TY - GEN
T1 - Approximating the Lévy-Frailty Marshall-Olkin Model for Failure Times
AU - Barrera, Javiera
AU - Lagos, Guido
N1 - Publisher Copyright:
© 2020 IEEE.
PY - 2020/12/14
Y1 - 2020/12/14
N2 - In this paper we approximate the last, close-to-first, and what we call quantile failure times of a system, when the system-components' failure times are modeled according to a Levy-frailty Marshall-Olkin (LFMO) distribution. The LFMO distribution is a fairly recent model that can be used to model components failing simultaneously in groups. One of its prominent features is that the failure times of the components are conditionally iid; indeed, the failure times are iid exponential when conditioned on the path of a given Lévy subordinator process. We are motivated by further studying the order statistics of the LFMO distribution, as recently Barrera and Lagos (2020) showed an atypical behavior for the upper-order statistics. We are also motivated by approximating the system when it has an astronomically large number of components. We perform computational experiments that show significative variations in the convergence speeds of our approximations.
AB - In this paper we approximate the last, close-to-first, and what we call quantile failure times of a system, when the system-components' failure times are modeled according to a Levy-frailty Marshall-Olkin (LFMO) distribution. The LFMO distribution is a fairly recent model that can be used to model components failing simultaneously in groups. One of its prominent features is that the failure times of the components are conditionally iid; indeed, the failure times are iid exponential when conditioned on the path of a given Lévy subordinator process. We are motivated by further studying the order statistics of the LFMO distribution, as recently Barrera and Lagos (2020) showed an atypical behavior for the upper-order statistics. We are also motivated by approximating the system when it has an astronomically large number of components. We perform computational experiments that show significative variations in the convergence speeds of our approximations.
UR - http://www.scopus.com/inward/record.url?scp=85103877971&partnerID=8YFLogxK
U2 - 10.1109/WSC48552.2020.9383929
DO - 10.1109/WSC48552.2020.9383929
M3 - Conference contribution
AN - SCOPUS:85103877971
T3 - Proceedings - Winter Simulation Conference
SP - 2389
EP - 2399
BT - Proceedings of the 2020 Winter Simulation Conference, WSC 2020
A2 - Bae, K.-H.
A2 - Feng, B.
A2 - Kim, S.
A2 - Lazarova-Molnar, S.
A2 - Zheng, Z.
A2 - Roeder, T.
A2 - Thiesing, R.
PB - Institute of Electrical and Electronics Engineers Inc.
T2 - 2020 Winter Simulation Conference, WSC 2020
Y2 - 14 December 2020 through 18 December 2020
ER -