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An algorithm to construct coherent systems using signatures

Part of: Survival analysis and censored data

Published online by Cambridge University Press:  16 September 2024

T. V. Rao  and
Sameen Naqvi
T. V. Rao*
Affiliation:
Indian Institute of Technology Hyderabad
Sameen Naqvi*
Affiliation:
Indian Institute of Technology Hyderabad
*
*Postal address: Indian Institute of Technology Hyderabad, Hyderabad-502285, India.
*Postal address: Indian Institute of Technology Hyderabad, Hyderabad-502285, India.
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Abstract

The system signature is a useful tool for studying coherent systems. For a given coherent system, various methods have been proposed in the literature to compute its signature. However, when any system signature is given, the literature does not address how to construct the corresponding coherent system(s). In this article we propose an algorithm to address this research gap. This algorithm enables the validation of whether a provided probability vector qualifies as a signature. If it does, the algorithm proceeds to generate the corresponding coherent system(s). To illustrate the applicability of this algorithm, we consider all three and four-dimensional probability vectors, verify if they are signatures, and finally obtain 5 and 20 coherent systems, respectively, which coincides with the literature (Shaked and Suarez-Llorens 2003).

Keywords

Coherent systemsfailure signaturemaximal signatureminimal cut setsprobability vectorsystem signature

MSC classification

Primary: 62N05: Reliability and life testing
Secondary: 62N99: None of the above, but in this section
Type
Original Article
Information
Journal of Applied Probability , First View , pp. 1 - 20
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Copyright
© The Author(s), 2024. Published by Cambridge University Press on behalf of Applied Probability Trust

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