Optimum Life Test Plan under the Thermal Stress Deterioration Using the Mechanical Strength

Abstract

The mathematical models to represent the relationship between the thermal stress and the deterioration rate for electrical insulation are well established based on the Arrhenius law and appropriate underlying probability distributions for constant thermal stress. There are two kinds of methods to deal with the thermal lifetime: one is the two-valued discrete model representing 0 for alive and 1 for dead, and the other is to use continuous value for the mechanical strength deterioration of the material. In this paper, we deal with the latter case. In the IEC (International Electrotechnical Commission) 60216-1, deterioration due to the thermal stress is represented by the mechanical strength, and the time showing 50% mechanical strength to the initial strength is defined as the failure time. For underlying probability distribution models, the normal distribution, the generalized Pareto distribution, and the generalized logistic distribution models are proposed. Based on these mathematical models proposed, we investigate the optimum life test plans for the 50% mechanical strength index. Using a real experimental case, we obtain the adequate parameter values for the simulation accelerated life test. The optimum parameters we seek are the most appropriate number of specimens at each stress level. Comparing the optimum test results and the conventional test results by equally allocated to each stress, the ratios of the prediction error for the optimum tests to that of conventional tests are around 85%. This consequence is very similar to that in the case of two-valued discrete model.