Non-binary decomposition trees—a method of reliability computation for systems with known minimal paths/cuts

A coherent system with independent components and known minimal paths (cuts) is considered. In order to compute its reliability, a tree structure T is constructed whose nodes contain the modified minimal paths (cuts) and numerical values. The value of a non-leaf node is a function of its child nodesʹ values. The values of leaf nodes are calculated from a simple formula. The value of the root node is the systemʹs failure probability (reliability). Subsequently, an algorithm computing the systemʹs failure probability (reliability) is constructed. The algorithm scans all nodes of T using a stack structure for this purpose. The nodes of T are alternately put on and removed from the stack, their data being modified in the process. Once the algorithm has terminated, the stack contains only the final modification of the root node of T, and its value is equal to the systemʹs failure probability (reliability).