Fuzzy Reliability Analysis Of Multi-State System

This thesis addresses the problem of fuzzy reliability for Multi-State System (MSS), which is a branch of fuzzy reliability theory. It deals with those systems for which one cannot formulate an "all or nothing" type of failure criterion. Such systems are able to perform their task with partial performance. The aim of the thesis is to develop a framework to analyze the reliabilities of such systems.Instead of traditional binary reliability theory, The fuzzy reliability theory is introduced into the analysis of reliability for MSS, which is devoted to many real-world systems which are composed of multi-state components that have different performance levels or several failure modes.The thesis is focused on the fuzzy reliability of MSS and contains the following contents:(1) The shortages of traditional binary state reliability theory are analyzed, the model of the reliability for MSS is built and fuzzy reliability is developed. Besides the basic models for calculating the reliabilities of some kind of MSS are studied.(2) Based on the MSS reliability theory and fuzzy reliability theory, basic methods for MSS reliability assessment, such as an extension of the Boolean method, basic random process, and the universal generating function model are systematically studied. Furthermore the models for calculating the fuzzy reliability of the repairable and non-repairable MSS are developed. A new method is proposed to calculate the reliability of a kind of dominant MSS.(3) The fuzzy reliability of the anti-wear of the component in mechanical system is studied, and that of gear is specially emphasized. A numerical model imitating the process of gear wear is proposed based on double cube Non-Uniform Rational B-Spline. Finally a formula to calculate the fuzzy reliability in gear transmission is deduced.Since the MSS reliability theory and the fuzzy reliability theory are studied primarily, the most efforts in this field are still devoted into the developing of the framework. The author tries to build the model of fuzzy reliability for MSS and find a feasible method for calculating the reliability. Much more efforts should be attached to this topic.