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In a system, there are identical replaceable components working for a giventask and a failed component is replaced by a functioning one in thecorresponding position, which characterizes a repairable system. Assuming thata replaced component lifetime has the same lifetime distribution as the oldone, a single component position can be represented by a renewal process andthe multiple components positions for a single system form a superposed renewalprocess. When the interest consists in estimating the component lifetimedistribution, there are a considerable amount of works that deal withestimation methods for this kind of problem. However, the information about theexact position of the replaced component is not available, that is, a maskedcause of failure. In this work, we propose two methods, a Bayesian and amaximum likelihood function approaches, for estimating the failure timedistribution of components in a repairable system with a masked cause offailure. As our proposed estimators consider latent variables, they yieldbetter performance results compared to commonly used estimators from theliterature. The proposed models are generic and straightforward for anyprobability distribution. Aside from point estimates, interval estimates arepresented for both approaches. Using several simulations, the performances ofthe proposed methods are illustrated and their efficiency and applicability areshown based on the so-called cylinder problem.

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