An extended optimal replacement model of systems subject to shocks

An extended optimal replacement model of systems subject to shocks

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Article ID: iaor20083622
Country: Netherlands
Volume: 175
Issue: 1
Start Page Number: 399
End Page Number: 412
Publication Date: Nov 2006
Journal: European Journal of Operational Research
Authors: , , ,
Keywords: optimization
Abstract:

A system is subject to shocks that arrive according to a non-homogeneous Poisson process. As shocks occur a system has two types of failures: type I failure (minor failure) is rectified by a minimal repair, whereas type II failure (catastrophic failure) is removed by replacement. The probability of a type II failure is permitted to depend on the number of shocks since the last replacement. This paper proposes a generalized replacement policy where a system is replaced at the nth type I failure or first type II failure or at age T, whichever occurs first. The cost of the minimal repair of the system at age t depends on the random part C(t) and deterministic part c(t). The expected cost rate is obtained. The optimal n* and optimal T* which would minimize the cost rate are derived and discussed. Various special cases are considered and detailed.

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