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December, 1979 A Reliability Growth Model Involving Dependent Components
N. A. Langberg, F. Proschan
Ann. Probab. 7(6): 1082-1087 (December, 1979). DOI: 10.1214/aop/1176994904


Earlier papers have shown how to convert competing risk models involving dependent random variables into models involving only independent random variables, while simultaneously preserving the distribution of the minimum and the probabilities of the various failure patterns. In the present paper, we consider a sequence of such conversions occurring at successive points in chronological time in which the independent random variables are becoming stochastically larger. We obtain results which essentially demonstrate that the limiting distributions in the sequence of dependent models "correctly" correspond to the limiting distributions in the sequence of independent models. These results have applications in reliability growth models and in biomedical competing risk models in which the competing risks are increasing with age; in these models dependency is permitted among the random variables.


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N. A. Langberg. F. Proschan. "A Reliability Growth Model Involving Dependent Components." Ann. Probab. 7 (6) 1082 - 1087, December, 1979.


Published: December, 1979
First available in Project Euclid: 19 April 2007

zbMATH: 0421.60078
MathSciNet: MR548905
Digital Object Identifier: 10.1214/aop/1176994904

Keywords: 62-15 , 62-80 , competing risks , dependent components , equivalent models , failure patterns , limit theorems , reliability growth , system failure

Rights: Copyright © 1979 Institute of Mathematical Statistics


Vol.7 • No. 6 • December, 1979
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