Bayes Availability Estimation of the “k-out-of-n” Partially Redundant System by Lognormal Prior Distributions

The “k-out-of-n” partially redundant reliability architecture is a flexible and economic configuration for many engineering systems, such as motor drive applications, in various industrial, aerospace and naval systems. The present study is aimed to develop a Bayesian statistical inference approach for the steady state availability estimation of such systems. The proposed approach is based upon Lognormal prior distributions for both hazard and repair rates. The Lognormal model appears indeed not only very flexible, but also particularly tailored for electronic devices, as motivated in the paper. A set of numerical applications with typical parameter values is illustrated in the study, showing - by means of a large sets of Monte Carlo simulations - that the proposed Bayesian statistical inference approach is very efficient, accurate and robust for the above availability estimation, particularly in the case of data scarcity, which is a key feature of such high reliability devices in view of parameter estimation. Beyond point estimation, the study also develops an efficient method to obtain the interval estimation of system availability by means of a suitable Beta distribution approximation. Also a robustness analysis of the above Lognormal model has been successfully developed.