论文信息 - Hazard rate properties of a general counting process stopped at an independent random time

Hazard rate properties of a general counting process stopped at an independent random time

In this work we provide sufficient conditions under which a general counting process stopped at a random time independent from the process belongs to the reliability decreasing reversed hazard rate (DRHR) or increasing failure rate (IFR) class. We also give some applications of these results in generalized renewal and trend renewal processes stopped at a random time.

F. G. Badía

[1] J. George Shanthikumar,et al. On increasing-failure-rate random variables , 2005 .

[2] Adriana Hornikova,et al. Stochastic Ageing and Dependence for Reliability , 2007, Technometrics.

[3] J. Shanthikumar,et al. Multivariate Stochastic Orders , 2007 .

[4] Ushio Sumita,et al. A USEFUL GENERALIZATION OF RENEWAL THEORY: COUNTING PROCESSES GOVERNED BY NON-NEGATIVE MARKOVIAN INCREMENTS , 1986 .

[5] Richard E. Barlow,et al. Statistical Theory of Reliability and Life Testing: Probability Models , 1976 .

[6] Harshinder Singh,et al. The Reversed Hazard Rate Function , 1998, Probability in the Engineering and Informational Sciences.

[7] A. W. Marshall,et al. Shock Models and Wear Processes , 1973 .

[8] Henry W. Block,et al. Laplace Transforms for Classes of Life Distributions , 1980 .

[9] J. Grandell. Mixed Poisson Processes , 1997 .

[10] Debasis Sengupta,et al. Log-concave and concave distributions in reliability , 1999 .

[11] Bo Henry Lindqvist,et al. The Trend-Renewal Process for Statistical Analysis of Repairable Systems , 2003, Technometrics.

[12] A. Müller,et al. Comparison Methods for Stochastic Models and Risks , 2002 .

[13] D. Yao,et al. Bivariate characterization of some stochastic order relations , 1991, Advances in Applied Probability.