Computations of Signatures of Coherent Systems with Five Components

Abstract

The signatures of coherent systems are useful tools to compute the system reliability functions, the system expected lifetimes and to compare different systems using stochastic orderings. It is well known that there exist 2, 5, and 20 different coherent systems with 2, 3, and 4 components, respectively. The signatures for these systems were given in Shaked and Suarez-Llorens (2003). In this article, we obtain an algorithm to compute all the coherent systems with n components and their signatures. Using this algorithm we show that there exist 180 coherent systems with 5 components and we compute their signatures.

Keywords:

• Coherent systems
• Exponential distribution
• Minimal signature
• Reliability
• Signature

Mathematics Subject Classification:

• 62N05
• 60E15

Acknowledgments

The authors wish to thank the anonymous referee for some comments which led to a significantly improved version of the article.

The first author is partially supported by Ministerio de Ciencia y Tecnología under grant MTM2006-12834.