Framework for estimating system reliability from full system and subsystem tests with dependence on dynamic inputs

This paper develops a framework for estimating the reliability-with confidence regions-of a complex system based on a combination of full system and subsystem (and/or component or other) tests where some of the subsystems are dependent on dynamic inputs (independent predictor variables). 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. The method of maximum likelihood estimation (MLE) is used to estimate subsystem and full system reliability. The MLE approach is well suited to providing asymptotic confidence bound through the Fisher information. As such, the Fisher information is derived for the general maximum likelihood estimator presented in the paper. A simple numerical study illustrates that the MLE recovers the reliability parameters of a system (plus some statistical uncertainty) when applied to a set of dynamic inputs and full system/subsystem output test data.