Importance and sensitivity analysis of multi-state systems using the universal generating function method

A method for the evaluation of element reliability importance in a multi-state system is proposed. The method is based on the universal generating function technique. It provides an effective importance analysis tool for complex series–parallel multi-state systems with a different physical nature of performance and takes into account a required performance (demand). The method is also extended for the sensitivity analysis of important multi-state system output performance measures: mean system performance and mean unsupplied demand during operating period. Numerical examples are given.