Estimation of component reliability from superposed renewal processes with masked cause of failure by means of latent variables (1807.01269v2)

Abstract: In a system, there are identical replaceable components working for a given task and a failed component is replaced by a functioning one in the corresponding position, which characterizes a repairable system. Assuming that a replaced component lifetime has the same lifetime distribution as the old one, a single component position can be represented by a renewal process and the multiple components positions for a single system form a superposed renewal process. When the interest consists in estimating the component lifetime distribution, there are a considerable amount of works that deal with estimation methods for this kind of problem. However, the information about the exact position of the replaced component is not available, that is, a masked cause of failure. In this work, we propose two methods, a Bayesian and a maximum likelihood function approaches, for estimating the failure time distribution of components in a repairable system with a masked cause of failure. As our proposed estimators consider latent variables, they yield better performance results compared to commonly used estimators from the literature. The proposed models are generic and straightforward for any probability distribution. Aside from point estimates, interval estimates 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.