AD806B6Cd01 - 146 Chiodo and Mazzanti: Bayesian Reliability...

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Chiodo and Mazzanti: Bayesian Reliability Estimation Based on a Weibull Stress-Strength Model 146 Bayesian Reliability Estimation Based on a Weibull Stress-Strength Model for Aged Power System Components Subjected to Voltage Surges E. Chiodo Department of Electrical Engineering University of Napoli via Claudio 21, 80125 Napoli, Italy and G. Mazzanti Department of Electrical Engineering University of Bologna, viale Risorgimento 2 40136 Bologna, Italy ABSTRACT 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 ap - plied to a novel Weibull stress-strength probabilistic model. This model holds, un - der proper simplifying hypotheses, for electrical components progressively de - graded 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 reliabil - ity function, thus obtaining a novel, physical, motivation for the sometimes ob - served characteristic of decreasing hazard rates. For the purpose of estimating the parameters of the above model, a Bayesian approach is developed taking into ac - count 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 knowl - edge 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 per - centiles 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. Index Terms — Reliability, stress-strength models, Bayesian statistics, Gamma, generalized Gamma, log-logistic distribution, Weibull distribution, power system components, electrical insulation.
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This note was uploaded on 06/08/2011 for the course ELECTRICAL 124 taught by Professor Ghjk during the Spring '11 term at Institute of Technology.

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AD806B6Cd01 - 146 Chiodo and Mazzanti: Bayesian Reliability...

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