Importance analysis of multi-state systems based on integrated direct partial logic derivatives

Reliability is very important characteristic of systems. One of the principal tasks of reliability analysis is evaluation of importance of individual system components for the system proper work. This investigation is known as importance analysis, and it can be qualitative or quantitative. The former focuses on identification of situations in which a change of component activity causes that system performance will change. Its results can be used to detect situations in which the component is critical for system failure/degradation or to propose procedures that are necessary for system repair. The main objective of quantitative analysis is to estimate and evaluate influence of a change of component activity on system performance, and its outcomes can be used to plan system maintenance or to optimize system availability. This paper focuses on importance analysis of multistate systems. It introduces new types of logic derivatives and uses them to identify different types of situations in which a system component is critical for system activity. Furthermore, these derivatives are also used to propose a complex framework for quantitative analysis of multi-state systems.