Performance Analysis of a Complex Robotic System using Fault Tree and Fuzzy Methodology S. P. Sharma1 , N. Sukavanam2 , Naveen Kumar3 and Ajay Kumar4 Indian Institute of Technology Roorkee Roorkee–247 667, INDIA Abstract In this paper, reliability analysis of complex robotic system has been stydied using Petri nets and Fuzzy Lambda-tau methodology. The present work is based on a multi-robotic system, in which two robots are working independently with a conveyer unit. Petri net (PN) is applied to represent the asynchronous and concurrent processing of the system. To enhance the relevance of the reliability study, fuzzy numbers are developed from available data of the components using fuzzy possibility theory to define membership functions. Various reliability parameters (such as MTBF, ENOF, reliability, availability etc.), are computed using Fuzzy Lambda-tau methodology. As the available data is imprecise, incomplete, vague and conflicting, the fuzzy methodology can deal easily with approximations. Finally, the results obtained by Fuzzy Lambda-tau methodology, are compared with those by fault tree.

Key Words: Fuzzy methodology, reliability parameters, linguistic variables and Fault tree.

References [1] B.S. Dhillion and C. Singh Engineering reliability: New techniques and applications, Wiley, New York,1991. [2] B.S. Dhillon, and N. Yang, “Availability analysis of a robot with safety system”, Microelectronics and Reliability, Vol. 36, No. 2, pp. 169-177, 1996. [3] K. Khodabandehloo, “Analysis of robot systems using fault and event trees: Case studies””, Reliability Engineering and System Safety, Vol. 53, No. 3, pp. 247-264, 1996. 1

Department of Department of 3 Department of 4 Corresponding 2

Mathematics, Email: [email protected] Mathematics, Email: [email protected] Mahtmatics, Email:[email protected] author: Department of Mathematics, Email: [email protected]

1

[4] I.D. Walker and J.R. Cavallaro, “The use of fault trees for the design of robots for hazardous environments”, Proceeding of IEEE Annual Reliability and Maintainability Symposium, Las Vegas, NV, USA, pp. 229235,1996. [5] S.B. Stancliff, J.M. Dolan, and A. Trebi-Ollenu, “Mission reliability estimation for repairable robot teams”, International Journal of Advanced Robotic Systems, Vol. 3, No. 2, pp. 155-164, 2006. [6] A. Kumar, S.P. Sharma and D. Kumar, “Robot reliability using Petri Nets and Fuzzy Lambda-Tau Methodology”, Proceeding of 3rd International Conference on Reliability and Safety Engineering, Udaipur, India, pp. 517-521, 2007. [7] K.Y. Cai, “System failure engineering and fuzzy methodology: An introductory overview”, Fuzzy Sets and Systems, Vol. 83, No. 2, pp. 113-133, 1996. [8] I.D. Walker and J.R. Cavailaro, “Failure mode analysis for a hazardous waste clean-up manipulator”, Reliability Engineering and System Safety, Vol. 53, No.3, pp. 277-290, 1996. [9] D. Singer, “A fuzzy set approach to fault tree and reliability analysis”, Fuzzy Sets and Systems, Vol. 34, No. 2, pp. 145-155, 1990. [10] S.M. Chen, “Fuzzy system reliability analysis using fuzzy number arithmetic operations”, Fuzzy Sets and Systems, Vol. 64, No. 1, pp. 3138,1994. [11] C.H. Cheng and D.L. Mon, “Fuzzy system reliability analysis by interval of confidence”, Fuzzy Sets and Systems, Vol. 56, No. 1, pp. 29-35,1993. [12] F. Baccelli, F.N. Serguei and B. Gaujal, “Parallel and distributed simulation of free choice Petri nets”, IEEE Transaction on Automatic Control, Vol. 41, No. 12, pp. 1751-77,1996. [13] A.A. Desrochers and R.Y. Al-Jaar, Applications of Petri Nets in manufacturing systems, IEEE Press, New York, NY,1995. [14] T. Liu, and S. Chiou, “The application of Petri nets to failure analysis”, Reliability Engineering and System Safety, Vol. 57, No. 2, pp. 12942,1997.

2

[15] C.A. Petri, Kommunikation mit Automaten, Bonn: Institut fur lnstrumentelle Mathematik, Schriften des IIM Nr. 3, 1962. Also, English translation, Communication with Automata, New York: Griffiss, Air Force Base.Tech. Rep. RADC-TR-65-377, vol.1, Suppl. 1, 1966. [16] M.L. Leuschen, I.D. Walker and J.R. Cavallaro, “Robot reliability through fuzzy Markov models”, in proceedings of Annual Reliability and Maintainability Symposium, Anaheim, CA, USA, pp. 209-214, 1998. [17] H. Zimmermann, Fuzzy Set Theory and its Applications, third ed., Kluwer Academic Publishers, Norwell, MA, USA, 2000.

3