Maximum likelihood analysis of component reliability using masked system life-test data

Life data from multicomponent systems are often analyzed to estimate the reliability of each system component. Due to the cost and diagnostic constraints, however, the exact cause of system failure might be unknown. Referring to such situations as being masked, the authors use a likelihood approach to exploit all the available information. They focus on a series system of three components, each with a constant failure rate, and propose a single numerical procedure for obtaining maximum-likelihood estimations (MLEs) in the general case. It is shown that, under certain assumptions, closed-form solutions for the MLEs can be obtained. The authors consider that the cause of system failure can be isolated to some subset of components, which allows them to consider the full range of possible information on the cause of system failure. The likelihood, while presented for complete data, can be extended to censoring. The general likelihood expressions can be used with various component life distributions, e.g., Weibull, lognormal. However, closed-form MLEs would most certainly be intractable and numerical methods would be required