For metallic material one is interested in estimating the fatigue limit although it is impossible to test if a specimen has infinite life. In this paper two models are compared. One model estimates the fatigue limit and another estimates the endurance limit. The model which estimates the endurance limit is a model which only uses the information that a specimen has broken or not broken at a certain stress level. The model which estimates the fatigue limit also uses the information about when the specimen is broken, i.e., after how many cycles the specimen breaks. The two models are compared, both on real and simulated staircase tests. It is shown that it is possible to estimate the distribution of the fatigue limit although the fatigue limit itself is impossible to observe. When the two models give very different estimates it indicates that the chosen run‐out level is too low.
A B S T R A C T The fatigue limit distribution is estimated using fatigue data and under the assumption that the fatigue limit is random. The stress levels for the broken and unbroken specimens are used. For the broken specimen the number of cycles to failure is also used. By combining the finite life and fatigue limit distribution it is possible to get the probability of not surviving a certain life. This probability is used to estimate a curved S-N curve by using the method of likelihood. The whole S-N curve is estimated at the same time. These curves show the predictive life given a certain stress level. The life and the quantile of the fatigue limit distribution are also predicted by using profile predictive likelihood. In this way the scatter around the S-N curve as well as the uncertainty of the S-N curve are taken into account.Keywords fatigue limit; finite life; predictive profile likelihood; staircase test.
N O M E N C L A T U R E1 = indicator function C = set of censored observations e yx = n x f , g = density function l y = likelihood function L p , L ps = profile predictive likelihood L p ,L ps = normalized profile predictive likelihood N f = finite life n ro = run-out level n x = life given a stress level S q = probability S = stress level S ∞ = fatigue limit U = set of uncensored observations x = ln e (S) y = ln e (N ) y ro = ln e (n ro ) Z = random variable θ = parameter µ = mean of fatigue limit distribution ν (x) = mean of logarithm of the finite life distribution σ 2 = variance of fatigue limit distribution τ 2 = variance of logarithm of the finite life distribution = standard normal cumulative distribution · = estimate Correspondence: Sara Lorén.
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