American Journal of Applied Mathematics and Statistics
ISSN (Print): 2328-7306 ISSN (Online): 2328-7292 Website: http://www.sciepub.com/journal/ajams Editor-in-chief: Mohamed Seddeek
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American Journal of Applied Mathematics and Statistics. 2015, 3(3), 105-110
DOI: 10.12691/ajams-3-3-4
Open AccessArticle

Semi-Markov Model of a Standby System with General Distribution of Arrival and Failure Times of Server

R.K. Bhardwaj1, and Ravinder Singh2

1Department of Statistics, Faculty of Physical Sciences, Punjabi University Patiala-147002 (Punjab), India

2Department of Statistics, Punjabi University Patiala-147002 (Punjab), India

Pub. Date: June 25, 2015

Cite this paper:
R.K. Bhardwaj and Ravinder Singh. Semi-Markov Model of a Standby System with General Distribution of Arrival and Failure Times of Server. American Journal of Applied Mathematics and Statistics. 2015; 3(3):105-110. doi: 10.12691/ajams-3-3-4

Abstract

The aim of this paper is to develop a stochastic model of a cold standby system consisting of two identical units and a service facility, called server. This paper considers the failure of server during operation. The semi-Markov approach is explored to develop the probabilistic model and regenerative point technique is used to derive expressions for system’s performance measures such as mean time to system failure, availability, profit etc. In the model the server takes some time to arrive at the system. The server, while on job, may fail. Upon failure it goes for treatment and rejoins thereafter. Both the arrival and failure times follow general distribution with different probability distribution functions. The numerical illustration, for a particular case, points out that both the server arrival and failure times significantly affect the system performance.

Keywords:
semi-markov model standby system server arrival time server failure

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