Bound-Constrained Expectation Maximization for Weibull Competing-Risks Device Reliability

Estimating the reliability of electronic devices involves identification of failure mechanisms and prediction of lifetimes. For parameter estimation and failure mode identification in Weibull competing-risks models, a differential-evolution-based global optimization approach has recently been developed, with the superiority of that approach demonstrated over the best-known local methods for the problem. In an effort to design a method faster than differential evolution for this problem, the present paper develops a new type of expectation maximization (EM) algorithm that is capable of handling bound constraints while optimizing the parameters of the Weibull component distributions. The differential-evolution-based approach guarantees a feasible, but not necessarily high-quality, solution in every run, while the proposed method offers no such guarantee. Despite this lack of guarantee, the proposed method is seen to produce results of a quality highly competitive with differential evolution. Numerical results on ten test cases, based on three real test datasets and two synthetic datasets, show that in terms of solution quality, the proposed method is competitive with differential evolution, while offering an average savings of about 64% in the computation time. Comparative performance analyses with the standard EM algorithm and the best-known local method L-BFGS-B are also provided. The numerical results are statistically validated. A new approach to model improvement via selective failure analysis is demonstrated as an application of the proposed algorithm. The proposed algorithm has the potential to be used for general-purpose likelihood maximization involving latent variables in diverse domains.