How Errors in Component Reliability Affect System Reliability

This paper studies how sampling variation in component reliability estimates affects the computation of system reliability that uses these estimates as input. If these components are in parallel they lead to an understatement of system reliability as the number of components k increases. In series, they lead to an overstatement as k increases. For a sample component reliability based on n observations, our results show that lim_{k → ∞} (k²/n) = 0 is required for the sample system reliability to converge in probability to the true system reliability.