Hostname: page-component-586b7cd67f-g8jcs Total loading time: 0 Render date: 2024-11-27T12:18:13.532Z Has data issue: false hasContentIssue false
  • English
  • Français

Estimation for a family of life distributions with applications to fatigue

Published online by Cambridge University Press:  14 July 2016

Z.W. Birnbaum  and
S.C. Saunders
Z.W. Birnbaum
Affiliation:
University of Washington
S.C. Saunders
Affiliation:
Boeing Scientific Research Laboratories, Seattle
Get access Rights & Permissions [Opens in a new window]

Summary

The estimation problem is studied for a new two-parameter family of life length distributions which has been previously derived from a model of fatigue crack growth. Maximum likelihood estimates of both parameters are obtained and iterative computing procedures are given and examined. A simple estimate of the median life is exhibited, shown to be consistent and then compared, favorably, with the maximum likelihood estimate. More important, the asymptotic distribution of this estimate is shown to be within the same class of distributions as the observations themselves. This model, and these estimation procedures, are tried by fitting this distribution to several extensive sets of fatigue data and then some comparisons of practical significance are made.

Type
Research Papers
Information
Journal of Applied Probability , Volume 6 , Issue 2 , August 1969 , pp. 328 - 347
Copyright
Copyright © Sheffield: Applied Probability Trust 

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

[1] Birnbaum, Z. W. and Saunders, S. C. (1969) A new family of life distributions. J. Appl. Prob. 6, 319–327.CrossRefGoogle Scholar
[2] Birnbaum, Z. W. and Saunders, S. C. (1958) A statistical model for life length of material. J. Amer. Statist. Assoc. 53, 151–160.CrossRefGoogle Scholar
[3] Buckland, W. R. (1964) Statistical Assessment of the Life Characteristic. Griffin, London.Google Scholar
[4] Cramer, H. (1951) Mathematical Methods of Statistics. Princeton University Press.Google Scholar
[5] Gumbel, E. J. (1958) Statistics of Extremes. Columbia University Press, New York.CrossRefGoogle Scholar
[6] Parzen, E. (1967) On models for the probability of fatigue failure of a structure. In Time Series Analysis Papers. Holden-Day, San Francisco.Google Scholar