Reliability modeling of a computer system with preventive maintenance and priority subject to maximum operation and repa
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ORIGINAL ARTICLE
Reliability modeling of a computer system with preventive maintenance and priority subject to maximum operation and repair times S. C. Malik
Received: 23 August 2012 / Revised: 1 January 2013 / Published online: 12 February 2013 © The Society for Reliability Engineering, Quality and Operations Management (SREQOM), India and The Division of Operation and Maintenance, Lulea University of Technology, Sweden 2013
Abstract The main focus of this paper is on the reliability modelling of a computer system considering the concepts of redundancy, preventive maintenance and priority in repair activities. Two identical units of a computer system are taken—one unit is initially operative and the other is kept as spare in cold standby. In each unit h/w and s/w work together and may fail independently from normal mode. There is a single server who visits the system immediately as and when needed. Server conducts preventive maintenance of the unit (computer system) after a maximum operation time. Repair of the h/w is done at its failure while s/w is upgraded from time to time as per requirements. If server unable to repair the h/w in a prespecific time (called maximum repair time), h/w is replaced by new one giving some replacement time. Priority to h/w repair is given over s/w up gradation if, in one unit s/w is under up-gradation and h/w fails in another operative unit. The failure time of h/w and s/w follows negative exponential distributions while the distributions of preventive maintenance, h/w repair/replacement and s/w up-gradation times are taken as arbitrary with different probability density functions. The expressions for several reliability and economic measures are derived in steady state using semi-Markov process and regenerative point technique. The graphical study of mean time to system failure (MTSF) and profit function has also been made giving particular values to various parameters and costs.
S. C. Malik (&) Department of Statistics, M.D. University, Rohtak, 124001 Haryana, India e-mail: [email protected]
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Keywords Computer system · Cold standby · Preventive maintenance · Maximum operation and repair times · H/w repair and replacement · S/w up-gradation · Reliability measures · Profit function Mathematics Subject Classification (2000) 60K10
90B25 ·
List of symbols E The set of regenerative states NO The unit is operative and in normal mode Cs The unit is cold standby a/b Probability that the system has hardware/ software failure k1 =k2 Constant hardware/software failure rate α0 Maximum operation time β0 Maximum repair time Pm/PM The unit is under preventive maintenance/ under preventive maintenance continuously from previous state WPm/ The unit is waiting for preventive maintenance/ WPM waiting for preventive maintenance from previous state HFur/ The unit is failed due to hardware and is HFUR under repair/under repair continuously from previous state HFurp/ The unit is failed due to hardware and is under HFURP replacement/under replacement continuously from previous state HFwr/ T
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