Hostname: page-component-848d4c4894-8kt4b Total loading time: 0 Render date: 2024-06-26T17:16:00.991Z Has data issue: false hasContentIssue false
  • English
  • Français

Reversed Preservation Properties for Series and Parallel Systems

Part of: Distribution theory - Probability Special processes

Published online by Cambridge University Press:  14 July 2016

Félix Belzunce ,
Helena Martínez-Puertas  and
José M. Ruiz
Félix Belzunce*
Affiliation:
Universidad de Murcia
Helena Martínez-Puertas*
Affiliation:
Universidad de Almería
José M. Ruiz*
Affiliation:
Universidad de Murcia
*
∗Postal address: Departamento Estadística e Investigación Operativa, Universidad de Murcia, Campus de Espinardo, 30100 Espinardo de Murcia, Spain.
∗∗Postal address: Departamento Estadística y Matemática Aplicada, Universidad de Almería, Campus de La Cañada, 04120 Almería, Spain. Email address: hmartinezp@terra.es
∗Postal address: Departamento Estadística e Investigación Operativa, Universidad de Murcia, Campus de Espinardo, 30100 Espinardo de Murcia, Spain.
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

Recently Li and Yam (2005) studied which ageing properties for series and parallel systems are inherited for the components. In this paper we provide new results for the increasing convex and concave orders, the increasing mean residual life (IMRL), decreasing failure rate (DFR), the new worse than used in expectation (NWUE), the increasing failure rate in average (IFRA), the decreasing failure rate in average (DFRA), and the new better than used in the convex order (NBUC) ageing classes.

Keywords

Increasing convex orderincreasing concave orderIMRLDFRNWUEIFRADFRANBUCparallel and series system

MSC classification

Secondary: 60E15: Inequalities; stochastic orderings 60K10: Applications (reliability, demand theory, etc.)
Type
Research Papers
Information
Journal of Applied Probability , Volume 44 , Issue 4 , December 2007 , pp. 928 - 937
Copyright
Copyright © Applied Probability Trust 2007 

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. (1981). Statistical Theory of Reliability and Life Testing. Probability Models. To Begin With, Silver Spring, MD.Google Scholar
Belzunce, F., Ruiz, J. M. and Ruiz, M. C. (2002). On preservation of some shifted and proportional orders by systems. Statist. Prob. Lett. 60, 141–154.CrossRefGoogle Scholar
Belzunce, F., Franco, M., Ruiz, J. M. and Ruiz, M. C. (2001). On partial orderings between coherent systems with different structures. Prob. Eng. Inf. Sci. 15, 273–293.Google Scholar
Boland, P. J., Shaked, M. and Shanthikumar, J. G. (1998). Stochastic ordering of order statistics. In Order Statistics; Theory & Methods (Handbook Statist. 16), eds Balakrishnan, N. and Rao, C. R., Elsevier, Amsterdam, pp. 89–103.Google Scholar
Boland, P. J., Hu, T., Shaked, M. and Shanthikumar, J. G. (2002). Stochastic ordering of order statistics. II. In Modeling Uncertainty: An Examination of Stochastic Theory, Methods and Applications, eds Dror, M. et al., Kluwer, Boston, MA, pp. 607–623.CrossRefGoogle Scholar
Cao, J. and Wang, Y. (1991). The NBUC and NWUC classes of life distributions. J. Appl. Prob. 28, 473–479. (Correction: 29 (1992), 753.)Google Scholar
Esary, J. D. and Proschan, F. (1963). Relationship between system failure rate and component failure rates. Technometrics 5, 183–189.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.Google Scholar
Franco, M., Ruiz, J. M. and Ruiz, M. C. (2001). On closure of the IFR(2) and NBU(2) classes. J. Appl. Prob. 38, 235–241.Google Scholar
Franco, M., Ruiz, J. M. and Ruiz, M. C. (2003). A note on closure of the ILR and DLR classes under formation of coherent systems. Statist. Papers 44, 279–288.CrossRefGoogle Scholar
Gertsbakh, I. B. (1989). Statistical Reliability Theory. Marcel Dekker, New York.Google 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
Lai, C. D. and Xie, M. (2006). Stochastic Aging and Dependence for Reliability. Springer, New York.Google Scholar
Li, X. and Yam, R. (2005). Reversed preservation properties of some negative aging conceptions and stochastic orders. Statist. Papers 46, 65–78.Google Scholar
Li, X., Li, Z. and Jing, B. (2000). Some results about the NBUC class of life distributions. Statist. Prob. Lett. 49, 229–237.CrossRefGoogle Scholar
Müller, A. and Stoyan, D. (2002). Comparison Methods for Stochastic Models and Risks. John Wiley, Chichester.Google Scholar
Pellerey, F. and Petakos, K. (2002). On closure property of the NBUC class under formation of parallel systems. IEEE Trans. Reliability 51, 452–454.Google Scholar
Ross, S. M. (1972). Introduction to Probability Models. Academic Press, New York.Google Scholar
Shaked, M. and Shanthikumar, J. G. (2007). Stochastic Orders. Springer, New York.CrossRefGoogle Scholar