Electrical insulation components reliability assessment and practical Bayesian estimation under a Log-Logistic model

This paper deals with the “physical reliability models” assessment and estimation for electrical insulation components. It is well known that the reliability model identification and estimation of most of the modern power system components, such as insulation components, may be better achieved, instead that using limited lifetime data, by the knowledge of the degradation mechanisms. Such mechanisms, which are responsible for component aging and failure, are indeed well established in the field of electrical insulation: this is also the case of the so called “Stress-Strength” models. In particular, the “Log-logistic” model, deduced by a suitable Weibull stress-strength probabilistic model, has found valid applications to the reliability assessment of the insulation components. In the framework of the estimation of such reliability model, a new Bayesian approach, based upon the “Odds Ratio” of the Log-logistic model is developed in this paper, based upon the properties that such information, being proportional to the reliability function, is available to the engineer on the basis of past data; moreover, being proportional to the Weibull scale parameter, allows to exploit known features of its conjugate prior Inverse Gamma distribution. Numerical examples and the results of extensive Monte Carlo simulations demonstrate the feasibility and efficiency of the proposed procedure.