On signature-based expressions of system reliability
arXiv:1010.0162 · doi:10.1016/j.jmva.2011.05.007
Abstract
The concept of signature was introduced by Samaniego for systems whose components have i.i.d. lifetimes. This concept proved to be useful in the analysis of theoretical behaviors of systems. In particular, it provides an interesting signature-based representation of the system reliability in terms of reliabilities of k-out-of-n systems. In the non-i.i.d. case, we show that, at any time, this representation still holds true for every coherent system if and only if the component states are exchangeable. We also discuss conditions for obtaining an alternative representation of the system reliability in which the signature is replaced by its non-i.i.d. extension. Finally, we discuss conditions for the system reliability to have both representations.
References in corpus (1)
Cited by in corpus (7)
- Computing system signatures through reliability functions
- Joint signature of two or more systems with applications to multistate systems made up of two-state components
- On modular decompositions of system signatures
- On the extensions of Barlow-Proschan importance index and system signature to dependent lifetimes
- Subsignatures of systems
- Limit distributions of the upper order statistics for the Lévy-frailty Marshall-Olkin distribution
- Limiting behavior of mixed coherent systems with Lévy-frailty Marshall-Olkin failure times