Percentile Life and Reliability As Performance Measures in Optimal System Design

Over the past several decades, optimal system reliability for a specified mission time has been thoroughly studied under diverse conditions of system structure, resource constraints, and options for reliability improvement. However, recent research has been directed towards maximizing the percentile life at a specified failure probability because reliability maximization problems are no longer applicable when there is no clear mission time. Thus far, only a few simple reliability-optimization problems have been reconsidered for the percentile life, leaving many variations as yet unsolved. The problem of maximizing the percentile life is very difficult, because it is impossible to analytically calculate the percentile life. We show that the optimal system design for maximizing the system reliability for a mission time is, in fact, the same as the one for maximizing the percentile life at some failure probability. This implies that repeated optimizations of the reliability by the selection of a mission time produces an optimal percentile life. The result is useful for settling many unsolved problems that involve maximizing the percentile life by using existing reliability-optimization algorithms.