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Some New Results on the Moment Generating Function Order and Related Life Distributions

Part of: Special processes Distribution theory

Published online by Cambridge University Press:  14 July 2016

Shuhong Zhang  and
Xiaohu Li
Shuhong Zhang*
Affiliation:
Lanzhou University
Xiaohu Li*
Affiliation:
Xiamen University
*
∗Postal address: School of Mathematics and Statistics, Lanzhou University, Lanzhou 730000, P. R. China.
∗∗Postal address: School of Mathematical Science, Xiamen University, Xiamen 361005, P. R. China. Email address: xhli@lzu.edu.cn
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Abstract

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In this paper we study the moment generating function order and the new better than used in the moment generating function order (NBUMG) life distributions. A closure property of this order under an independent random sum is deduced, and stochastic comparisons among the block replacement policy, the age replacement policy, the complete repair policy, and the minimal repair policy of an NBUMG component are investigated.

Keywords

Age replacementblock replacementcomplete repairminimal repairrandom sum

MSC classification

Secondary: 62E10: Characterization and structure theory 60K10: Applications (reliability, demand theory, etc.)
Type
Research Article
Information
Journal of Applied Probability , Volume 47 , Issue 4 , December 2010 , pp. 923 - 933
Copyright
Copyright © Applied Probability Trust 2010 

References

Barlow, R. E. and Proschan, F. (1981). Statistical Theory of Reliability and Life Testing. Holt, New York.Google Scholar
Belzunce, F., Ortega, E. and Ruiz, J. M. (1999). The Laplace order and ordering of residual lives. Statist. Prob. Lett. 42, 145–156.Google Scholar
Belzunce, F., Ortega, E.-M. and Ruiz, J. M. (2005). A note on replacement policy comparisons from NBUC lifetime of the unit. Statist. Papers 46, 509–522.Google Scholar
Belzunce, F., Ortega, E.-M. and Ruiz, J. M. (2006). Comparison of expected failure times for several replacement policies. IEEE Trans. Reliab. 55, 490–495.Google Scholar
Block, H. W., Langberg, N. A. and Savits, T. H. (1990). Maintenance comparisons: block policies. J. Appl. Prob. 27, 649–657.Google Scholar
Block, H. W., Langberg, N. A. and Savits, T. H. (1993). Repair replacement policies. J. Appl. Prob. 30, 194–206.Google Scholar
Klar, B. (2002). A note on the -class of life distributions. J. Appl. Prob. 39, 11–19.Google Scholar
Klar, B. and Müller, A. (2003). Characterizations of classes of lifetime distributions generalizing the NBUE class. J. Appl. Prob. 40, 20–32.Google Scholar
Klefsjö, B. (1983). A useful ageing property based on the Laplace transform. J. Appl. Prob. 20, 615–626.Google Scholar
Lai, C.-D. and Xie, M. (2006). Stochastic Ageing and Dependence for Reliability. Springer, New York.Google Scholar
Li, X. (2004). Some properties of aging notions based on the moment-generating-function order. J. Appl. Prob. 41, 927–934.CrossRefGoogle Scholar
Marshall, A. W. and Olkin, I. (2007). Life Distributions. Springer, New York.Google Scholar
Marshall, A. W. and Proschan, F. (1972). Classes of distributions applied in replacement, with renewal theory implications. In Proc. 6th Berkeley Symp. Math. Statistics Prob., Vol. I, University of California Press, Berkeley, CA, pp. 395–415.Google Scholar
Müller, A. and Stoyan, D. (2002). Comparison Methods for Stochastic Models and Risks. John Wiley, Chichester.Google Scholar
Shaked, M. and Shanthikumar, J. G. (2007). Stochastic Orders. Springer, New York.Google Scholar
Wang, W. Y. (1996). Life distribution classes and two-unit standby redundant system. , Chinese Academy of Sciences.Google Scholar
Yue, D. and Cao, J. (2001). The NBUL class of life distribution and replacement policy comparisons. Naval Res. Logistics 48, 578–591.Google Scholar