Reliability and Availability Analysis of a Four-component Repairable System with Different Failure and Repair Rates using Markov Modeling

Author(s)	Dr. M. Gayathri
Country	India
Abstract	Markov modelling provides an effective mathematical framework for analysing the reliability and availability of repairable systems in which component failures and repairs occur randomly over time. In the present study, a four-component repairable system with different failure rates and repair rates is considered. The system is represented by a continuous-time Markov chain (CTMC) consisting of sixteen possible states corresponding to the different combinations of good and failed states of the four components. The transition rate matrix is formulated by assigning distinct failure rates and repair rates , i=1,2,3,4, to the four components. The Kolmogorov forward equations are obtained from the transition matrix and are used to determine the state probabilities. Numerical computations are carried out for different combinations of failure and repair rates. The results demonstrate the influence of component failure nd repair rates on the performance of the repairable system. The proposed model can be useful for reliability assessment and maintenance planning of systems consisting of multiple repairable components
Keywords	Markov model, repairable system, reliability, availability, failure rate, repair rate, MTBF, four-component system, Kolmogorov forward equations.
Field	Mathematics
Published In	Volume 7, Issue 3, May-June 2025
Published On	2025-05-05
DOI	https://doi.org/10.36948/ijfmr.2025.v07i03.87258

About IJFMR Fees & Payment Current Issue Publication Archive	Submit Research Paper Track Submission Status Publication Guidelines Publication Ethics Peer Review & Plagiarism	Join as a Reviewer Editors & Reviewers Reviewer Referral Program Get Reviewer Membership Certi.	Website/Journal Policies Usage Policy Content Policies Privacy Policy

Contact Us		+91-9687-828-838	editor@ijfmr.com

International Journal For Multidisciplinary Research