Reliability of two-stage weighted-k-out-of-n systems with components in common

This paper extends the existing one-stage weighted-k-out-of-n model to two-stage weighted-k-out-of-n models with components in common. Algorithms are developed to calculate the system reliability, and generate the minimal cuts & minimal paths of two-stage weighted-k-out-of-n systems. Reliability bounds for systems with s-dependent component failures are investigated based on the generated minimal cuts & minimal paths. Two types of two-stage weighted-k-out-of-n models, the SW-k-out-of-n model, and the PW-k-out-of-n model, can be applied to investigate reliability issues in network applications, such as the project management, and the shortest path problems. Examples are provided to demonstrate the developed models & algorithms.