Value of Information for Comparing Dependent Repairable Assemblies and Systems

This article presents an approach for comparing alternative repairable systems and calculating the value of information obtained by testing a specified number of such systems. More specifically, an approach is presented to determine the value of information that comes from field testing a specified number of systems in order to appropriately estimate the reliability metric associated with each of the respective repairable systems. Here the reliability of a repairable system will be measured by its failure rate. In support of the decision-making effort, the failure rate is translated into an expected utility based on a utility curve that represents the risk tolerance of the decision-maker. The algorithm calculates the change of the expected value of the decision with the sample size. The change in the value of the decision represents the value of information obtained from testing. The approach uses a Bayesian probability model, which allows the decision-maker to incorporate subjective priors on the reliability performance of the design alternatives. The dependency is modeled using copulas to couple the marginal prior distributions of the alternatives to a single, joint prior. The procedure being presented in this article uses Markov chain Monte Carlo (MCMC) simulation to determine the posterior probability density and the resulting expected utility of the decision. The approach considers design alternatives based on failure rate metric, for example, the number of failures per unit (FPU) or the number of failures per unit time λ, and utilizes Archimedean copulas to couple the dependent marginals that describe the priors for each design alternative’s failure per unit behavior. This article is an extension of the paper “Assessing the Value of Information for Multiple, Correlated Design Alternatives” [6], which presented an approach for determining optimal sample sizes for assessing correlated non-repairable design alternatives based on the prior estimate of their joint failure probability.