Random Sampling Method For The Importance Measures Of Multi-state System

In system engineering a practical and difficult problem is to identify those components that mostly influence the system behavior with respect to safety and reliability.In this regard,the information provided by importance measures gives useful insights for safe and efficient operation of the system.Indeed,in a wide variety of technological areas importance measures have been shown to allow design engineers tracing the system weakness and figure out the “bottleneck” of the system so as to guide actions for effective system improvement both in the design and in operation.Importance measures have received attention since the early times of risk and reliability analysis and have been defined in several ways based on different probabilistic perspectives and applications for system made up of binary components(i.e.only two possible conditions of the components are considered: functioning or faulty).Yet these early theories of which were developed hypothetically without considering the real problem encountered.In this thesis the definition of the most valuable classical importance measures are generalized to multi-state system constituted by multi-state components and we propose 4 importance measures to judge the relative strength of a component in a multi-state system.The mathematical proof has been given at the same time.Then the traditional analytical approaches and numerical methods have been presented which allows the estimating of all the proposed importance measures in repairable multi-state systems.Finally,this thesis presents a computational framework for implementing an advanced Monte Carlo simulation,called subset simulation for the evaluation of the importance measures in order to increase the efficiency of the numerical simulation when accounting for the small probability problems.The informative content provided by the introduced importance measures as well as the stability and the robustness of the subset simulation has been examined with respect to several multi-state systems.