Estimation of component reliability in repairable series systems with masked cause of failure by means of latent variables

In this work, we propose two methods, a Bayesian and a maximum likelihood model, for estimating the failure time distribution of components in a repairable series system with a masked (i.e., unknown) cause of failure. As our proposed estimators also consider latent variables, they yield better performance results compared to commonly used estimators from the literature. The failure time model considered here is the Weibull distribution but the proposed models are generic and straightforward for any probability distribution. Besides point estimation, interval estimations are presented for both approaches. Using several simulations, the performances of the proposed methods are illustrated and their efficiency and applicability are shown based on the so-called cylinder problem.