Hostname: page-component-8448b6f56d-dnltx Total loading time: 0 Render date: 2024-04-24T09:30:39.028Z Has data issue: false hasContentIssue false
  • English
  • Français

On the closure of the IFR(2) and NBU(2) classes

Part of: Distribution theory - Probability Survival analysis and censored data

Published online by Cambridge University Press:  14 July 2016

Manuel Franco ,
José M. Ruiz  and
M. Carmen Ruiz
Manuel Franco*
Affiliation:
Universidad de Murcia
José M. Ruiz*
Affiliation:
Universidad de Murcia
M. Carmen Ruiz*
Affiliation:
Universidad Politécnica de Cartagena
*
∗ Postal address: Departamento Estadística e I.O., Universidad de Murcia, 30100 Murcia, Spain.
∗ Postal address: Departamento Estadística e I.O., Universidad de Murcia, 30100 Murcia, Spain.
∗∗∗ Postal address: Departamento Matemática Aplicada y Estadística, Universidad Politécnica Cartagena, 30203 Murcia, Spain.
Get access Rights & Permissions [Opens in a new window]

Abstract

In this note, we give some preservation results for the classes IFR(2), NBU(2) and their dual classes under the formation of special coherent systems. Further, we show with examples that the relationships among these aging classes and others are strictly one-way implications.

Keywords

coherent systemsparallel systemsseries systemsIFR(2)NBU(2)

MSC classification

Primary: 60E15: Inequalities; stochastic orderings
Secondary: 62N05: Reliability and life testing
Type
Short Communications
Information
Journal of Applied Probability , Volume 38 , Issue 1 , March 2001 , pp. 235 - 241
Copyright
Copyright © by the Applied Probability Trust 2001 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Footnotes

This work was partly supported by DGES(MEC), Grant PB96-1105.

References

Abouammoh, A., and El-Neweihi, E. (1986). Closure of the NBUE and DMRL classes under formation of parallel systems. Statist. Prob. Lett. 4, 223–225.Google Scholar
Barlow, R. E., and Proschan, F. (1975). Statistical Theory of Reliability and Life Testing, Probability Models. To Begin With, Silver Spring, MD.Google Scholar
Bryson, M. C., and Siddiqui, M. M. (1969). Some criteria for ageing. J. Amer. Statist. Assoc. 64, 1472–1483.Google Scholar
Cao, J., and Wang, Y. (1991). The NBUC and NWUC classes of life distributions. J. Appl. Prob. 28, 473–479.CrossRefGoogle Scholar
Deshpande, J. V., Kochar, S. C., and Singh, H. (1986). Aspects of positive ageing. J. Appl. Prob. 23, 748–758.Google Scholar
Esary, J. D., Marshall, A. W., and Proschan, F. (1970). Some reliability applications of the hazard transform. SIAM J. Appl. Math. 18, 849–860.CrossRefGoogle Scholar
Hendi, M. I., Mashhour, A. F., and Montasser, M. A. (1993). Closure of the NBUC class under formation of parallel systems. J. Appl. Prob. 30, 975–978.Google Scholar
Li, X., and Kochar, S. C. (2001). Some new results involving NBU(2) class of life distributions. J. Appl. Prob. 38, 242–247.Google Scholar
Li, X., Li, Z., and Jing, B. (2000). Some results about the NBUC class of life distributions. Statist. Prob. Lett. 46, 229–237.Google Scholar
Pellerey, F., and Petakos, K. (2000). On closure property of the NBUC class under formation of parallel systems. Tech. Rept, Dipartimento di Matematica, Statistica ed Informatica, Universitá di Bergamo.Google Scholar
Sabnis, S. V., and Nair, M. R. (1997). Coherent structures and unimodality. J. Appl. Prob. 34, 812–817.Google Scholar
Sengupta, D., and Nanda, A. K. (1999). Log-concave and concave distributions in reliability. Naval Res. Logist. 46, 419–433.Google Scholar
Shaked, M., and Shanthikumar, J. G. (1994). Stochastic orders and their applications. Academic Press, New York.Google Scholar