Genetic algorithm to maximize a lower-bound for system time-to-failure with uncertain component Weibull parameters

A genetic algorithm (GA) is used to solve the redundancy allocation problem when the objective is to maximize a lower percentile of the system time-to-failure distribution and the available components have random Weibull scale parameters. The GA searches the prospective solution space using an adaptive penalty to consider both feasible and infeasible solutions until converging to a feasible recommended system design. The objective function is intractable and a bi-section search is required as a function evaluator. Previously, this problem has most often been formulated to maximize system reliability instead of a lower-bound on system time-to-failure. Most system designers and users are risk-averse, and maximization of a lower percentile of the system time-to-failure distribution is a more conservative strategy (i.e. less risky) compared to maximization of the mean or median of the time-to-failure distribution. The only previous research to consider a lower percentile of system time-to-failure, also required that all component Weibull parameters are known. Those findings have been extended to address problems where the Weibull shape parameter is known, or can be accurately estimated, but the scale parameter is a random variable. Results from over 90 examples indicate that the preferred system design is sensitive to the user's perceived risk.