Statistical Papers

, Volume 46, Issue 4, pp 509–522 | Cite as

A note on replacement policy comparisons from NBUC lifetime of the unit

  • Félix Belzunce
  • Eva-María Ortega
  • José M. Ruiz
Articles

Abstract

Age and block replacement policies are commonly used in order to reduce the number of in-service failures when the systems are functioning indefinitely. In reliability theory, the lifetime of a system can be modeled by means of the NBUC aging class that is characterized throughout comparisons of the residual lives in the sense of the icx order. The purpose of this paper is to establish stochastic comparisons between the age (block) replacement policy and a renewal process with no planned replacements when the lifetime of the unit is NBUC.

AMS Subject Classification

60K15 60K10 

Key words and phrases

icx order NBUC aging class renewal processes age and block replacement policies 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [1]
    Barlow, R. E. and Proschan, F. (1981).Statistical Theory of Reliability and Life Testing: Probability Models. Holt, Rinehart and Winston, New York.Google Scholar
  2. [2]
    Belzunce, F., Ortega, E.-M. and Ruiz, J. M. (2001). “A note on stochastic comparisons of excess lifetimes of renewal processes”, J. Appl. Prob.,38, 1–7.MathSciNetGoogle Scholar
  3. [3]
    Belzunce, F. and Shaked, M. (2001). “Stochastic comparisons of mixtures of convexly ordered distributions with applications in reliability”, Stat. & Prob. Lett.,53, 363–372.MATHCrossRefMathSciNetGoogle Scholar
  4. [4]
    Brown, M. (1980). “Bounds, inequalities, and monotonicity properties for some specialized renewal processes”, Ann. Prob.,8, 227–240.MATHGoogle Scholar
  5. [5]
    Brown, M. (1981). “Further monotonicity properties for specialized renewal processes”, Ann. Prob.,9, 891–895.MATHGoogle Scholar
  6. [6]
    Cao, J. and Wang, Y. (1991). “The NBUC and NWUC classes of life distributions”. J. Appl. Prob.,28, 473–479.MATHCrossRefMathSciNetGoogle Scholar
  7. [7]
    Cao, J. and Wang, Y. (1992). Correction. J. Appl. Prob.,29, 753.CrossRefMathSciNetGoogle Scholar
  8. [8]
    Fagiuoli, E. and Pellerey, F. (1994). “Preservation on certain Classes of Life Distributions under Poisson Shock Models”, J. Appl. Prob.,31, 458–465.MATHCrossRefMathSciNetGoogle Scholar
  9. [9]
    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.MATHCrossRefMathSciNetGoogle Scholar
  10. [10]
    Hu, T. and Xie, H. (2002). “Proofs of the closure property of NBUC and NBU(2) under convolution”, J. Appl. Prob.,39, 224–227.MATHCrossRefMathSciNetGoogle Scholar
  11. [11]
    Li, X., Li, Z. and Jing, B. (2000). “Some results about NBUC class of life distributions”, Stat. & Prob. Lett.,46, 229–237.MATHCrossRefMathSciNetGoogle Scholar
  12. [12]
    Marshall, A. W., and Proschan, F. (1972). “Classes of distributions applicable in replacement with renewal theory implication”, Proc. 6th Berkeley Symp. Math. Statist. Prob.,1, 395–415.MathSciNetGoogle Scholar
  13. [13]
    Müller, J. and Stoyan, D. (2002).Comparison Methods for Stochastic Models and Risks. John Wiley and Sons, Chiechester.MATHGoogle Scholar
  14. [14]
    Pellerey, F. and Petakos, K. (2002). “On closure property of the NUBC class under formation of parallel systems”, IEEE Transactions on Reliability,51, 452–454.CrossRefGoogle Scholar
  15. [15]
    Savits, T. H. (1991). “Repair Policies and Stochastic Order” inStochastic Orders and Decision under Risk, IMS Lecture Notes-Monograph Series, 19.Google Scholar
  16. [16]
    Shaked, M. and Shanthikumar, J.G. (1994).Stochastic Orders and Their Applications. Academic Press, London.MATHGoogle Scholar
  17. [17]
    Shaked, M. and Zhu, H. (1992). “Some results on block replacement policies and renewal theory”, J. Appl. Prob.,29, 932–946.MATHCrossRefMathSciNetGoogle Scholar
  18. [18]
    Stoyan, D. (1983).Comparison Methods for Queues and Other Stochastic Models. John Wiley and Sons, Chiechester.MATHGoogle Scholar
  19. [19]
    Yue, D. and Cao, J. (2001). “The NBUL class of Life Distribution and Replacement Policy Comparisons”, Naval Research Logistics,48, 578–591.MATHCrossRefMathSciNetGoogle Scholar

Copyright information

© Springer-Verlag 2005

Authors and Affiliations

  • Félix Belzunce
    • 1
  • Eva-María Ortega
    • 2
  • José M. Ruiz
    • 1
  1. 1.Dpto. Estadística e Investigación OperativaUniversidad de Murcia, Campus de EspinardoEspinardo (Murcia)Spain
  2. 2.Dpto. Estadística y Matemática Aplicada, Centro de Investigación OperativaUniversidad Miguel HernándezOrihuela (Alicante)Spain

Personalised recommendations