African Journal of
Mathematics and Computer Science Research

  • Abbreviation: Afr. J. Math. Comput. Sci. Res.
  • Language: English
  • ISSN: 2006-9731
  • DOI: 10.5897/AJMCSR
  • Start Year: 2008
  • Published Articles: 254

Full Length Research Paper

Probabilistic analysis of two warm standby system with instructions at need

G. S. Mokaddis
  • G. S. Mokaddis
  • Department of Mathematics, Faculty of Science, Ain Shams University, Cairo, Egypt
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Y. M. Ayed
  • Y. M. Ayed
  • Department of Mathematics, Faculty of Science, Suez University, Suez, Egypt
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H. S. AL-Hajeri
  • H. S. AL-Hajeri
  • College of Business Administration, Kuwait University, Kuwait
  • Google Scholar

  •  Accepted: 20 February 2013
  •  Published: 28 February 2013




This paper is concerned with two unit warm standby systems having one expert repairman and one assistant repairman. The assistant is called only if the expert repairman is busy. The assistant repairman who may repair the failed unit after getting instructions by his master; but sometimes the assistant repairman may repair it without having the need of instructions for doing repair with probability p and q, respectively. Techniques of the semi-Markov processes and regenerative processes are used to obtain various measures of system effectiveness mean time to system failure (MTSF), availability analysis, busy period of an expert repairman, busy period of an assistant repairman and profit incurred.


Key words: Mean time to system failure (MTSF), availability, warm standby.