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Stochastic Modeling of a System of Non-Identical Units with Conditional Failure of Repairman

Naveen Kumar, S. C Malik


A stochastic model for a system of two non-identical units is developed by considering the idea of repairman failure. Each unit has two modes: operative and complete failure. The units are non-identical in nature due to their different failure rates and so one is called the main unit and the other is duplicate unit. Initially, the main unit is operative and the duplicate unit is taken as spare in cold standby. The repairman is subjected to failure while repairing the main unit and so the failure is named as conditional failure. The failure time of the units and of the repairman follow negative exponential distribution whereas, the distributions of repair time of the units and treatment time of the repairman are taken as arbitrary with different probability density functions. The system is analyzed at different epochs by using semi-Markov process and regenerative point technique. The expressions for some significant reliability characteristics like mean time to system failure (MTSF), availability and finally for the profit function are derived in steady state. The graphical behavior of these measures has also been critically examined for arbitrary values of the parameters.

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K. Murari; V. Goyal; Comparison of two-unit cold standby reliability models with three types of repair facilities, Microelectronics Reliability, 24(1) 35-49 (1984).

J. Singh; A warm standby redundant system with common cause failures, Reliab. Engg. And Sys. Safety, 26(2) 135–141 (1989).

M. S. Kadyan; S. Chander; A. S. Grewal; Stochastic analysis of non-identical units reliability models with priority and different modes of failure. Decision and Mathematical Sciences, 9(1-3) 59 – 82 (2004).

S. C. Malik; Reliability Modeling of a Computer System with Preventive Maintenance and Priority Subject to Maximum Operation and Repair Times. International Journal of System Assurance Engineering and Management, 4(1) 94-100 (2013).

V.J.Munday;Permila; S.C.Malik; Reliability Modelling of a Computer System with Hardware Redundancy Subject to Preventive Maintenance. International Journal of Statistics and Reliability Engineering, 3(2) 176-189 (2016).

Upma; S.C.Malik; Cost Benefit Analysis of System of Non-identical units under Preventive Maintenance and Replacement. Journal of Reliability and Statistical Studies, 9(2) 17-27 (2016).


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