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Simulation Analysis of System Life when Component Lives are Determined by a Marked Point Process

Part of: Mathematical economics

Published online by Cambridge University Press:  19 February 2016

Sheldon M. Ross
Sheldon M. Ross*
Affiliation:
University of Southern California
*
∗ Postal address: Department of Industrial and Systems Engineering, University of Southern California, Los Angeles, CA 90089, USA. Email address: smross@usc.edu.
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Abstract

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We consider an r component system having an arbitrary binary monotone structure function. We suppose that shocks occur according to a point process and that, independent of what has already occurred, each new shock is one of r different types, with respective probabilities p1, …, pr. We further suppose that there are given integers n1, …, nr such that component i fails (and remains failed) when there have been a total of ni type-i shocks. Letting L be the time at which the system fails, we are interested in using simulation to estimate E[L], E[L2], and P(L > t). We show how to efficiently accomplish this when the point process is (i) a Poisson, (ii) a renewal, and (iii) a Hawkes process.

Keywords

Simulationmarked point processvariance reductionrenewal processconditional expectationHawkes processPoissonization

MSC classification

Primary: 91B70: Stochastic models 68U20: Simulation
Type
Research Article
Information
Journal of Applied Probability , Volume 51 , Issue 2 , June 2014 , pp. 377 - 386
Copyright
© Applied Probability Trust 

Footnotes

This material is based upon work supported by, or in part by, the US Army Research Laboratory and the US Army Research Office under contract/grant number W911NF-11-1-0115.

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