Reversed hazard function of uncertain lifetime

Article
  • 46 Downloads

Abstract

Reversed hazard function is widely applied in reliability analysis. This paper considers the human uncertainty in a system, and employs uncertain variable to model the lifetime of a component. Concepts of mean residual life and residual entropy are proposed to describe a failed system, and their relationships with the reversed hazard function are discussed. In addition, this paper provides some applications of reversed hazard function to the mean past lifetime and past entropy.

Keywords

Uncertain variable Hazard distribution Reversed hazard function 

References

  1. Brito, G., Zequeira, I. R., & Valdés, E. J. (2011). On the hazard rate and reversed hazard rate orderings in two-component series systems with active redundancies. Statistics and Probability Letters, 81, 201–206.MathSciNetCrossRefMATHGoogle Scholar
  2. Dai, W., & Chen, X. W. (2012). Entropy of function of uncertain variables. Mathematical and Computer Modelling, 55(3-4), 754–760.MathSciNetCrossRefMATHGoogle Scholar
  3. Finkelstein, M. (2002). On the reversed hazard rate. Reliability Engineering and System Safety, 78, 71–75.CrossRefGoogle Scholar
  4. Fussell, J. B. (1975). How to hand-calculate system reliability and safety characteristics. IEEE Transactions on Reliability, 24(3), 169–174.CrossRefGoogle Scholar
  5. Gao, R., & Yao, K. (2016). Importance index of components in uncertain random systems. Knowledge-Based Systems, 109, 208–217.CrossRefGoogle Scholar
  6. Gao, Y. (2011). Shortest path problem with uncertain arc lengths. Computers and Mathematics with Applications, 62(6), 2591–2600.MathSciNetCrossRefMATHGoogle Scholar
  7. Gupta, C. R., & Gupta, D. R. (2007). Proportional reversed hazard rate model and its applications. Journal of Statistical Planning and Inference, 137, 525–3536.MathSciNetMATHGoogle Scholar
  8. Kahneman, D., & Tversky, A. (1979). Prospect theory: An analysis of decision under risk. Econometrica, 47(2), 263–292.CrossRefMATHGoogle Scholar
  9. Kang, R., Zhang, Q. Y., Zeng, Z. G., Zio, E., & Li, X. Y. (2016). Measuring reliability under epistemic uncertainty: Review on non-probabilistic reliability metrics. Chinese Journal of Aeronautics, 29(3), 571–579.CrossRefGoogle Scholar
  10. Ke, H., & Yao, K. (2016). Block replacement policy in uncertain environment. Reliability Engineering and System Safety, 148, 119–124.CrossRefGoogle Scholar
  11. Kuo, W., Zhang, W., & Zuo, M. J. (1990). A consecutive k-out-of-n: G system: the mirror image of a consecutive k-out-of-n: F system. IEEE Transactions on Reliability, 39(2), 244–253.CrossRefMATHGoogle Scholar
  12. Li, X. H., Da, G. F., & Zhao, P. (2010). On reversed hazard rate in general mixture models. Statistics and Probability Letters, 80, 654–661.MathSciNetCrossRefMATHGoogle Scholar
  13. Li, X., & Liu, B. (2009). Hybrid logic and uncertain logic. Journal of Uncertain Systems, 3(2), 83–94.MathSciNetGoogle Scholar
  14. Liu, B. (2007). Uncertainty theory (2nd ed.). Berlin: Springer.MATHGoogle Scholar
  15. Liu, B. (2009). Some research problems in uncertainty theory. Journal of Uncertain Systems, 3(1), 3–10.Google Scholar
  16. Liu, B. (2010a). Uncertain risk analysis and uncertain reliability analysis. Journal of Uncertain Systems, 4(3), 163–170.Google Scholar
  17. Liu, B. (2010b). Uncertainty theory: A branch of mathematics for modeling human uncertainty. Berlin: Springer.CrossRefGoogle Scholar
  18. Liu, Y. H., & Ha, M. H. (2010). Expected value of function of uncertain variables. Journal of Uncertain Systems, 4(3), 181–186.Google Scholar
  19. Peng, Z. X., & Iwamura, K. (2010). A sufficient and necessary condition of uncertainty distribution. Journal of Interdisciplinary Mathematics, 13(3), 277–285.MathSciNetCrossRefMATHGoogle Scholar
  20. Qin, Z. F., & Kar, S. (2013). Single-period inventory problem under uncertain environment. Applied Mathematics and Computation, 219(18), 9630–9638.MathSciNetCrossRefMATHGoogle Scholar
  21. Rosyida, I., Peng, J., Chen, L., Widodo, W., Indrati, R., & Sugeng, K. A. (2016). An uncertain chromatic number of an uncertain graph based on alpha-cut coloring. Fuzzy Optimization and Decision Making,.  https://doi.org/10.1007/s10700-016-9260-x.Google Scholar
  22. Yao, K. (2015). A formula to calculate the variance of uncertain variable. Soft Computing, 19(10), 2947–2953.CrossRefMATHGoogle Scholar
  23. Yao, K., & Ralescu, D. A. (2014). Age replacement policy in uncertain environment. Iranian Journal of Fuzzy Systems, 10(4), 1991–1997.MathSciNetGoogle Scholar
  24. Zeng, Z. G., Wen, M. L., & Kang, R. (2013). Belief reliability: A new metrics for products’ reliability. Fuzzy Optimization and Decision Making, 12(1), 15–27.MathSciNetCrossRefGoogle Scholar
  25. Zhang, Z. Q., Ralescu, A. D., & Liu, W. Q. (2016). Valuation of interest rate ceiling and floor in uncertain financial market. Fuzzy Optimization and Decision Making, 15(2), 139–154.MathSciNetCrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2017

Authors and Affiliations

  1. 1.Department of StatisticsUniversity of Sistan and BaluchestanZahedanIran
  2. 2.School of Economics and ManagementHebei University of TechnologyTianjinChina

Personalised recommendations