Analysis of a Complex System Modelled by a Marked Point Process and Assuming Vacations for a Repairman

Tiwari Nidhi () and Singh Suraj Bhan ()
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Tiwari Nidhi: Department of Mathematics, Statistics and Computer Science, G. B. Pant University of Agriculture and Technology, Pantnagar, India.
Singh Suraj Bhan: Department of Mathematics, Statistics and Computer Science, G. B. Pant University of Agriculture and Technology, Pantnagar, India.

Stochastics and Quality Control, 2010, vol. 25, issue 2, 221-242

Abstract: In this paper a system consisting of two subsystems A and B is analyzed. A has only one unit while B has two units, B1 and B2, connected in such a manner that B2 is in hot standby with B1. The system is modelled by a marked point process. There are two repairmen namely a supervisor and a novice. The supervisor is always present, while the novice might be in vacation. Two types of failure of the components of B are considered. The model is analyzed under “preemptive-repeat repair discipline”. By employing Laplace transformation and assuming the Gumbel–Hougaard copula, the state transition probabilities, reliability, availability and expected profit are obtained along with the steady state behaviour of the system. At the end some special cases of the system are investigated.

Keywords: Marked point process; Laplace transformation; preemptive-repeat repair discipline; Gumbel–Hougaard copula (search for similar items in EconPapers)
Date: 2010
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DOI: 10.1515/eqc.2010.016

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