Reliability of components of coherent systems: estimates in presence of masked data

Abstract: The reliability of a system of components depends on reliability of each component. Thus, the initial statistical work should be the estimation of the reliability of each component of the system. This is not an easy task because when the system fails, the failure time of a given component can not be observed, that is, censored data. Rodrigues et al. (2017) presented a solution for reliability estimation of components when it is avaliable the system failure time and the status of each component at the time of system failure (if it had failed before, after or it is responsible for system failure). However, there are situations it may be difficult to identify the status of components at the moment of system failure. Such cases are systems with masked causes of failure. Since parallel and series systems are the simplest systems, innumerous alternative solutions for these two systems have been appeared in the literature. To the best of our knowledge, this seems to be the first work that considers the general case of coherent systems. The three-parameter Weibull distribution is considered as the component failure time model. Identically distributed failure times is not required restrictions. Furthermore, there is no restriction on the subjective choice of prior distributions but preference has been given to continuous prior distributions; these priors represent well the nuances of the environment that the system operates. The statistical work of obtaining quantities of the posterior distribution is supported by the Metropolis within Gibbs algorithm. With several simulations, the excellent performance of the model was evaluated. We also consider a computer hard-drives real dataset in order to present the practical relevance of the proposed model.