A Bayes Analysis of Availability for a System Consisting of Several Independent Subsystems

A Bayes analysis of system availability A is carried out on the basis of snapshot data obtained on each of the N component subsystems. Application of Bayes formula, using a natural conjugate prior probability density function (pdf), yields the posterior pdf of subsystem availability. Determination of the posterior pdf of system availability requires the derivation of the pdf of the product of N independent random variables, which is accomplished through the use of the Mellin integral transform. From the knowledge of the posterior pdf of A, confidence limits on system availability can be obtained.