## Computations of signatures of coherent systems with five components.(English)Zbl 1183.62178

Summary: 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 by M. Shaked and A. Suarez-Llorens [J. Am. Stat. Assoc. 98, No. 463, 693–702 (2003; Zbl 1040.62093)]. 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.

### MSC:

 62N05 Reliability and life testing 65C60 Computational problems in statistics (MSC2010) 60E15 Inequalities; stochastic orderings 62Q05 Statistical tables

Zbl 1040.62093
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### References:

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