A dynamic lognormal stress-strength reliability model with application to power system insulation devices

In order to develop a reliability model for power system devices, such as insulating materials, subjected to both stresses and aging, the paper proposes a dynamic “stress-strength” model. The model is based upon Lognormal distributions for stress and strength, including their dynamic variability, giving rise to a new probability distribution, the so-called Shining distribution, seeming appropriate for insulation devices. The main features of the model are illustrated, showing that it possesses a non monotone hazard rate function. Its approximations with some of the most popular reliability models adopted in this field, such as the Weibull, Normal or Lognormal distribution is discussed, with some caveats regarding lifetime quantiles and hazard rate assessment. Then, Maximum Likelihood method for the statistical inference on the above model is discussed, with emphasis on interval estimation, which can be performed by means of a Beta distribution approximation of the unknown estimator distribution. The method gives satisfactory results, as shown in the last part of the paper.