Estimation of component reliability from superposed renewal processes by means of latent variables

We present a new way to estimate the lifetime distribution of a reparable system consisted of similar (equal) components. We consider as a reparable system, a system where we can replace a failed component by a new one. Assuming that the lifetime distribution of all components (originals and replaced ones) are the same, the position of a single component can be represented as a renewal process. There is a considerable amount of works related to estimation methods for this kind of problem. However, the data has information only about the time of replacement. It was not recorded which component was replaced. That is, the replacement data are available in an aggregate form. Using both Bayesian and a maximum likelihood function approaches, we propose an estimation procedure for the lifetime distribution of components in a repairable system with aggregate data. Based on a latent variables method, our proposed method out-perform the commonly used estimators for this problem. The proposed procedure is generic and can be used with any lifetime probability model. Aside from point estimates, interval estimates are presented for both approaches. The performances of the proposed methods are illustrated through several simulated data, and their efficiency and applicability are shown based on the so-called cylinder problem. The computational implementation is available in the R package srplv.