Optimum Replacement of a System Subject to Shocks: A Mathematical Lemma

Prem S. Puri and Harshinder Singh
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Prem S. Puri: Purdue University, West Lafayette, Indiana
Harshinder Singh: Panjab University, Chandigarh, India

Operations Research, 1986, vol. 34, issue 5, 782-789

Abstract: We consider a system that is subject to shocks that occur randomly over time. We assume that the system must be replaced after it has functioned for a random length of time τ, a moment of a major failure that is a stopping time with respect to the process { N ( t ), t ≥ 0} that models the number of shocks occurring in [0, t ]. It may, however, be economical to replace the system at time min( t , τ) prior to its failure, for some fixed but optimally chosen t . Costs are due to shocks, maintenance and replacement. We introduce an optimality criterion, based on cost considerations, which we use to find an optimal replacement time t 0 . In the process, we prove a general mathematical lemma that helps in arriving at the optimal replacement time for general classes of processes { N ( t )}, stopping times τ and the cost structures involved. We also give a discrete time version of the lemma.

Keywords: 570 stopping times; 723 point processes; 730 maintenance/replacement costs (search for similar items in EconPapers)
Date: 1986
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