Analysis of Redundant System with Facility for Repair/Replacement of Substandard Unit
Savita
Savita, Department of Mathematics, Hindu College, Sonipat (Haryana), India.
Manuscript received on 09 May 2026 | First Revised Manuscript received on 25 June 2026 | Second Revised Manuscript received on 23 September 2026 | Manuscript Accepted on 15 October 2026 | Manuscript published on 30 October 2026 | PP: 43-46 | Volume-6 Issue-2, October 2026 | Retrieval Number: 100.1/ijam.B122005021025 | DOI: 10.54105/ijam.B1220.05021025
Open Access | Editorial and Publishing Policies | Cite | Zenodo | OJS | Indexing and Abstracting
© The Authors. Published by Lattice Science Publication (LSP). This is an open-access article under the CC-BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/)
Abstract: This paper analyses a system with two non-identical units, one of higher quality than the other. The inferior-quality unit can be repaired or replaced with a similar one. These systems occur in the electronics industry, hospitals, and other settings. A general time distribution is used for repair times. A technician for repair/replacement is consistently available with the system. This analysis evaluates the system’s reliability through various measures. Practical examples include assessing system performance, analysing its effectiveness, and understanding its behaviour under different circumstances. Reliability measures are calculated to evaluate the system’s performance. An exponential time distribution is used for failure; for other time distributions, reliability measures that assess system effectiveness are obtained. The average time the system operates before experiencing a failure, the time the system is operational and available for use, how often the repairman needs to visit the system for maintenance actions, the period when the repairman is busy due to maintenance tasks, and the profit generated by the system are calculated using mathematical techniques that model the system’s behaviour, using the Semi-Markov procedure and the method of regenerative points. MATLAB is used for numerical and graphical analysis. By combining mathematical models, statistical distributions, and computational tools like MATLAB, this analysis provides insights into the system’s behaviour and effectiveness.
Keywords: Mean Failure Time, Uptime, Busy Period, Substandard, Regenerative Point Method.
Scope of the Article: Statistics and Probability Theory