A Bayesian Note on Reliability Growth During a Development Testing Program

Abstract

The problem of estimating the reliability of a system which is undergoing development testing is considered from a Bayesian standpoint. Formally, m sets of binomial trials are performed under conditions which lead to an ordering, θ <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sub> < θ <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2m</sub> , of the binomial parameters. The parameter of interest is θ <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">m</sub> , the final underlying reliability of the system. The marginal posterior pdf for θ <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">m</sub> is easily obtained when uniform prior pdf's are assumed. The method is illustrated.