Table of Contents
International Journal of Quality, Statistics, and Reliability
Volume 2012 (2012), Article ID 847416, 9 pages
Research Article

Reliability Modeling and Optimization Using Fuzzy Logic and Chaos Theory

1Department of Industrial Engineering and Management, Jerusalem College of Technology-Machon Lev, Jerusalem 91160, Israel
2Department of Information Technology and Computer Engineering, Vinnytsia National Technical University, Vinnitsia 21021, Ukraine
3Department of Mechanical Engineering, Afeka-Tel Aviv Academic College of Engineering, Tel Aviv 69107, Israel

Received 6 February 2012; Accepted 3 September 2012

Academic Editor: Satish Bukkapatnam

Copyright © 2012 Alexander Rotshtein et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


Fuzzy sets membership functions integrated with logistic map as the chaos generator were used to create reliability bifurcations diagrams of the system with redundancy of the components. This paper shows that increasing in the number of redundant components results in a postponement of the moment of the first bifurcation which is considered as most contributing to the loss of the reliability. The increasing of redundancy also provides the shrinkage of the oscillation orbit of the level of the system’s membership to reliable state. The paper includes the problem statement of redundancy optimization under conditions of chaotic behavior of influencing parameters and genetic algorithm of this problem solving. The paper shows the possibility of chaos-tolerant systems design with the required level of reliability.