×

Moment-independent importance measure of basic random variable and its probability density evolution solution. (English) Zbl 1383.60005

Summary: To analyze the effect of basic variable on failure probability in reliability analysis, a moment-independent importance measure of the basic random variable is proposed, and its properties are analyzed and verified. Based on this work, the importance measure of the basic variable on the failure probability is compared with that on the distribution density of the response. By use of the probability density evolution method, a solution is established to solve two importance measures, which can efficiently avoid the difficulty in solving the importance measures. Some numerical examples and engineering examples are used to demonstrate the proposed importance measure on the failure probability and that on the distribution density of the response. The results show that the proposed importance measure can effectively describe the effect of the basic variable on the failure probability from the distribution density of the basic variable. Additionally, the results show that the established solution on the probability density evolution is efficient for the importance measures.

MSC:

60A10 Probabilistic measure theory
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] Satelli A. Sensitivity analysis for importance assessment. Risk Anal, 2002, 22(3): 579–590 · doi:10.1111/0272-4332.00040
[2] Iman R L, Hora S C. A robust measure of uncertainty importance for use in fault tree system analysis. Risk Anal, 1990, 10(3): 401–406 · doi:10.1111/j.1539-6924.1990.tb00523.x
[3] Satelli A. Sensitivity analysis for importance assessment. Risk Anal, 2002, 22(3): 579–590 · doi:10.1111/0272-4332.00040
[4] Helton J C, Davis F J. Latin hypercube sampling and the propagation of uncertainty in analysis of complex systems. Reliab Eng Syst Safe, 2003, 81(1): 23–69 · doi:10.1016/S0951-8320(03)00058-9
[5] Chun M H, Han S J, Tak, N I. An uncertainty importance measure using a distance metric for the change in a cumulative distribution function. Reliab Eng Syst Safe, 2007, 70: 313–321 · doi:10.1016/S0951-8320(00)00068-5
[6] Borgonovo E. A new uncertainty importance measure. Reliab Eng Syst Safe, 2007, 92(6): 771–784 · doi:10.1016/j.ress.2006.04.015
[7] Li J, Chen J B. The probability density evolution analysis of stochastic dynamic system. Prog Nat Sci, 2003, 16(6): 712–719 · doi:10.1080/10020070312331344290
[8] Li J, Chen J B, Fan W L. The equivalent extreme-value event and evaluation of the structural system reliability (in Chinese). Struct safe, 2007, 29(2): 112–131 · doi:10.1016/j.strusafe.2006.03.002
[9] Zhang T F. Computational Fluid Dynamics (in Chinese). 2nd ed. Dalian: Dalian University of Technology Press, 2007. 32–39
[10] Chen J B, Li J. Strategy of selecting points via number theoretical method in probability density evolution analysis of stochastic response of structure (in Chinese). Acta Mech Sin, 2006, 38(1): 134–140
[11] Hua L K, Wang Y. Applications of Number Theory to Numerical Analysis (in Chinese). Beijing: Science Press, 1978. 209–229
[12] Lu Z Z, Liu C L, Yue Z F. Probabilistic safe analysis of the working life of a powder-metallurgy turbine disk. Mater Sci Eng A, 2005, 395(1–2): 153–159 · doi:10.1016/j.msea.2004.12.008
[13] Liang C T, Yang C Y. Multi-linage mechanism optimization design of double acting compressor (in Chinese). J Shanxi Inst Mech Eng, 1986, (3): 13–21
[14] Heng S Q, Wang S. Structure Reliability Analysis and Design (in Chinese). Beijing: National Defence Industry Press, 1993. 104–120
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.