Markovian analysis of unreliable multi-components redundant fault tolerant system with working vacation and F-policy

This investigation presents admission control policy for the fault tolerant system comprising of multi-components operating machines and multiple types of warm standbys under the maintenance of single unreliable server. The concepts of F-policy which deals with the controlling of inflow of failed machines and imperfect coverage are incorporated to make Markov model formulation more realistic. The unreliable repairman takes some time before allowing the failed machines to wait in the system for the repair job. The successive over relaxation (SOR) method is used to obtain the system state probabilities at the steady state which are further used to evaluate other system indices including the mean queue length of failed machines, mean number of standby machines, throughput, etc. By constructing the cost function in terms of various performance indices and associated cost elements, the optimal repair rate is determined so that the maintenance of the concerned failure prone FTS can be done in an economic manner. The hybrid soft computing approach based on a neuro-fuzzy inference system is implemented to compare the results obtained by SOR method and neuro-fuzzy approach. *Corresponding author: Rakesh Kumar Meena, Department of Mathematics, IIT Roorkee, Roorkee 247667, India E-mails: [email protected], [email protected] Reviewing editor: Benchawan Wiwatanapataphee, Curtin University, Australia Additional information is available at the end of the article ABOUT THE AUTHORS Madhu Jain is faculty in the Department of Mathematics, IIT Roorkee, Roorkee, India. She is a recipient of two gold medals of Agra University at MPhil level. There are more than 400 research publications in refereed international/ national journals and more than 20 books to her credit. Thirty-five candidates have received their PhD under her supervision. Her current research interest includes the performance modeling, stochastic modeling, soft computing, bio-informatics, reliability engineering, and queueing theory. She has visited several reputed universities/institutes in the USA, Canada, UAE, Australia, UK, Germany, France, Holland, Belgium, the Netherlands, and Taiwan. Rakesh Kumar Meena is a research scholar at the Department of Mathematics, Indian Institute of Technology Roorkee, Uttarakhand, India. He received his MSc degree in Applied Mathematics from Indian Institute of Technology Roorkee. His area of research interest includes queueing theory, reliability, stochastic modeling, performance analysis of fault tolerant systems, and soft computing. PUBLIC INTEREST STATEMENT Due to unavoidable failures of the machining parts not only the functioning of the organization/ system is stopped but also result in the reputation loss and degradation in the quality of products. To ensure the pre-specified system efficiency and to achieve the production goal, the system designers have to pay much attention toward the fault tolerance strategies by designing the appropriate maintenance and redundancy policies. The features of recovery and reboot should be taken into account for the smooth functioning of the real-time machining systems in particular when there is requirement of high reliability. The indices established in this study to characterize the performance of the system can be helpful in the up gradation of the existing and for the future design of the new machining systems. Received: 10 September 2016 Accepted: 12 March 2017 First Published: 18 March 2017 Page 1 of 17 © 2017 The Author(s). This open access article is distributed under a Creative Commons Attribution (CC-BY) 4.0 license. Rakesh Kumar Meena