Reliability estimation and confidence regions from subsystem and full system tests via maximum likelihood

Abstract

This paper develops a rigorous and practical method for estimating the reliability---with confidence regions---of a complex system based on a combination of full system and subsystem (and/or component or ot her) tests. It is assumed that the system is composed of multiple processes (e.g., the subsystems and/or components within subsystems), where the subsystems may be arranged in series, parallel (i.e., redundant), combination series/parallel, or other mode. Maximum likelihood estimation (MLE) is used to estimate the overall system reliability based on this fusion of multiple sources of information. Interestingly, for a given number of subsystems and/or components, the performance metric (likelihood function) does not change with the system configuration; rather, only the optimization constraints change, leading to an appropriate MLE. The MLE approach is well suited to providing asymptotic or finite-sample confidence bounds through the use of Fisher information or Monte Carlo sampling (bootstrap). The paper establishes formal conditions for the convergence of the MLE to the true system reliability.