Recursive Disjoint Products, Inclusion-Exclusion, and Min-Cut Approximations

Abstract

Three different ways to estimate the reliability of an s-coherent system are compared: 1) recursive disjoint products (DP), 2) recursive inclusion-exclusion (IE), and 3) minimal-cut approximations based on partial information. The following three points are made. 1. Recursive DP and recursive IE are mathematically identical and obtain the same numerical values at each step of the recursion, although the recursive system-reliability functions are different. 2. Recursive DP seems to result in fewer comparisons and a shorter polynomial than recursive IE, and therefore also less work, for small scale systems, such as the 2-out-of-4:G example discussed herein. I do not yet know if this comparative advantage persists for larger systems. 3. For complex highly reliable systems, min-cut approximations based on partial information, that sacrifice some accuracy for convenience and ease of computation are preferable to min-path exact methods since the approximations come very close to the true value of the reliability with comparably little effort, in some cases requiring only hand calculations.