On computing signatures of coherent systems

A Note on the Comparisons among Coherent Systems

 Using the concept of system signature introduced by Samaniego (1985), Kochar et al. (1999) compared the lifetimes of the systems in which the lifetimes of the components are independent and identically distributed (i.i.d.) random variables. Their results are extended to the systems with exchangeable components by Navarro et al. (2005). This paper gives some alternative proofs to obtain th...

Bounds for reliability of IFRA coherent systems using signatures

The reliability of any coherent system is the probability that it completes a mission of time t without failure. To calculate it one needs to know the structure function of the system and the distribution of the component life times which we assume to be independent and identically distributed continuous positive valued random variables. In this paper we bring together (i) the single crossing p...

Signatures of Coherent Systems Built with Separate Modules

The signature is an important structural characteristic of a coherent system. Its computation, however, is often rather involved and complex. We analyze several cases where this complexity can be considerably reduced. These are the cases when a ‘large’ coherent system is obtained as a series, parallel, or recurrent structure built from ‘small’modules with known signature. Corresponding formulae...

On the cardinality index of fuzzy measures and the signatures of coherent systems

Boolean and pseudo-Boolean functions play a central role in various areas of applied mathematics. We will focus here on their use in decision making, cooperative game theory, and engineering reliability theory. A discrete fuzzy measure on the finite set X = {1, . . . ,n} is a nondecreasing set function μ : 2 → [0,1] satisfying the boundary conditions μ(∅) = 0 and μ(X) = 1. For any subset S ⊆ X ...

On Coherent Systems of Type