Model Robustness Analysis of a Bayes Stress-Strength Reliability Estimation with Limited Data

The “stress-strength” reliability model is discussed in the paper as a very efficient method for reliability assessment. Emphasis is given to its robustness, in view of unavoidable model uncertainty. Such uncertainty on reliability models is a key feature of modern components, characterized by a high degree of technological innovations and/or reliability, and so by a limited amount of field data. This occurs for many power system applications, as those related to insulation components, which are the key object of the studies of the paper. In particular, here a Bayesian inference method for the estimation of the above model is illustrated, when Normal or Lognormal models hold for stress and strength. The performance of these estimators are empirically analysed through extensive numerical simulations under a wide range of parameter values. All the results show not only the efficiency of Bayes estimation but also its being strongly "robust". Indeed, many simulations were performed in order to develop a robustness analysis with respect to departures from basic model distributions (e.g. assuming Weibull distributions instead of Lognormal ones for stress and strength). Efficiency and robustness are excellent for very small sample sizes, a very desirable property in view of the above applications.