Asymptotics of the total down time for an alternating renewal process

Wiesław Dziubdziela

Mathematica Applicanda (1983)

  • Volume: 11, Issue: 23
  • ISSN: 1730-2668

Abstract

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We investigate the asymptotic behavior of total down time of a system in which the breakdown process is an alternating renewal process, under the assumption that the probability of breakdown in a single cycle converges to zero. Using a theorem of R. Serfozo [J. Appl. Probab. 17 (1980), no. 2, 423–431; MR0568952], we find necessary and sufficient conditions for the convergence of the total down time to a compound Poisson process. We use these results in analyzing three examples: pairs of elements subject to detectable and undetectable breakdown (the Murphy and Phillips models), pairs of elements with a cold reserve served by one server; and an element with a temporal reserve.

How to cite

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Wiesław Dziubdziela. "Asymptotics of the total down time for an alternating renewal process." Mathematica Applicanda 11.23 (1983): null. <http://eudml.org/doc/293269>.

@article{WiesławDziubdziela1983,
abstract = {We investigate the asymptotic behavior of total down time of a system in which the breakdown process is an alternating renewal process, under the assumption that the probability of breakdown in a single cycle converges to zero. Using a theorem of R. Serfozo [J. Appl. Probab. 17 (1980), no. 2, 423–431; MR0568952], we find necessary and sufficient conditions for the convergence of the total down time to a compound Poisson process. We use these results in analyzing three examples: pairs of elements subject to detectable and undetectable breakdown (the Murphy and Phillips models), pairs of elements with a cold reserve served by one server; and an element with a temporal reserve.},
author = {Wiesław Dziubdziela},
journal = {Mathematica Applicanda},
keywords = {Applications; Reliability, availability, maintenance, inspection},
language = {eng},
number = {23},
pages = {null},
title = {Asymptotics of the total down time for an alternating renewal process},
url = {http://eudml.org/doc/293269},
volume = {11},
year = {1983},
}

TY - JOUR
AU - Wiesław Dziubdziela
TI - Asymptotics of the total down time for an alternating renewal process
JO - Mathematica Applicanda
PY - 1983
VL - 11
IS - 23
SP - null
AB - We investigate the asymptotic behavior of total down time of a system in which the breakdown process is an alternating renewal process, under the assumption that the probability of breakdown in a single cycle converges to zero. Using a theorem of R. Serfozo [J. Appl. Probab. 17 (1980), no. 2, 423–431; MR0568952], we find necessary and sufficient conditions for the convergence of the total down time to a compound Poisson process. We use these results in analyzing three examples: pairs of elements subject to detectable and undetectable breakdown (the Murphy and Phillips models), pairs of elements with a cold reserve served by one server; and an element with a temporal reserve.
LA - eng
KW - Applications; Reliability, availability, maintenance, inspection
UR - http://eudml.org/doc/293269
ER -

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