Arya Bhatta Journal of Mathematics and Informatics
  • Year: 2026
  • Volume: 18
  • Issue: 1

Reliability Analysis on Degradation Models Having Various Types of Faults Using Regenerative Point Graphical Technique

1Research Scholar, Dept. of Mathematics, BMU (Baba Mastnath University)Asthal Bohar, Rohtak (Haryana)

2Professor, Dept. of Mathematics, BMU (Baba Mastnath University)Asthal Bohar, Rohtak (Haryana)

3Assistant Professor, Dept. of Mathematics, Ch. Bansi Lal G.C.W. Tosham, Bhiwani (Haryana)

*Email Id: p.rawaldhia@gmail.com

**ashutosh8200@rediffmail.com

***rjkmr661@gmail.com

Abstract

This work uses the Regenerative Point Graphical Technique (RPGT) to analyze the behavior of a two-unit system with preventative maintenance, degeneration in one unit following complete failure, and flawless repair in the other unit. At first, both units OF and OA are operating at maximum capacity. Unit OF may have two different kinds of failures: direct failures and partial failures, whereas unit OA may experience direct failures. The units are inspected and repaired as needed by a single server (repairman). Unit OF cannot be returned to its initial capacity in the event of a total failure, but the server fixes the unit in the event of a partial failure (before to complete failure) i.e, it is in a condition of degradation. A fuzzy notion is utilized to identify a unit’s operating status or failure. Unit OF gets swapped out with a new one if the server reports that it cannot be repaired. OF transition diagram of the system is created to identify primary circuits, secondary circuits, tertiary circuits, and base state using exponential failure rates, general repair rates, and different probabilities. RPGT is used to formulate and solve the problem. Failure and repair are statistically unrelated. To examine how the system behaves in a steady state, expressions for system metrics such as the mean time to system failure, availability, number of server visits, and server busy period are assessed. The impact of failure and repair rates on the average time to system failure, availability, anticipated number of server visits, and server busy period is examined using specific scenarios. Additionally, profit optimization is covered. Tables are used to explain system behavior.

Keywords

RPGT (Regenerative point technique), Markov-process, expected uptime, meantime t0 system failure and degradation