N.S.  Temraz, M.A.  El-Damcese, 
    Analysis of Availability and Reliability for Repairable Parallel Systems with Different Failure Rates,
    Asian Journal of Information Technology,
    Volume 9,Issue 4,
    2010,
    Pages 231-237,
    ISSN 1682-3915,
    ajit.2010.231.237,
    (https://makhillpublications.co/view-article.php?doi=ajit.2010.231.237)
    Abstract: This study presents Markov models for analysis of availability and reliability for parallel repairable system subject to three types of failure rates (e.g., human, hardware and software) and common cause failure rate. The problem addressed is how applying a Continuous-Time Markov Chain (CTMC) to evaluate availability, reliability and Mean Time to System Failure (MTTFs) for parallel system with repair. In this study, assumed that the working time and the repair time of each component are both arbitrary distributed (e.g., Weibull, exponentially distributed). The Markov method is used to develop generalized expressions for system state probabilities, system availability, system reliability and system mean time to failure. A numerical example is presented in order to illustrate the performance of the model.
    Keywords: Markov models;arbitrary distribution for failure/repair rates;Repairable parallel system;availability;reliability;component