Reliability of multi-state systems with various dependency structures between components

In recent years, the universal generating function (UGF) technique has gained widespread application in the analysis of multi-state system (MSS) reliability. This approach enables the derivation of the complete performance distribution of an MSS by employing algebraic procedures on the performance distributions of its individual components. In this paper, the existing UGF approach for systems with independent components is further extended for systems with components having different preceding components’ memory (PCM). Based on the derived UGF, we obtain the reliability of the system. Moreover, we provide algorithms corresponding to the developed methodologies, and demonstrate the same through several numerical examples.