Some advances in importance sampling of reliability models based on zero variance approximation

D.P. Reijsbergen; Pieter-Tjerk de Boer; Willem R.W. Scheinhardt; Sandeep Juneja

Some advances in importance sampling of reliability models based on zero variance approximation

D.P. Reijsbergen, Pieter-Tjerk de Boer, Willem R.W. Scheinhardt, Sandeep Juneja

Stochastic Operations Research

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › Academic

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Abstract

We are interested in estimating, through simulation, the probability of entering a rare failure state before a regeneration state. Since this probability is typically small, we apply importance sampling. The method that we use is based on finding the most likely paths to failure. We present an algorithm that is guaranteed to produce an estimator that meets the conditions presented in [10] [9] for vanishing relative error. We furthermore demonstrate how the procedure that is used to obtain the change of measure can be executed a second time to achieve even further variance reduction, using ideas from [5], and also apply this technique to the method of failure biasing, with which we compare our results.

Original language	Undefined
Title of host publication	Proceedings of the Ninth International Workshop on Rare Event Simulation, RESIM 2012
Place of Publication	Trondheim, Norway
Publisher	NTNU University Press
Pages	30-35
Number of pages	6
ISBN (Print)	not assigned
Publication status	Published - Jun 2012
Event	9th International Workshop on Rare Event Simulation, RESIM 2012 - Trondheim, Norway Duration: 25 Jun 2012 → 27 Jun 2012 Conference number: 9

Publication series

Name
Publisher	NTNU University Press

Workshop

Workshop	9th International Workshop on Rare Event Simulation, RESIM 2012
Abbreviated title	RESIM
Country/Territory	Norway
City	Trondheim
Period	25/06/12 → 27/06/12

Keywords

METIS-287909
IR-80762
EWI-22015
Zero variance approximation
Importance sampling
Rare event simulation

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Cite this

@inproceedings{6bd9d2149bb94ff99461a7749ba2d4b0,

title = "Some advances in importance sampling of reliability models based on zero variance approximation",

abstract = "We are interested in estimating, through simulation, the probability of entering a rare failure state before a regeneration state. Since this probability is typically small, we apply importance sampling. The method that we use is based on finding the most likely paths to failure. We present an algorithm that is guaranteed to produce an estimator that meets the conditions presented in [10] [9] for vanishing relative error. We furthermore demonstrate how the procedure that is used to obtain the change of measure can be executed a second time to achieve even further variance reduction, using ideas from [5], and also apply this technique to the method of failure biasing, with which we compare our results.",

keywords = "METIS-287909, IR-80762, EWI-22015, Zero variance approximation, Importance sampling, Rare event simulation",

author = "D.P. Reijsbergen and {de Boer}, Pieter-Tjerk and Scheinhardt, {Willem R.W.} and Sandeep Juneja",

year = "2012",

month = jun,

language = "Undefined",

isbn = "not assigned",

publisher = "NTNU University Press",

pages = "30--35",

booktitle = "Proceedings of the Ninth International Workshop on Rare Event Simulation, RESIM 2012",

note = "9th International Workshop on Rare Event Simulation, RESIM 2012 ; Conference date: 25-06-2012 Through 27-06-2012",

}

Reijsbergen, DP, de Boer, P-T , Scheinhardt, WRW & Juneja, S 2012, Some advances in importance sampling of reliability models based on zero variance approximation. in Proceedings of the Ninth International Workshop on Rare Event Simulation, RESIM 2012. NTNU University Press, Trondheim, Norway, pp. 30-35, 9th International Workshop on Rare Event Simulation, RESIM 2012, Trondheim, Norway, 25/06/12.

Some advances in importance sampling of reliability models based on zero variance approximation. / Reijsbergen, D.P.; de Boer, Pieter-Tjerk ; Scheinhardt, Willem R.W. et al.
Proceedings of the Ninth International Workshop on Rare Event Simulation, RESIM 2012. Trondheim, Norway: NTNU University Press, 2012. p. 30-35.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › Academic

TY - GEN

T1 - Some advances in importance sampling of reliability models based on zero variance approximation

AU - Reijsbergen, D.P.

AU - de Boer, Pieter-Tjerk

AU - Scheinhardt, Willem R.W.

AU - Juneja, Sandeep

N1 - Conference code: 9

PY - 2012/6

Y1 - 2012/6

N2 - We are interested in estimating, through simulation, the probability of entering a rare failure state before a regeneration state. Since this probability is typically small, we apply importance sampling. The method that we use is based on finding the most likely paths to failure. We present an algorithm that is guaranteed to produce an estimator that meets the conditions presented in [10] [9] for vanishing relative error. We furthermore demonstrate how the procedure that is used to obtain the change of measure can be executed a second time to achieve even further variance reduction, using ideas from [5], and also apply this technique to the method of failure biasing, with which we compare our results.

AB - We are interested in estimating, through simulation, the probability of entering a rare failure state before a regeneration state. Since this probability is typically small, we apply importance sampling. The method that we use is based on finding the most likely paths to failure. We present an algorithm that is guaranteed to produce an estimator that meets the conditions presented in [10] [9] for vanishing relative error. We furthermore demonstrate how the procedure that is used to obtain the change of measure can be executed a second time to achieve even further variance reduction, using ideas from [5], and also apply this technique to the method of failure biasing, with which we compare our results.

KW - METIS-287909

KW - IR-80762

KW - EWI-22015

KW - Zero variance approximation

KW - Importance sampling

KW - Rare event simulation

M3 - Conference contribution

SN - not assigned

SP - 30

EP - 35

BT - Proceedings of the Ninth International Workshop on Rare Event Simulation, RESIM 2012

PB - NTNU University Press

CY - Trondheim, Norway

T2 - 9th International Workshop on Rare Event Simulation, RESIM 2012

Y2 - 25 June 2012 through 27 June 2012

ER -