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.
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References
Barlow, R. E. and Proschan, F. (1981).Statistical Theory of Reliability and Life Testing: Probability Models. Holt, Rinehart and Winston, New York.
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.
Belzunce, F. and Shaked, M. (2001). “Stochastic comparisons of mixtures of convexly ordered distributions with applications in reliability”, Stat. & Prob. Lett.,53, 363–372.
Brown, M. (1980). “Bounds, inequalities, and monotonicity properties for some specialized renewal processes”, Ann. Prob.,8, 227–240.
Brown, M. (1981). “Further monotonicity properties for specialized renewal processes”, Ann. Prob.,9, 891–895.
Cao, J. and Wang, Y. (1991). “The NBUC and NWUC classes of life distributions”. J. Appl. Prob.,28, 473–479.
Cao, J. and Wang, Y. (1992). Correction. J. Appl. Prob.,29, 753.
Fagiuoli, E. and Pellerey, F. (1994). “Preservation on certain Classes of Life Distributions under Poisson Shock Models”, J. Appl. Prob.,31, 458–465.
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.
Hu, T. and Xie, H. (2002). “Proofs of the closure property of NBUC and NBU(2) under convolution”, J. Appl. Prob.,39, 224–227.
Li, X., Li, Z. and Jing, B. (2000). “Some results about NBUC class of life distributions”, Stat. & Prob. Lett.,46, 229–237.
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.
Müller, J. and Stoyan, D. (2002).Comparison Methods for Stochastic Models and Risks. John Wiley and Sons, Chiechester.
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.
Savits, T. H. (1991). “Repair Policies and Stochastic Order” inStochastic Orders and Decision under Risk, IMS Lecture Notes-Monograph Series, 19.
Shaked, M. and Shanthikumar, J.G. (1994).Stochastic Orders and Their Applications. Academic Press, London.
Shaked, M. and Zhu, H. (1992). “Some results on block replacement policies and renewal theory”, J. Appl. Prob.,29, 932–946.
Stoyan, D. (1983).Comparison Methods for Queues and Other Stochastic Models. John Wiley and Sons, Chiechester.
Yue, D. and Cao, J. (2001). “The NBUL class of Life Distribution and Replacement Policy Comparisons”, Naval Research Logistics,48, 578–591.
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Supported by Ministerio de Ciencia y Tecnología under grant BFM2000-0362
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Belzunce, F., Ortega, EM. & Ruiz, J.M. A note on replacement policy comparisons from NBUC lifetime of the unit. Statistical Papers 46, 509–522 (2005). https://doi.org/10.1007/BF02763002
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DOI: https://doi.org/10.1007/BF02763002