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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.

Design optimization occurs through a series of decisions that are a standard part of the product development process. Decisions are made anywhere from concept selection to the design of the assembly and manufacturing processes. The effectiveness of these decisions is based on the information available to the decision maker. Decision analysis provides a structured approach for quantifying the value of information that may be provided to the decision maker. This paper presents a process for determining the value of information that can be gained by evaluating linearly correlated design alternatives. A unique approach to the application of Bayesian Inference is used to provide simulated estimates in the expected utility with increasing observations sizes. The results provide insight into the optimum observation size that maximizes the expected utility when assessing correlated decision alternatives.

Importance Sampling is a popular method for reliability assessment. Although it is significantly more efficient than standard Monte Carlo simulation if a suitable sampling distribution is used, in many design problems it is too expensive. The authors have previously proposed a method to manage the computational cost in standard Monte Carlo simulation that views design as a choice among alternatives with uncertain reliabilities. Information from simulation has value only if it helps the designer make a better choice among the alternatives. This paper extends their method to Importance Sampling. First, the designer estimates the prior probability density functions of the reliabilities of the alternative designs and calculates the expected utility of the choice of the best design. Subsequently, the designer estimates the likelihood function of the probability of failure by performing an initial simulation with Importance Sampling.

A complete probabilistic model of uncertainty in probabilistic analysis and design problems is the joint probability distribution of the random variables. Often, it is impractical to estimate this joint probability distribution because the mechanism of the dependence of the variables is not completely understood. This paper proposes modeling dependence by using copulas and demonstrates their representational power. It also compares this representation with a Monte-Carlo simulation using dispersive sampling.