Applying Bootstrap Methods to System Reliability

We present a fully enumerated bootstrap method to find the empirical system lifetime distribution for a coherent system modeled by a reliability block diagram. Given failure data for individual components of a coherent system, the bootstrap empirical system lifetime distribution derived here will be free of resampling error. We further derive distribution-free expressions for the bias associated with the bootstrap method for estimating the mean system lifetimes of parallel and series systems with statistically identical components. We show that bootstrapping underestimates the mean system lifetime for parallel systems and overestimates the mean system lifetime for series systems, although both bootstrap estimates are asymptotically unbiased. The expressions for the bias are evaluated for several popular parametric lifetime distributions. Supplementary materials for this article are available online.