TY - JOUR

T1 - A natural conjugate prior for the nonhomogeneous poisson process with an exponential intensity function

AU - Huang, Yeu Shiang

AU - Bier, Vicki M.

N1 - Funding Information:
This paper was prepared in part with the support of the U.S. Nuclear Regulatory Commission (NRC) under Award No. NRC-04-93-083. The opinions, findings, conclusions and recommendations expressed herein are those of the authors and do not necessarily reflect the views of the NRC,

PY - 1999

Y1 - 1999

N2 - This article presents a natural conjugate prior for the nonhomogeneous Poisson process (NHPP) with an exponential intensity function, for modeling the failure rate of repairable systems. The behavior of the conjugate prior distribution with respect to its parameters is studied, and the use of this prior in Bayesian estimation is compared to two other estimation approaches (the use of independent prior distributions, and the bivariate normal distribution). The use of the conjugate prior proposed here facilitates Bayesian statistical analysis of aging. In particular, the proposed prior allows us to explicitly account for dependence between the initial failure rate and the aging rate. This is a significant improvement over the assumptions made in most prior work (either the assumption that the aging rate is known, or the assumption that the initial failure rate and the aging rate are independent). Monte Carlo simulation shows that Bayesian estimation using the proposed prior generally performs at least as well as Bayesian estimation using independent priors for the initial failure rate and the aging rate, except in the case where the prior distribution underestimates both the initial failure rate and the aging rate.

AB - This article presents a natural conjugate prior for the nonhomogeneous Poisson process (NHPP) with an exponential intensity function, for modeling the failure rate of repairable systems. The behavior of the conjugate prior distribution with respect to its parameters is studied, and the use of this prior in Bayesian estimation is compared to two other estimation approaches (the use of independent prior distributions, and the bivariate normal distribution). The use of the conjugate prior proposed here facilitates Bayesian statistical analysis of aging. In particular, the proposed prior allows us to explicitly account for dependence between the initial failure rate and the aging rate. This is a significant improvement over the assumptions made in most prior work (either the assumption that the aging rate is known, or the assumption that the initial failure rate and the aging rate are independent). Monte Carlo simulation shows that Bayesian estimation using the proposed prior generally performs at least as well as Bayesian estimation using independent priors for the initial failure rate and the aging rate, except in the case where the prior distribution underestimates both the initial failure rate and the aging rate.

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U2 - 10.1080/03610929908832368

DO - 10.1080/03610929908832368

M3 - Article

AN - SCOPUS:0442322257

VL - 28

SP - 1479

EP - 1509

JO - Communications in Statistics - Theory and Methods

JF - Communications in Statistics - Theory and Methods

SN - 0361-0926

IS - 6

ER -