2017/07/11 by Agatha Sacramento Rodrigues, Rodrigues, Agatha Sacramento, Carlos Alberto de Bragança Pereira +3
Decision Sciences · Mathematics · #Advanced Statistical Methods and Models #FOS: Computer and information sciences #Methodology (stat.ME) #Probabilistic and Robust Engineering Design #Statistical Distribution Estimation and Applications #Statistical Methods and Bayesian Inference
paper · pdf · doi:10.48550/arxiv.1707.03173
openalex publication_date 2017/07/11 · openalex created_date 2022/10/03 · openalex updated_date 2026/07/28
The reliability of a system of components depends on reliability of each\ncomponent. Thus, the initial statistical work should be the estimation of the\nreliability of each component of the system. This is not an easy task because\nwhen the system fails, the failure time of a given component can not be\nobserved, that is, censored data. Rodrigues et al. (2017) presented a solution\nfor reliability estimation of components when it is avaliable the system\nfailure time and the status of each component at the time of system failure (if\nit had failed before, after or it is responsible for system failure). However,\nthere are situations it may be difficult to identify the status of components\nat the moment of system failure.\n Such cases are systems with masked causes of failure. Since parallel and\nseries systems are the simplest systems, innumerous alternative solutions for\nthese two systems have been appeared in the literature. To the best of our\nknowledge, this seems to be the first work that considers the general case of\ncoherent systems. The three-parameter Weibull distribution is considered as the\ncomponent failure time model. Identically distributed failure times is not\nrequired restrictions. Furthermore, there is no restriction on the subjective\nchoice of prior distributions but preference has been given to continuous prior\ndistributions; these priors represent well the nuances of the environment that\nthe system operates. The statistical work of obtaining quantities of the\nposterior distribution is supported by the Metropolis within Gibbs algorithm.\nWith several simulations, the excellent performance of the model was evaluated.\nWe also consider a computer hard-drives real dataset in order to present the\npractical relevance of the proposed model.\n