parameters of the original constant stress test plan. Finally, an example of the equivalent design was provided, which we changed the stress loading mode from constant-stress to step-stress. Different equivalent plans has been presented by changing the stress loading modes to reduce the test time or lower the cost of test under condition of the same accuracy of life prediction.