Bayesian reliability estimation based on a Weibull stress-strength model for aged power system components subjected to voltage surges

Reliability assessment of aged electrical components in the presence of over-stresses (e.g. voltage surges) is not an easy task. In this paper, a new methodology for solving this problem is illustrated, which is based on a Bayesian approach applied to a novel Weibull stress-strength probabilistic model. This model holds, under proper simplifying hypotheses, for electrical components progressively degraded by service stresses during operating life, thus having a chance to be broken by overstresses sooner or later. Further assumptions lead to a log-logistic reliability function, thus obtaining a novel, physical, motivation for the sometimes observed characteristic of decreasing hazard rates. For the purpose of estimating the parameters of the above model, a Bayesian approach is developed taking into account that in practice, while data on stress are generally available, the same does not hold for strength data, due also to the high reliability level and innovative technology of many electrical components. The degree of uncertainty on the knowledge of stress distribution parameters may be described by means of adequate prior distributions. The proposed approach enables the analytical determination of prior and posterior distributions of reliability and related parameters, such as given percentiles of service life, and their Bayes point and interval estimates. The details of the procedure are extensively shown in the paper, thus proving its analytical feasibility and simplicity of implementation. For the sake of illustration, a numerical application relevant to distribution cable insulation subjected to switching voltage surges is presented. The efficiency of the proposed procedure in comparison with the well-known maximum-likelihood estimation procedure is also shown through extensive Monte Carlo simulations. Moreover, extensive analyses are carried out in order to assess the robustness of the proposed model; the results show that the estimates obtained by the proposed Bayesian procedure are excellent even when the true prior model is different from the one assumed.