Calculating system-reliability via the knowledge of structure function is not new. Such attempts have been made in the classical 1975 book by Barlow & Proschan, But they had to compromise with the increasing complexity of a system. This paper overcomes this problem through a new representation of the structure function, and demonstrates that the well-known systems considered in the state-of-art follow this new representation. With this new representation, the important reliability calculations, such as Birnbaum reliability-importance, become simple. The Chaudhuri, et al. (J. Applied Probability, 1991) bounds which exploit the knowledge of structure function were implemented by our simple and easy-to-use algorithm for some s-coherent structures,viz,s-series,s-parallel, 2-out-of-3:G, bridge structure, and a fire-detector system. The Chaudhuri bounds are superior to the Min-max and Barlow-Proschan bounds (1975). This representation is useful in implementing the Chaudhuri bounds, which are superior to the min-max, Barlow & Proschan bounds on the system reliability most commonly used in practice. With this representation of the structure function, the computation of important reliability measures such as the Birnbaum structural and reliability importance are easy. The drawbacks of the Aven algorithm for computing system reliability are that it depends on the initial choice of some parameters, and can not deal with the case when the component survivor functions belong to the IFRA class of life distributions. When the components have IFRA life, then the Chaudhuri bounds could be the best choice for the purpose of predicting reliability of a very complex s-coherent structure. The knowledge of some quantile of the component distributions is enough to obtain the Chaudhuri bounds whereas in order to implement by min-max bounds, a complete description of the component life distributions is required. The Barlow-Proschan bound is not valid for the important part of the system life, and is point-wise, The Chaudhuri bounds do fairly well for the useful part of the system life, and they coincide with the exact system reliability when the components are exponentially distributed. Thus, the use of Chaudhuri bounds is recommended for general use, especially when cost and/or time are critical. The C-H-A algorithm (in this paper) is simple and easy to use. It depends on the knowledge of the path sets of a given structure, Standard software packages are available (CAFTAIN, Hoyland & Rausand, p 145, 1994) to provide the minimal path sets of any s-coherent system. The C-H-A algorithm has been programmed in SAS, S-PLUS, and MATLAB, Different computer codes of the algorithm are available on request from Prof. G. Chaudhuri, This method of predicting system reliability is under patent consideration at Indiana University, USA.
