Reliability modeling of a computer system with preventive maintenance and priority subject to maximum operation and repair times

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 pre-specific 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.