Probabilistic Analysis of a Robot System with Redundant Safety Units and Common-Cause Failures
ABSTRACT
This paper presents reliability and availability analyses of a model representing a system having one robot and n-redundant safety units with common-cause failures. At least k safety units must function successfully for the robot system success. The robot and other failure rates and the partially failed system repair rates are assumed constant and the failed robot-safety system repair time is assumed arbitrarily distributed. Markov and supplementary variable methods were used to perform mathematical analysis of this model. Generalized expressions for state probabilities, system availabilities, reliability, mean time to failure, and variance of time to failure are developed. Plots of some resulting expressions are shown.
This paper presents reliability and availability analyses of a model representing a system having one robot and n-redundant safety units with common-cause failures. At least k safety units must function successfully for the robot system success. The robot and other failure rates and the partially failed system repair rates are assumed constant and the failed robot-safety system repair time is assumed arbitrarily distributed. Markov and supplementary variable methods were used to perform mathematical analysis of this model. Generalized expressions for state probabilities, system availabilities, reliability, mean time to failure, and variance of time to failure are developed. Plots of some resulting expressions are shown.
KEYWORDS
robot, safety, availability, reliability, common-cause failures, failure, repair, redundancy
robot, safety, availability, reliability, common-cause failures, failure, repair, redundancy
Cite this paper
nullB. DHILLON and Z. LI, "Probabilistic Analysis of a Robot System with Redundant Safety Units and Common-Cause Failures," Intelligent Information Management, Vol. 1 No. 3, 2009, pp. 150-158. doi: 10.4236/iim.2009.13022.
nullB. DHILLON and Z. LI, "Probabilistic Analysis of a Robot System with Redundant Safety Units and Common-Cause Failures," Intelligent Information Management, Vol. 1 No. 3, 2009, pp. 150-158. doi: 10.4236/iim.2009.13022.
References
[1] P. Nicolaisen, “Safety problems related to robots,” Robotics, Vol. 3, pp. 205–211, 1987. [2] M. Nagamachi, “Ten fatal accidents due to robots in Japan,” in Ergonomics of Hybird Automated Systems I, eds. H. R. Karwowski and M. R. Parsaei, Elsevier, Amsterdam, pp. 391–396, 1988. [3] B. S. Dhillon, “Robot reliability and safety,” Springer- Verlag, New York, 1991. [4] J. Fryman, “Future expectations in international robot safety,” Robotic World, Vol. 24, No. 2, pp. 12–13, 2006. [5] S. Neil, “Improving robot safety, managing automation,” Vol. 18, No. 10, pp. 18–21, 2003. [6] D. Kulic and E. Croft, “Pre-collision safety strategies for human-robot interaction,” Autonomous Robots, Vol. 22, No. 2, pp. 149–164, 2007. [7] E. J. Vanderperre and S. S. Makhanov, “Overall availability of a robot with internal safety device,” Computers and Industrial Engineering, Vol. 56, No. 1, pp. 236–240, 2009. [8] S. Haddadin, S. A. Albu-SuchaCurrency, and G. Hirzinger, “Requirements for safe robots: measurements, analysis and new insights,” International Journal of Robotics, Vol. 28, No. 11–12, pp. 1507–1527, 2009. [9] J. P. Merlet, “Interval analysis and reliability in robotics,” International Journal of Reliability and Safety, Vol. 3, No. 1–3, pp. 104–130, 2009. [10] B. S. Dhillon and S. Cheng, “Probabilistic analysis of a repairable robot-safety system composed of (n-1) standby robots, A Safety Unit, and a Switch,” Journal of Quality in Maintenance Engineering, Vol. 14, No. 3, pp. 306–323, 2009. [11] B. S. Dhillon, “Reliability engineering in systems design and operation,” Van Nostrand Reinhold, New York, 1983. [12] D. P. Gaver, “Time to failure and availability of paralleled systems with repair,” IEEE Transactions on Reliability, Vol. 12, pp. 30–38, 1963. [13] R. C. Grag, “Dependability of a complex system having two types of components,” IEEE Transactions on Reliability, Vol. 12, pp. 11–15, 1963. [14] B. S. Dhillon, “Design reliability: fundamentals and applications,” CRC Press, Boca Raton, Florida, 1999. [15] R. M. Corless, “Essential MAPLE: An introduction to scientific programmers,” Springer–Verlag, New York, 1995.
[1] P. Nicolaisen, “Safety problems related to robots,” Robotics, Vol. 3, pp. 205–211, 1987. [2] M. Nagamachi, “Ten fatal accidents due to robots in Japan,” in Ergonomics of Hybird Automated Systems I, eds. H. R. Karwowski and M. R. Parsaei, Elsevier, Amsterdam, pp. 391–396, 1988. [3] B. S. Dhillon, “Robot reliability and safety,” Springer- Verlag, New York, 1991. [4] J. Fryman, “Future expectations in international robot safety,” Robotic World, Vol. 24, No. 2, pp. 12–13, 2006. [5] S. Neil, “Improving robot safety, managing automation,” Vol. 18, No. 10, pp. 18–21, 2003. [6] D. Kulic and E. Croft, “Pre-collision safety strategies for human-robot interaction,” Autonomous Robots, Vol. 22, No. 2, pp. 149–164, 2007. [7] E. J. Vanderperre and S. S. Makhanov, “Overall availability of a robot with internal safety device,” Computers and Industrial Engineering, Vol. 56, No. 1, pp. 236–240, 2009. [8] S. Haddadin, S. A. Albu-SuchaCurrency, and G. Hirzinger, “Requirements for safe robots: measurements, analysis and new insights,” International Journal of Robotics, Vol. 28, No. 11–12, pp. 1507–1527, 2009. [9] J. P. Merlet, “Interval analysis and reliability in robotics,” International Journal of Reliability and Safety, Vol. 3, No. 1–3, pp. 104–130, 2009. [10] B. S. Dhillon and S. Cheng, “Probabilistic analysis of a repairable robot-safety system composed of (n-1) standby robots, A Safety Unit, and a Switch,” Journal of Quality in Maintenance Engineering, Vol. 14, No. 3, pp. 306–323, 2009. [11] B. S. Dhillon, “Reliability engineering in systems design and operation,” Van Nostrand Reinhold, New York, 1983. [12] D. P. Gaver, “Time to failure and availability of paralleled systems with repair,” IEEE Transactions on Reliability, Vol. 12, pp. 30–38, 1963. [13] R. C. Grag, “Dependability of a complex system having two types of components,” IEEE Transactions on Reliability, Vol. 12, pp. 11–15, 1963. [14] B. S. Dhillon, “Design reliability: fundamentals and applications,” CRC Press, Boca Raton, Florida, 1999. [15] R. M. Corless, “Essential MAPLE: An introduction to scientific programmers,” Springer–Verlag, New York, 1995.