Posbist Reliability Theory for Coherent Systems

Abstract

The conventional reliability theory is built on the probability assumption and the binary-state assumption [1]. It has been successfully used for solving various reliability problems. However, it is not suitable when the failure probabilities concerned are very small (e.g., 10^-7) or when there is a lack of sufficient data. As a result, researchers have been searching for new models and new reliability theories that overcome the shortcomings of the classical probabilistic definition of reliability. Among others, we mention the works by Tanaka et al. [2], Singer [3], Onisawa [4], Cappelle and Kerre [5], Cremona and Gao [6], Utkin and Gurov [7], Cai et al [1, 8, 9], Huang [10-12], and Huang et al [13-18]. All these researchers have attempted to define reliability in terms other than the probabilistic definition. The fuzzy set concept represents a new paradigm of accounting for uncertainty. Two new assumptions in these definitions include the fuzzy-state assumption and the possibility assumption. The fuzzy state assumption indicates that the state of a piece of equipment can be represented by a fuzzy variable. The possibility assumption indicates that the reliability of a piece of equipment needs to be measured subjectively. These two new assumptions have been used in place of the conventional probability and the binary-state assumption.