Based On Possibility Theory Of Fuzzy Reliability Design

Fuzzy reliability theory based on possibility theory (i.e., possibilistic reliability theory), one of the important domains of fuzzy reliability theory, is studied in the present dissertation.Possibility theory is initiated in 1978 by L. A. Zadeh, a famous American cybernetics expert. The foundation of possibility theory provides a theoretical framework for practical applications of fuzzy set theory. Fuzzy reliability theory based on possibility theory is that: possibility measure instead of probability measure in probability reliability theory is used to attempt to solve some problems that are difficult, or impossible to solve with probability reliability theory, e.g., some complex systems or new products of which necessary statistical data are scarce, some components of which failure probabilities are very small, linguistic information and human error, etc.The main research content consists of two parts. The first part is mostly based on posbist reliability theory by Cai, as follows:(1) The construction of possibility distribution, which is the first fundamental issue associated with applications of the possibilistic reliability theory, is studied. It is presented that all methods developed for generating membership functions can be used to construct relevant possibility distributions. At the same time, the principles and the methods for constructing possibility distributions are summarized. Finally, A method used to generate the L - R type possibility distribution is provided combined with the possibilistic reliability analysis of fatigue of mechanical parts.(2) A detailed analysis of the posbist reliability of typical system structures is provided.The universe of discourse is expanded from(0,+∞) to (-∞,+∞), thus, the models of posbistreliability of typical systems are simplified. On the basis of this, expressions of the posbist reliability of typical system structures including series, parallel, series-parallel, parallel-series. and cold standby systems are developed and Cai's important work in this field is extended.(3) Event failure behavior is characterized in the context of possibility measures and a model of posbist fault tree analysis of coherent systems is presented. The model provides a new feasible approach for the practical application of posbist reliability theory.In the second part, a method of structural possibilistic reliability is discussed. A newtopology |U|_∞ = sup|U₁| as the new state space or variaoies, is introaucea toEuclidean space, and the failure behavior of structures is characterized in the context of possibility measures rather than probability measures.