TY - GEN
T1 - On the estimation of the mean time to failure by simulation
AU - Glynn, Peter W.
AU - Nakayama, Marvin K.
AU - Tuffin, Bruno
N1 - Funding Information:
This work has been supported in part by the National Science Foundation under Grant No. CMMI-1537322. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the authors and do not necessarily reflect the views of the National Science Foundation.
Publisher Copyright:
© 2017 IEEE.
Copyright:
Copyright 2019 Elsevier B.V., All rights reserved.
PY - 2017/6/28
Y1 - 2017/6/28
N2 - The mean time to failure (MTTF) of a stochastic system is often estimated by simulation. One natural estimator, which we call the direct estimator, simply averages independent and identically distributed copies of simulated times to failure. When the system is regenerative, an alternative approach is based on a ratio representation of the MTTF. The purpose of this paper is to compare the two estimators. We first analyze them in the setting of crude simulation (i.e., no importance sampling), showing that they are actually asymptotically identical in a rare-event context. The two crude estimators are inefficient in different but closely related ways: the direct estimator requires a large computational time because times to failure often include many transitions, whereas the ratio estimator entails estimating a rare-event probability. We then discuss the two approaches when employing importance sampling; for highly reliable Markovian systems, we show that using a ratio estimator is advised.
AB - The mean time to failure (MTTF) of a stochastic system is often estimated by simulation. One natural estimator, which we call the direct estimator, simply averages independent and identically distributed copies of simulated times to failure. When the system is regenerative, an alternative approach is based on a ratio representation of the MTTF. The purpose of this paper is to compare the two estimators. We first analyze them in the setting of crude simulation (i.e., no importance sampling), showing that they are actually asymptotically identical in a rare-event context. The two crude estimators are inefficient in different but closely related ways: the direct estimator requires a large computational time because times to failure often include many transitions, whereas the ratio estimator entails estimating a rare-event probability. We then discuss the two approaches when employing importance sampling; for highly reliable Markovian systems, we show that using a ratio estimator is advised.
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U2 - 10.1109/WSC.2017.8247921
DO - 10.1109/WSC.2017.8247921
M3 - Conference contribution
AN - SCOPUS:85044511013
T3 - Proceedings - Winter Simulation Conference
SP - 1844
EP - 1855
BT - 2017 Winter Simulation Conference, WSC 2017
A2 - Chan, Victor
PB - Institute of Electrical and Electronics Engineers Inc.
T2 - 2017 Winter Simulation Conference, WSC 2017
Y2 - 3 December 2017 through 6 December 2017
ER -