TY - JOUR

T1 - Approximate zero-variance Monte Carlo estimation of Markovian unreliability

AU - Delcoux, J. L.

AU - Labeau, P. E.

AU - Devooght, J.

PY - 1998/3

Y1 - 1998/3

N2 - Monte Carlo simulation has become an important tool for the estimation of reliability characteristics, since conventional numerical methods are no more efficient when the size of the system to solve increases. However, evaluating by a simulation the probability of occurrence of very rare events means playing a very large number of histories of the system, which leads to unacceptable computation times. Acceleration and variance reduction techniques have to be worked out. We show in this paper how to write the equations of Markovian reliability as a transport problem, and how the well known zero-variance scheme can be adapted to this application. But such a method is always specific to the estimation of one quantity, while a Monte Carlo simulation allows to perform simultaneously estimations of diverse quantities. Therefore, the estimation of one of them could be made more accurate while degrading at the same time the variance of other estimations. We propound here a method to reduce simultaneously the variance for several quantities, by using probability laws that would lead to zero-variance in the estimation of a mean of these quantities. Just like the zero-variance one, the method we propound is impossible to perform exactly. However we show that simple approximations of it may be very efficient.

AB - Monte Carlo simulation has become an important tool for the estimation of reliability characteristics, since conventional numerical methods are no more efficient when the size of the system to solve increases. However, evaluating by a simulation the probability of occurrence of very rare events means playing a very large number of histories of the system, which leads to unacceptable computation times. Acceleration and variance reduction techniques have to be worked out. We show in this paper how to write the equations of Markovian reliability as a transport problem, and how the well known zero-variance scheme can be adapted to this application. But such a method is always specific to the estimation of one quantity, while a Monte Carlo simulation allows to perform simultaneously estimations of diverse quantities. Therefore, the estimation of one of them could be made more accurate while degrading at the same time the variance of other estimations. We propound here a method to reduce simultaneously the variance for several quantities, by using probability laws that would lead to zero-variance in the estimation of a mean of these quantities. Just like the zero-variance one, the method we propound is impossible to perform exactly. However we show that simple approximations of it may be very efficient.

UR - http://www.scopus.com/inward/record.url?scp=0032027267&partnerID=8YFLogxK

U2 - 10.1016/S0306-4549(97)00065-0

DO - 10.1016/S0306-4549(97)00065-0

M3 - Article

AN - SCOPUS:0032027267

SN - 0306-4549

VL - 25

SP - 259

EP - 283

JO - Annals of nuclear energy

JF - Annals of nuclear energy

IS - 4-5

ER -