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Statistics after E739

ASTM E739, the guide for statistical analysis of linearized stress-life and strain-life data, was withdrawn in January 2024 with no published replacement. The active ASTM replacement effort, work item WK88010, states why: the legacy methods cannot handle censored data, runouts, or nonlinear regression. Its technical basis is the maximum-likelihood framework of Meeker, Escobar, Pascual and coauthors, arXiv:2212.04550.

lcf-strain-life implements both layers and says which is which.

The classical layer

Everything the withdrawn E739 and common design practice prescribe:

  • The linearized regression with life as the dependent variable, \(\log_{10} N = A + B \log_{10}(\varepsilon_a)\), fit_log_life.
  • Confidence and prediction intervals on the fitted line.
  • The lack-of-fit F test when replicate levels exist.
  • One-sided tolerance design curves, mean minus k times sigma with the exact Owen factor, design_life, and MMPDS-style A and B basis values.
  • Outlier screening, Grubbs and generalized ESD, with influence diagnostics.
  • Staircase fatigue-limit analysis, Dixon-Mood per ISO 12107.

These remain correct for complete samples inside the tested interval, and E739's own caveat is enforced: predictions outside the fitted amplitude range carry an extrapolation warning.

The maximum-likelihood layer

What the replacement effort points to, implemented and labeled:

Censored fits that keep runouts

fit_log_life_censored fits the same line by maximum likelihood. Observed failures contribute the density, runouts contribute the survival probability. Nothing is deleted. The life scatter is lognormal by default, Weibull, smallest extreme value on log life, as an option, and AIC is reported so the two can be compared. Every fit carries standard errors from the observed information, the log likelihood, and a convergence flag.

Design bounds without the complete-sample assumption

The Owen factor assumes a complete normal sample. With runouts that assumption is false. design_life_ml gives the one-sided lower confidence bound on the life quantile by profile likelihood, Venzon and Moolgavkar 1988, or by the Wald method. On complete samples it agrees closely with the Owen bound, that agreement is a test in the suite, and with censoring it remains meaningful where the Owen construction does not.

The full curve, not just a line

E739 restricted itself to linearized fits. fit_strain_life_censored fits the combined Basquin plus Coffin-Manson curve

\[ \varepsilon_a = \frac{\sigma_f'}{E}(2N_f)^b + \varepsilon_f'(2N_f)^c \]

directly by censored maximum likelihood with lognormal life scatter.

An honest caveat is intrinsic to that model: the four constants are strongly correlated when inferred from total strain alone, and on sparse data the elastic exponent can collapse toward zero. The fitted curve is well determined inside the tested strain range even then. The result reports standard errors and a weak_identifiability warning, and the branch-wise linear fits remain the method of choice when separated elastic and plastic strains are available.

Quantifying what deletion did

compare_runout_handling fits the same data three ways, runouts deleted with the Owen factor, censored ML with the Owen factor, censored ML with the profile bound, and reports the design-life ratios. Whether deletion was optimistic or pessimistic depends on the data. The point is that the difference becomes a number instead of a habit.

Random fatigue limit

For stress-life data with a fatigue limit, fit_rfl implements the Pascual-Meeker random fatigue limit model, validated by exact reproduction of the published laminate-panel fit.

Choosing a method

Situation Use
Complete sample, linear range fit_log_life plus design_life
Runouts present fit_log_life_censored plus design_life_ml
Combined curve needed, or censoring with curvature fit_strain_life_censored
Fatigue limit suspected fit_rfl
Deciding lognormal versus Weibull compare aic of the censored fits

Sources

Methods and their citations are registered in lcf.citations and rendered in the physics review. The statistics layer follows Meeker, Escobar, Pascual et al., arXiv:2212.04550, Meeker and Escobar, Statistical Methods for Reliability Data, Wiley 1998, Owen 1963 and 1968, Venzon and Moolgavkar 1988, Pascual and Meeker 1999, and the withdrawn ASTM E739-23 for the classical layer.