Hazard rate ordering of order statistics and systems

Journal of Applied Probability

Volumn 43, Issue 2, 2006, Pages 391-408

  Navarro, Jorge ^a   Shaked, Moshe ^b,c  

^a UNIVERSITY OF MURCIA   (Spain)

^b UNIVERSITY OF ARIZONA   (United States)

^c University of Arizona   (United States)

Author keywords

Cause specificity; Coherent system; Exchangeable distribution; Farlie Gumbel Morgenstern distribution; Freund distribution; Hazard gradient; Hazard rate order; Signature; Stochastic order

Indexed keywords

EID: 33845344692     PISSN: 00219002     EISSN: None     Source Type: Journal    
DOI: 10.1239/jap/1152413730     Document Type: Article

References (22)

1. BAGGS, G. E. AND NAGARAJA, H. N. (1996). Reliability properties of order statistics from bivariate exponential distributions. Commun. Statist. Stoch. Models 12, 611-631.
2. BARLOW, R. E. AND PROSCHAN, F. (1975). Statistical Theory of Reliability and Life Testing. Probability Models. Holt, Rinehart and Winston, New York.
3. BLOCK, H. AND JOE, H. (1997). Tail behavior of the failure rate functions of mixtures. Lifetime Data Anal. 3, 269-288.
4. BLOCK, H. W., LI, Y. AND SAVITS, T. H. (2003). Initial and final behaviour of failure rate functions for mixtures and systems. J. Appl. Prob. 40, 721-740.
5. BLOCK, H. W., SAVITS, T. H. AND SHAKED, M. (1982). Some concepts of negative dependence. Ann. Prob. 10, 765-772.
6. FREUND, J. E. (1961). A bivariate extension of the exponential distribution. J. Amer. Statist. Assoc. 56, 971-977.
7. HOLT, J. D. (1978). Competing risk analyses with special reference to matched pair experiments. Biometrika 65, 159-165.
8. JOHNSON, N. L. AND KOTZ, S. (1975). A vector multivariate hazard rate. J. Multivariate Anal. 5, 53-66,498.
9. KARLIN, S. AND RINOTT, Y. (1980). Classes of orderings of measures and related correlation inequalities. II. Multivariate reverse rule distributions. J. Multivariate Anal. 10, 499-516.
10. KOCHAR, S., MUKERJEE, H. AND SAMANIEGO, F. J. (1999). The "signature" of a coherent system and its application to comparisons among systems. Naval Res. Logistics 46, 507-523.
11. KORWAR, R. (2003). On stochastic orders for the lifetime of a k-out-of-n system. Prob. Eng. Inf. Sci. 17, 137-142.
12. LI, Y. (2005). Asymptotic baseline of the hazard rate function of mixtures. J. Appl. Prob. 42, 892-901.
13. MARSHALL, A. W. (1975). Some comments on the hazard gradient. Stoch. Process. Appl. 3, 293-300.
14. NAVARRO, J. AND HERNANDEZ, P. J. (2004a). How to obtain bathtub-shaped failure rate models from normal mixtures. Prob. Eng. Inf. Sci. 18, 511-531.
15. NAVARRO, J. AND HERNANDEZ, P. J. (2004b). Properties of the failure rate functions of generalized mixtures. Tech. Rep., Facultad de Matematicas, Universidad de Murcia.
16. NAVARRO, J., RUIZ, J. M. AND SANDOVAL, C. J. (2004). Properties of coherent systems with dependent components. To appear in Commun. Statist. Theory Meth.
17. NAVARRO, J., RUIZ, J. M. AND SANDOVAL, C. J. (2005). A note on comparisons among coherent systems with dependent components using signatures. Statist. Prob. Lett. 72, 179-185.
18. PRENTICE, R. L. et al. (1978). The analysis of failure times in the presence of competing risks. Biometrics 34, 541-554.
19. SAMANIEGO, F. J. (1985). On the closure of the IFR class under formation of coherent systems. IEEE Trans. Reliab. 34, 69-72.
20. SCARSINI, M. AND SHARED, M. (1999). Distributions with known initial hazard rate functions. J. Statist. Planning Infer. 78, 39-55.
21. SHARED, M. AND SHANTHIRUMAR, J. G. (1994). Stochastic Orders and Their Applications. Academic Press, Boston, MA.
22. SHAKED, M. AND SUAREZ-LLORENS, A. (2003). On the comparison of reliability experiments based on the convolution order. J. Amer. Statist. Assoc. 98, 693-702.