Hostname: page-component-78c5997874-4rdpn Total loading time: 0 Render date: 2024-11-10T23:19:31.075Z Has data issue: false hasContentIssue false
  • English
  • Français

Study of Hazard Rate Functions on the Cumulative Damage Phenomenon

Published online by Cambridge University Press:  31 March 2011

K. S. Wang
K. S. Wang*
Affiliation:
Department of Mechanical Engineering, National Central University Jhongli, Taiwan 32001, R.O.C.
*
*Chair Professor, corresponding author
Get access

Abstract

In this paper different failure mechanisms which yield cumulative damage are investigated through two types of hazard rate functions. They have been studied during the past two decades. Type A was developed early by assuming the hazard rate as a function of reliability. There are two kinds of trend, one follows the negative logistic decay model, the other the negative Gompertz decay. Some modifications are suggested according to the failure tendency and convenience of fittings. Type B is developed recently by assuming the hazard rate as a function of the expected operation time, T, which is defined as the integration of reliability over the time, normalized by the mean-time-between-failure. In both types the proposed hazard rates grow with the time monotonically. Typical examples are taken to examine these models, meanwhile the comparisons with the Weibull-typed distribution are also made. The results show that the most of proposed relations are successful in the expression of cumulative damage phenomenon, especially the Type B is a better choice even compared with the Weibull-typed description in some respects. The advantages of the models are discussed based on the physical meanings involved in the parameters.

Keywords

Hazard rate functionCumulative damage
Type
Articles
Information
Journal of Mechanics , Volume 27 , Issue 1 , March 2011 , pp. 47 - 55
Copyright
Copyright © The Society of Theoretical and Applied Mechanics, R.O.C. 2011

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

1.Rao, S. S., Reliability-Based Design, McGraw-Hill, Inc., New York (1993).Google Scholar
2.Wang, K. S., Chang, S. T. and Shen, Y. C., “Dynamic Reliability Models for Fatigue Crack Growth Problem,” Engineering Fracture Mechanics, 54, pp. 543–556 (1996).CrossRefGoogle Scholar
3.Wang, K. S., Wan, E. H. and Yang, W. C., “A Preliminary Investigation of New Mechanical Product Development Based on Reliability Theory,” Reliability Engineering & System Safety, 40, pp. 187–194 (1993).CrossRefGoogle Scholar
4.Wang, K. S., Hsu, F. S. and Liu, P. P., “Modeling the Bathtub Shape Hazard Rate Function in Terms of Reliability,” Reliability Engineering & System Safety, 75, pp. 397–406 (2002).CrossRefGoogle Scholar
5.Wang, K. S., Hsu, F. S. and Chang, H. L., “Investigation of Cumulative Damage Based on the Reliability,” Journal of Mechanics, 16, pp. 131–139 (2000).Google Scholar
6.Wang, K. S., Chen, C. S. and Huang, J. J., “Dynamic Reliability Behavior for Sliding Wear of Carburized Steel,” Reliability Engineering & System Safety, 58, pp. 31–41 (1997).CrossRefGoogle Scholar
7.Wang, K. S., Lin, W. S. and Hsu, F. S., “A New Approach for Determining the Reliability of Cutting Tool,” The International Journal of Advanced Manufacturing Technology, 17, pp. 705–709 (2001).CrossRefGoogle Scholar
8.Wang, K. S. and Shen, Y. C., “Fatigue Life Prediction for Metal Constant Average Stress,” Journal of Mechanics, 13, pp. 245–254 (1997).Google Scholar
9.Shen, Y. C., “Investigation of Metal Fatigue Based on Reliability,” Department of Mechanical Engineering, National Central University, R.O.C., Master's Thesis (1999).Google Scholar
10.Chen, C. L., Tsai, Y. T. and Wang, K. S., “Characteristics of Reliability-Dependent Hazard Rate for Composites Under Fatigue Loading,” Journal of Mechanics, 25, pp. 195–203 (2009).CrossRefGoogle Scholar
11.Wang, K. S., Liu, W. E., Yang, Y. H. and Chen, C. L., “Investigation of Hazard Rate as a Constant Difference and Constant Ratio of Reliability,” The 32-nd National Conference of Chinese Society of Mechanical Engineering, R.O.C. (2008).Google Scholar
12.Wang, K. S., Shih, E. C., Pao, H. R. and Shen, Y. C., “Comparison of Cumulative Failure Rate with Weibull-typed Distribution,” National Conference of Mechanics, Taiwan, F027 (2000).Google Scholar
13.Davis, D. J., “An Analysis of Some Failure Data,” Journal of the American Statistical Association, 47, pp. 113–150 (1952).CrossRefGoogle Scholar
14.Winsor, C. P., “The Gompertz Curve as a Growth Curve,” Proceedings of the National Academy of Sciences, 18, pp. 1–8 (1932).CrossRefGoogle ScholarPubMed
15.France, P. W., Duncan, W. J., Smith, D. J. and Beales, K. J., “Strength and Fatigue of Multi-component Optical Glass Fibers,” Journal of Materials Science, 18, pp. 785–792 (1983).CrossRefGoogle Scholar
16.Liu, W. E., “Investigation of Different Types of Hazard Rates as a Function of Reliability,” Department of Mechanical Engineering, National Central University, R.O.C., Master's Thesis (2008).Google Scholar
17.Maor, E., e: The Story of a Number, princeton university press, U.S.A. (1994).Google Scholar
18.Wang, K. S., Guo, S. Y. and Yang, Y. H., “The Study of Hazard Rate Function with Cumulative Damage,” The 26th National Conference of Chinese Mechanical Engineering, Taiwan, B05–002 (2009).Google Scholar
19.Kapur, K. C. and Lamberson, L. R., Reliability in Engineering Design, John Wiley & Sons, New York (1977).Google Scholar
20.Chen, C. L. and Wang, K. S., “Effects of Fatigue Loading Adjustment on the Dynamical Reliability of Composite,” 2010 International Conference on Risk and Reliability Management, Beijing, China.Google Scholar