ABSTRACT
Chapter 3
Some concepts of
dependence and aging
3.1 Introduction
In this chapter we study some concepts of stochastic orderings, dependence and
aging properties for vectors of random quantities.
Such notions provide the essential tools for obtaining inequalities on condi-
tional probability distributions of residual lifetimes, namely for the conditional
probabilities of the type
PfT
h+1
> s
h+1
; :::; T
n
> s
n
jT
= t
; :::; T
h
= t
h
; T
h+1
> r
h+1
; :::; T
n
> r
n
g
(3.1)
considered in the previous chapter.
