A Bayesian Approach to Reliability-Based Optimization With Incomplete Information

In engineering design, information regarding the uncertain variables or parameters is usually in the form of finite samples. Existing methods in optimal design under uncertainty cannot handle this form of incomplete information; they have to either discard some valuable information or postulate existence of additional information. In this article, we present a reliability-based optimization method that is applicable when information of the uncertain variables or parameters is in the form of both finite samples and probability distributions. The method adopts a Bayesian Binomial inference technique to estimate reliability, and uses this estimate to maximize the confidence that the design will meet or exceed a target reliability. The method produces a set of Pareto trade-off designs instead of a single design, reflecting the levels of confidence about a design’s reliability given certain incomplete information. As a demonstration, we apply the method to design an optimal piston-ring/cylinder-liner assembly under surface roughness uncertainty.