Optimum and semi-optimum life test plans of electrical insulation for thermal stress

Assuming that the Arrhenius law holds between the thermal stress and the lifetime, and that the logarithmic lifetime follows some consistent probability distributions at a constant stress. Under such life models, it is crucial to show the optimum test design from an efficiency viewpoint. It would also be useful to know the semi-optimum test plan in which the efficiency is close to that in the optimum one and the test condition is simple. The optimization target is to find the optimum number of test specimens at each test stress level, and we consider the case that the number of stress level is three. The criterion for optimality is measured by the root mean squared error for the lifetime in use condition. To take into account the reality, we used the parameter values in a real experimental case. Comparing the optimum results with those using the conventional test method where test specimens are equally allocated to each test stress level, we have found that there is only a small difference between the optimum test result and the conventional test result if linearity of the Arrhenius plot is required. We may regard the conventional test plan as one of the semi-optimum test plans. We have checked the consistency between the theoretical results and the simulation results.