Open Access
February, 1978 Converting Dependent Models into Independent ones, Preserving Essential Features
N. Langberg, F. Proschan, A. J. Quinzi
Ann. Probab. 6(1): 174-181 (February, 1978). DOI: 10.1214/aop/1176995624


Let $T$ denote the life length of a series system of $n$ components having respective life lengths $T_1,\cdots, T_n$, not necessarily independent. We give necessary and sufficient conditions for the existence of a set of independent random variables $\{H_I\}, I$ a subset of $\{1,\cdots, n\}$, such that the life length of the original series system and the occurrence of its failure pattern (set of components whose simultaneous failure coincides with that of the system) have the same joint distribution as the life length of a derived series system of components having life lengths $\{H_I\}$ and the occurrence of the corresponding failure pattern of the derived system. We also exhibit explicitly the distributions of these independent random variables $\{H_I\}$. This extends the results of Miller while using more elementary methods.


Download Citation

N. Langberg. F. Proschan. A. J. Quinzi. "Converting Dependent Models into Independent ones, Preserving Essential Features." Ann. Probab. 6 (1) 174 - 181, February, 1978.


Published: February, 1978
First available in Project Euclid: 19 April 2007

zbMATH: 0382.62083
MathSciNet: MR461827
Digital Object Identifier: 10.1214/aop/1176995624

Primary: 62N05
Secondary: 62E10

Keywords: Coherent system , dependent , equivalence in life length and failure pattern , failure pattern , fatal shock model , Independent , life length , multivariate exponential distribution

Rights: Copyright © 1978 Institute of Mathematical Statistics

Vol.6 • No. 1 • February, 1978
Back to Top