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The NBUL class of life distribution and replacement policy comparisons
Author(s) -
Yue Dequan,
Cao Jinhua
Publication year - 2001
Publication title -
naval research logistics (nrl)
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.665
H-Index - 68
eISSN - 1520-6750
pISSN - 0894-069X
DOI - 10.1002/nav.1035
Subject(s) - class (philosophy) , residual , laplace transform , random variable , stochastic ordering , mathematics , distribution (mathematics) , shock (circulatory) , renewal theory , property (philosophy) , statistics , combinatorics , discrete mathematics , computer science , algorithm , mathematical analysis , philosophy , artificial intelligence , medicine , epistemology
Let X and X τ denote the lifetime and the residual life at age τ of a system, respectively. X is said to be a NBUL random variable if X τ is smaller than X in Laplace order, i.e., X τ ≤ L X . We obtain some characterizations for this class of life distribution by means of the lifetime of a series system and the residual life at random time. We also discuss preservation properties for this class of life distribution under shock models. Finally, under the assumption that the lifetimes have the NBUL property, we make stochastic comparisons between some basic replacement policies. © 2001 John Wiley & Sons, Inc. Naval Research Logistics 48: 578–591, 2001.