Effects of Cracking Test Conditions on Estimation Uncertainty for Weibull Parameters Considering Time-Dependent Censoring Interval

Abstract

It is extremely difficult to predict the initiation time of cracking due to a large time spread in most cracking experiments. Thus, probabilistic models, such as the Weibull distribution, are usually employed to model the initiation time of cracking. Therefore, the parameters of the Weibull distribution are estimated from data collected from a cracking test. However, although the development of a reliable cracking model under ideal experimental conditions (e.g., a large number of specimens and narrow censoring intervals) could be achieved in principle, it is not straightforward to quantitatively assess the effects of the ideal experimental conditions on model estimation uncertainty. The present study investigated the effects of key experimental conditions, including the time-dependent effect of the censoring interval length, on the estimation uncertainties of the Weibull parameters through Monte Carlo simulations. The simulation results provided quantified estimation uncertainties of Weibull parameters in various cracking test conditions. Hence, it is expected that the results of this study can offer some insight for experimenters developing a probabilistic crack initiation model by performing experiments.

Effects of Styrene-Acrylic Sizing on the Mechanical Properties of Carbon Fiber Thermoplastic Towpregs and Their Composites

“…The dimensions tested and methods used are described in the sections above. The data processing was inspired by the survival probability deduced from Weibull’s two-parameter model [ 37 , 38 ]. This model is based on a weakest link theory, in which the failure is considered to come from the weakest part of the fibers.…”

A quantile variant of the expectation–maximization algorithm and its application to parameter estimation with interval data

“…Other examples of grouped and censored data can also be found in the statistics and engineering literature. 10,11,28,36–40 These censored and grouped data can also be regarded as interval-censored data. Thus, the proposed method can be easily applicable to these data.…”

A Deterministic and Probabilistic Framework for Forecasting of Time-Series Damage States and Associated End-of-lIfe of a Pressurizer Water Reactor Surge Line under Design-Basis and Grid-Load-Following Loading Conditions

“…This assumption is reasonable at least for the macroscopic-scale damage creating variable (here the strain amplitude) versus the corresponding life data. [35]. Therefore, let us assume that the fatigue life can be described as a random variable that follows the Weibull distribution as follows:…”

“…6.16 and 6.17. Thus, we used a numerical false position method, because it is known that the Newton-Raphson method does not always converge to the true estimates in MLE [35]. The resulting estimates are as follows:…”

“…Engineers usually use the Weibull distribution to model the failure time (i.e., lifetime) or strength of a given material in a probabilistic way. Although it is well known that the Weibull distribution is appropriate when the given material is brittle [33], we adopted the Weibull distribution for the fatigue life model because the fatigue specimens were relatively large to apply the extremal value theorem [34,35].…”