¹National Huwei Institute of Technology, Huwei, Yunlin, Taiwan

Correspondence: Y-C Hsieh, Department of Industrial Management, National Huwei Institute of Technology, Huwei, Yunlin 632, Taiwan. E-mail: yhsieh@sparc.nhit.edu.tw

Received 1 March 2002; Accepted 1 March 2003.

Abstract

In 1970, Esary and Proschan proposed simple formulae for the system reliability lower bound and system reliability upper bound. Their formulae of reliability bounds have been classic and have been incorporated into almost all recent textbooks on reliability. In this paper, we decompose a coherent system into several consecutive-k-out-of-n : F(G) systems, and then based upon their exact formulae for system reliabilities, we develop new formulae for both reliability lower bound and reliability upper bound for the coherent system. In addition, we show that the new proposed reliability bounds are superior to those of Esary and Proschan for all coherent systems when the minimal cut/path sets have elements in common. Numerical results are reported, compared and discussed for various systems.