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Weibull or Lognormal Distribution to Characterize Fatigue Life Scatter – Which is More Suitable? – Continued Cover

Weibull or Lognormal Distribution to Characterize Fatigue Life Scatter – Which is More Suitable? – Continued

Fatigue of Aircraft Structures
Volume 2024 (2024): Issue 16 (December 2024)
By: Rob Plaskitt,  Chris Wynn-Jones and  Andrew Halfpenny  
Open Access
|Jul 2025

Figures & Tables

Figure 1.

Lognormal and 3-parameter Weibull distribution of Schijve dataset fatigue test results a) reproduced from Schijve (2009, figure 12.3), and b) reanalysis for this paper.
Lognormal and 3-parameter Weibull distribution of Schijve dataset fatigue test results a) reproduced from Schijve (2009, figure 12.3), and b) reanalysis for this paper.

Figure 2.

2-parameter Weibull distribution of Schijve dataset fatigue test results a) reproduced from Brot (2017, figure 18), and b) reanalysis for this paper.
2-parameter Weibull distribution of Schijve dataset fatigue test results a) reproduced from Brot (2017, figure 18), and b) reanalysis for this paper.

Figure 3.

Lognormal distribution of Schijve dataset fatigue test results a) reproduced from Brot (2017, figure 19), and b) reanalysis for this paper.
Lognormal distribution of Schijve dataset fatigue test results a) reproduced from Brot (2017, figure 19), and b) reanalysis for this paper.

Figure 4.

Lognormal and Weibull distribution of Schijve dataset fatigue test results a) with 3-parameter Weibull as used in Schijve analysis (2009), and b) with 2-parameter Weibull as used in Brot analysis in (2017).
Lognormal and Weibull distribution of Schijve dataset fatigue test results a) with 3-parameter Weibull as used in Schijve analysis (2009), and b) with 2-parameter Weibull as used in Brot analysis in (2017).

Figure 5.

Lognormal and 2- and 3-parameter Weibull distributions of HBK dataset (logarithmic x-axis with numbers excluded to maintain data confidentiality).
Lognormal and 2- and 3-parameter Weibull distributions of HBK dataset (logarithmic x-axis with numbers excluded to maintain data confidentiality).

Figure 6.

Lognormal and 2- and 3-parameter Weibull distributions of HBK dataset with confidence bounds for the lower tail of the distributions between 0.01% and 50% (logarithmic x-axis with numbers excluded to maintain data confidentiality).
Lognormal and 2- and 3-parameter Weibull distributions of HBK dataset with confidence bounds for the lower tail of the distributions between 0.01% and 50% (logarithmic x-axis with numbers excluded to maintain data confidentiality).

Fatigue test results in Kilo Cycles (specimen number)_

636 (13G)1160 (13J)1461 (12F)
707 (13H)1167 (12H)1511 (13C)
801 (13K)1262 (13A)2119 (12C)
1038 (12K)1265 (13B)2132 (13D)
1090 (13E)1404 (12G)2158 (12D)
1102 (12J)1418 (13F)2368 (12E)

Extrapolated fatigue life normalised to γ (gamma) at probability of failure (reliability)_

% Probability of failure (% reliability)Lognormal2-parameter Weibull3-parameter Weibull
1% (99%)1.3830.7861.293
0.1% (99.9%)0.5840.1301.029
0.01% (99.99%)0.2880.0221.003
0.001% (99.999%)0.1550.0041.000
0.0001% (99.9999%)0.0890.0011.000

Extrapolated fatigue life (Kilo Cycles) at probability of failure at 0_01% (=99_99% reliability)_

DistributionFigure 2a distribution fitFigure 2b distribution fit
Weibull8686.3
Lognormal300303.4

Extrapolated fatigue life normalised to γ(gamma) at probability of failure (reliability)_

% Probability of failure (% reliability)Lognormal2-parameter Weibull3-parameter Weibull
1% (99%)1.0360.7231.157
0.1% (99.9%)0.7700.3521.044
0.01% (99.99%)0.6030.1711.013
0.001% (99.999%)0.4870.0841.004
0.0001% (99.9999%)0.4030.0411.001

Extrapolated fatigue life (Kilo Cycles) at probability of failure (reliability)_

% Probability of failure (% reliability)Lognormal2-parameter Weibull3-parameter Weibull γ (gamma) = 503.4
1% (99%)521.7363.8582.5
0.1% (99.9%)387.5177.1525.7
0.01% (99.99%)303.486.3509.7
0.001% (99.999%)245.342.1505.2
0.0001% (99.9999%)202.820.5503.9
DOI: https://doi.org/10.2478/fas-2024-0011 | Journal eISSN: 2300-7591 | Journal ISSN: 2081-7738
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Language: English
Page range: 131 - 146
Published on: Jul 7, 2025
Published by: ŁUKASIEWICZ RESEARCH NETWORK – INSTITUTE OF AVIATION
In partnership with: Paradigm Publishing Services
Publication frequency: 1 issue per year
Keywords:
Fatigue life scatter,
Weibull,
lognormal,
statistical distributions
Related subjects:
Engineering,
Introductions and overviews,
Engineering, other

© 2025 Rob Plaskitt, Chris Wynn-Jones, Andrew Halfpenny, published by ŁUKASIEWICZ RESEARCH NETWORK – INSTITUTE OF AVIATION
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

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