Information management for estimating system reliability using imprecise probabilities and precise Bayesian updating

Engineering design decision-making often requires estimating system reliability based on component reliability data. Although this data may be scarce, designers frequently have the option to acquire more information by expending resources. Designers thus face the dual questions of deciding how to update their estimates and identifying the most useful way to collect additional information. This paper explores the management of information collection using two approaches: precise Bayesian updating and methods based on imprecise probabilities. Rather than dealing with abstract measures of total uncertainty, we explore the relationships between variance-based sensitivity analysis of the prior and estimates of the posterior mean and variance. By comparing different test plans for a simple parallel-series system with three components, we gain insight into the tradeoffs that occur in managing information collection. Our results show that to consider the range of possible test results is more useful than conducting a variance-based sensitivity analysis.