Discrete Time Semi-Markov Model of a Two Non-Identical Unit Cold Standby System with Preventive Maintenance with Three Modes
American Journal of Theoretical and Applied Statistics
Volume 4, Issue 4, July 2015, Pages: 277-290
Received: May 28, 2015; Accepted: Jun. 10, 2015; Published: Jun. 30, 2015
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Authors
Medhat Ahmed El-Damcese, Mathematics Department, Faculty of Science, Tanta University, Tanta, Egypt
Naglaa Hassan El-Sodany, National Accounts Department, Central Agency for Public Mobilization and Statistics, Cairo, Egypt
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Abstract
This paper presents the reliability and availability measures of a two non-identical unit cold standby redundant system (unit-1 is operating, and unit-2 is cold standby) using semi-Markov process under discrete parametric Markov-Chain i.e. failure and repair times of a unit and time to PM and PM time are taken as discrete random variables assuming three different modes (normal (N) mode, partial failure (P) mode and total failure (F) mode) of each unit. The unit-1 is sent for preventive maintenance (PM) after its working for a random period of time assuming that the failure and repair times of a unit and time to PM and PM time are taken as discrete random variables having geometric distributions with different parameters. A single repairman is available with the system for PM of unit-1 and repair of both units. The system is considered in up-state if only one or two units are operative or in partial failure (P) mode. After some basic definitions and notations, we obtain various measures of system effectiveness; reliability, availability, mean time to failure, busy period of repairman due to PM of unit-1, busy period of repairman due to repair of unit-1 and unit-2 from total failure, and the expected profit function using regenerative point technique. The mathematical problem thus developed has next been solved numerically and graphically represented by the aid of Maple program.
Keywords
Semi-Markov, Discrete-Time, Cold Standby, Reliability, Mean Sojourn Time, Regenerative Point Technique
To cite this article
Medhat Ahmed El-Damcese, Naglaa Hassan El-Sodany, Discrete Time Semi-Markov Model of a Two Non-Identical Unit Cold Standby System with Preventive Maintenance with Three Modes, American Journal of Theoretical and Applied Statistics. Vol. 4, No. 4, 2015, pp. 277-290. doi: 10.11648/j.ajtas.20150404.18
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