18,555 research outputs found
Aging functions and multivariate notions of NBU and IFR
For d≥2, let X=(X1, …, Xd) be a vector of exchangeable continuous lifetimes with joint survival function . For such models, we study some properties of multivariate aging of that are described by means of the multivariate aging function , which is a useful tool for describing the level curves of . Specifically, the attention is devoted to notions that generalize the univariate concepts of New Better than Used and Increasing Failure Rate. These multivariate notions are satisfied by random vectors whose components are conditionally independent and identically distributed having univariate conditional survival function that is New Better than Used (respectively, Increasing Failure Rate). Furthermore, they also have an interpretation in terms of comparisons among conditional survival functions of residual lifetimes, given a same history of observed survivals
On modular decompositions of system signatures
Considering a semicoherent system made up of components having i.i.d.
continuous lifetimes, Samaniego defined its structural signature as the
-tuple whose -th coordinate is the probability that the -th component
failure causes the system to fail. This -tuple, which depends only on the
structure of the system and not on the distribution of the component lifetimes,
is a very useful tool in the theoretical analysis of coherent systems.
It was shown in two independent recent papers how the structural signature of
a system partitioned into two disjoint modules can be computed from the
signatures of these modules. In this work we consider the general case of a
system partitioned into an arbitrary number of disjoint modules organized in an
arbitrary way and we provide a general formula for the signature of the system
in terms of the signatures of the modules.
The concept of signature was recently extended to the general case of
semicoherent systems whose components may have dependent lifetimes. The same
definition for the -tuple gives rise to the probability signature, which may
depend on both the structure of the system and the probability distribution of
the component lifetimes. In this general setting, we show how under a natural
condition on the distribution of the lifetimes, the probability signature of
the system can be expressed in terms of the probability signatures of the
modules. We finally discuss a few situations where this condition holds in the
non-i.i.d. and nonexchangeable cases and provide some applications of the main
results
Reliability of systems with dependent components based on lattice polynomial description
Reliability of a system is considered where the components' random lifetimes
may be dependent. The structure of the system is described by an associated
"lattice polynomial" function. Based on that descriptor, general framework
formulas are developed and used to obtain direct results for the cases where a)
the lifetimes are "Bayes-dependent", that is, their interdependence is due to
external factors (in particular, where the factor is the "preliminary phase"
duration) and b) where the lifetimes' dependence is implied by upper or lower
bounds on lifetimes of components in some subsets of the system. (The bounds
may be imposed externally based, say, on the connections environment.) Several
special cases are investigated in detail
- …