Bounding the times to failure of 2-component systems

IEEE Transactions on Reliability

Volumn 53, Issue 4, 2004, Pages 542-550

  Berleant, Daniel ^a   Zhang, Jianzhong ^a  

^a Iowa State University   (United States)

Author keywords

Cdf envelopes; DEnv; Dependency bounds; Functions of random variables; Model uncertainty; Uncertainty quantification

Indexed keywords

CORRELATION METHODS; FAILURE ANALYSIS; MATHEMATICAL MODELS; PROBABILITY DENSITY FUNCTION; PROBABILITY DISTRIBUTIONS; RANDOM PROCESSES; SYSTEMS ANALYSIS;

CUMULATIVE DISTRIBUTION FUNCTION; DEPENDENCY BOUNDS; MODEL UNCERTAINTY; UNCERTAINTY QUANTIFICATION;

RELIABILITY THEORY;

EID: 10244246566     PISSN: 00189529     EISSN: None     Source Type: Journal    
DOI: 10.1109/TR.2004.837315     Document Type: Article

References (21)

1. D. Berleant, "Automatically verified reasoning with both intervals and probability density functions," Interval Computations, no. 2, pp. 48-70, 1993.
2. D. Berleant and C. Goodman-Strauss, "Bounding the results of arithmetic operations on random variables of unknown dependency," Reliable Computing, vol. 4, no. 2, pp. 147-165.
3. D. Berleant et al., "Statool: a tool for Distribution Envelope Determination (DEnv), an interval-based algorithm for arithmetic on random variables," Reliable Computing, vol. 9, no. 2, pp. 91-108, 2003.
4. D. Berleant and J. Zhang. Using correlation to improve envelopes around derived distributions. Reliable Computing [Online] http:// class.ee. iastate.edu/berleant/home/
5. D. Berleant, Representation and problem solving with the Distribution Envelope Determination (DEnv) method. Reliability Engineering and System Safety [Online] http://class.ee.iastate.edu/berleant/home/
6. C. Bunea and T. Bedford, "The effect of model uncertainty on maintenance optimization," IEEE Trans. Rel., vol. 51, pp. 486-493, Dec. 2002.
7. C. Carreras and I. D. Walker, "Interval methods for fault-tree analysis in robotics," IEEE Trans. Rel., vol. 50, pp. 3-11, Mar. 2001.
8. A. G. Colombo and R. J. Jaarsma, "A powerful numerical method to combine random variables," IEEE Trans. Rel., vol. R-29, pp. 126-129, June 1980.
9. J. A. Cooper, S. Ferson, and L. R. Ginzburg, "Hybrid processing of stochastic and subjective uncertainty data," Risk Analysis, vol. 16, no. 6, pp. 785-791, 1996.
10. R. A. Evans, "Point estimates - no; interval estimates - yes," IEEE Trans. Rel., vol. 51, p. 258, Sept. 2002.
11. S. Ferson, RAMAS Risk Calc 4.0: Risk Assessment With Uncertain Numbers. Boca Raton: Lewis Press, 2002.
12. S. Ferson, "What Monte Carlo cannot do," Human and Environmental Risk Assessment, vol. 2, pp. 990-1007, Dec. 1996.
13. M. J. Frank et al., "Best-possible bounds for the distribution of a sum - a problem of Kolmogorov," Probability Theory and Related Fields, vol. 74, pp. 199-211, 1987.
14. J. Hall and J. Lawry. Generation, combination and extension of random set approximations to coherent lower and upper probabilities. Reliability Engineering and System Safety [Online] http:// www.cen.bris.ac.uk/civil/staff/jwh/Publications/publications.html
15. G. E. Ingram, E. L. Welker, and C. R. Herrmann, "Designing for reliability based on probabilistic modeling using remote access computer systems," in Proc. 7th Reliability and Maintainability Conf., American Society of Mechanical Engineers, 1968, pp. 492-500.
16. S. Kaplan, "On the method of discrete probability distributions in risk and reliability calculations - application to seismic risk assessment," Risk Analysis, vol. 1, no. 3, pp. 189-196, 1981.
17. R. B. Nelsen, "An introduction to copulas," in Lecture Notes in Statistics. Heidelberg: Springer-Verlag, 1999, vol. 139.
18. H. Regan, S. Ferson, and D. Berleant. Equivalence of methods for uncertainty propagation of real-valued random variables. Int. J. Approximate Reasoning [Online]. http://class.ee.iastate.edu/berleant/ home/
19. J. K. Vaurio, "Treatment of general dependencies in system fault-tree and risk analysis," IEEE Trans. Rel., vol. 51, pp. 278-287, Sept. 2002.
20. R. Williamson and T. Downs, "Probabilistic arithmetic I: numerical methods for calculating convolutions and dependency bounds," Int. J. Approximate Reasoning, vol. 4, pp. 89-158, 1990.
21. T. Zhang and M. Horigome, "Availability and reliability of system with dependent components and time-varying failure and repair rates," IEEE Trans. Rel., vol. 50, pp. 151-158, June 2001.