k-out-of-n: G system with repair: the D-policy

Publication Type : Journal Article

Publisher : Int.Jl. of Computers and Operations Research, Pergamon Press

Source : Int.Jl. of Computers and Operations Research, Pergamon Press, Volume 28, Issue 10, p.973 - 981 (2001)

Keywords : k-out-of-n: G system, Markov processes, Reliability

Campus : Amritapuri

School : School of Arts and Sciences

Department : Mathematics

Verified : Yes

Year : 2001

Abstract : In this paper we consider a k-out-of-n: G system with repair under D-policy. According to this policy whenever the workload exceeds a threshold D a server is called for repair and starts repair one at a time. He is sent back as soon as all the failed units are repaired. The repaired units are assumed to be as good as new. The repair time and failure time distributions are assumed to be exponential. We obtain the system state distribution, system reliability, expected length of time the server is continuously available, expected number of times the system is down in a cycle and several other measures of performance. We compute the optimal D value which maximizes a suitably defined cost function.Scope and purposeThis paper considers a repair policy, called D-policy, of a k-out-of-n: G system. In a k-out-of-n: G system, the system functions as long as there are atleast k operational units. The server activation cost is high once it becomes idle due to all failed units repaired. Hence it is activated when the accumulated amount of work reaches D. This paper examines the optimal D-value by bringing in costs such as the cost of system being down, the server activation cost. Activating the server the moment the first failure takes place may involve very heavy fixed cost per cycle (a cycle is the duration from a point at which the server becomes idle to the next epoch at which it becomes idle after being activated). The other extreme of server activation only after n−k+1 units fail leads to the system being down for a long duration in each cycle. Hence the need for the optimal D-policy. A brief account of k-out-of-n: G system can be had in Ross (Ross, SM. Introduction to probability models, 6th ed., New York: Academic Press, 1997). The results obtained here find direct applications in reliability engineering, Production systems, Satellite communication, etc.

Cite this Research Publication : A. Krishnamoorthy and Dr. Usha Kumari P. V., “k-out-of-n: G system with repair: the D-policy”, Int.Jl. of Computers and Operations Research, vol. 28, no. 10, pp. 973 - 981, 2001.