Computations of Signatures of Coherent Systems with Five Components

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 Shaked , M. , Suarez-Llorens , A. ( 2003 ). On the comparison of reliability experiments based on the convolution order . Journal of the American Statistical Association 98 : 693 – 702 .[Taylor & Francis Online], [Web of Science ®] , [Google Scholar]). 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.