Convergence analysis for maximum likelihood-based reliability estimation from subsystem and full system tests

A recent paper (Spall, 2009) introduced a method for estimating the reliability of a complex system based on a combination of full system and subsystem (and/or component or other) tests. It is assumed that the system is composed of multiple 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. The MLE approach is well suited to providing asymptotic or finite-sample confidence bounds through the use of Fisher information or bootstrap Monte Carlo-based sampling. This paper provides essential convergence theory for the method of Spall (2009).