A theory of independent fuzzy probability for system reliability

J. Dunyak, I.W. Saad, D. Wunsch
1999 IEEE transactions on fuzzy systems  
Fuzzy fault trees provide a powerful and computationally efficient technique for developing fuzzy probabilities based on independent inputs. The probability of any event that can be described in terms of a sequence of independent unions, intersections, and complements may be calculated by a fuzzy fault tree. Unfortunately, fuzzy fault trees do not provide a complete theory: many events of substantial practical interest cannot be described only by independent operations. Thus, the standard fuzzy
more » ... extension (based on fuzzy fault trees) is not complete since not all events are assigned a fuzzy probability. Other complete extensions have been proposed, but these extensions are not consistent with the calculations from fuzzy fault trees. In this paper, we propose a new extension of crisp probability theory. Our model is based on n n n independent inputs, each with a fuzzy probability. The elements of our sample space describe exactly which of the n n n input events did and did not occur. Our extension is complete since a fuzzy probability is assigned to every subset of the sample space. Our extension is also consistent with all calculations that can be arranged as a fault tree. Our approach allows the reliability analyst to develop complete and consistent fuzzy reliability models from existing crisp reliability models. This allows a comprehensive analysis of the system. Computational algorithms are provided both to extend existing models and develop new models. The technique is demonstrated on a reliability model of a three-stage industrial process.
doi:10.1109/91.771085 fatcat:fb3qx5wuvneihfs6xkbzuk4pgq