Optimum Life Test Plans of Electrical Insulation for Thermal Stress Under the Arrhenius Law



We search for the 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. The optimization target is to find the optimum number of test specimens at each test stress level, and we consider the case of 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. Two situations are considered: one is the fundamental situation, the other is the weakest situation. Comparing the optimum results in the fundamental situation with those using the conventional test method where test specimens are equally allocated to each test stress level, we have found that the confidence interval for the predicted value in the optimum case becomes around 80–85 % of that in the conventional test. However, there is only a small difference between the optimum test result and the conventional test result if linearity of the Arrhenius plot is required. It would 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. In that sense, we have found that we may regard the conventional test plan as one of the semi-optimum test plans. In the weakest situation where the weakest specimen determines the system failure, similar properties are observed except the Arrhenius curve shift.


Arrhenius law Electrical insulation Generalized logistic distribution Generalized Pareto distribution Life test plans Normal distribution Thermal stress 



The authors would like to express the deepest appreciation to Dr. Okamoto, Central Research Institute of Electric Power Industry, Dr. Sakumura, Chuo University, and Mr. Kiyosue, Kyushu Institute of Technology, for their cooperation to this work.


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© Springer Science+Business Media Dordrecht 2015

Authors and Affiliations

  1. 1.Kyushu Institute of TechnologyIizukaJapan

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