  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.
