Weibull Cumulative Distribution Function Research Articles

Effect of gastric acids on the mechanical properties of conventional and CAD/CAM resin composites - An in-vitro study

ObjectivesDental erosion in patients with gastroesophageal reflux disease (GERD) is a current and frequent condition that may compromise the mechanical properties and clinical durability of resin-based composites (RBCs). This study assessed the mechanical properties of conventional and computer-aided design/computer-aided manufacturing (CAD/CAM) RBCs subsequent to simulated gastric acid aging. Materials and methodThree conventional and three CAD/CAM composites were assessed. They were divided into an experimental group (exposed to simulated gastric acid aging) and a control group (no aging). Both groups were analyzed for Vickers microhardness (VHN), wear and flexural strength over a period of six months. The failure rate probability for each RBC was calculated through the Weibull cumulative distribution function (m). Statistical analysis was conducted using repeated measures ANOVA, 3-way ANOVA, a non-parametric Kruskal-Wallis and U Mann-Whitney tests (α = 0.05). ResultsThe mechanical properties of all the RBCs dropped significantly after aging (p < 0.05). Lower VHN and flexural strength values, along with greater wear values were evident in the experimental groups, though the effects of the treatment varied between RBCs. The Weibull m of all the RBCs decreased over time. ConclusionConventional RBCs might show greater reduction in mechanical properties compared to CAD/CAM RBCs when exposed to gastric acid attack. Thus, CAD/CAM composites may represent a suitable choice for the treatment of patients presenting erosive issues.

About the Necessity to Consider Membrane Electrolyte Degradation Statistically

Polymer Electrolyte Membrane Fuel Cells (PEMFCs) are subjected to aging under pure mechanical, pure chemical and the combination of both stressors. Progression of degradation leads to membrane failures. In this study, seven different accelerated stress test (AST) protocols are applied to degrade two types of commercially available membrane electrode assemblies (MEAs) to demonstrate the necessity to evaluate lifetime of this system with statistical methods. In total, data from 56 samples is reported. Membrane lifetime is derived from hydrogen crossover and open circuit voltage (OCV) which is tracked over the course of degradation. The characteristic membrane lifetime distribution of each AST protocol is described via a cumulative Weibull distribution function (CDF). As a result, the scatter of lifetime distribution correlates with the lifetime itself and thus conclude that less repeats are required for ASTs creating short lifetimes compared to those causing long lifetimes. As the latter is required especially for membrane lifetime prediction, these conclusions are relevant for anybody designing the lifetime of PEMFC stacks.

A new hysteresis model based on Weibull cumulative distribution function and Jiles–Atherton hysteresis model

A new hysteresis model based on Weibull cumulative distribution function and Jiles–Atherton hysteresis model

Межа максимальної ефективності роботи вітроелектричних установок із заданими типорозмірами у конкретних вітрокліматичних умовах

In the paper, the parameters of 115 types of existing wind turbines (WT) were analyzed and their power curves were modeled by using the Weibull cumulative distribution function (CDF). On the basis of these data, regression equations were obtained for the CDF parameters for the power curves of WT due to their main sizes: the nameplate capacity of the generator P and the rotor D. Based on the analysis of the obtained 115 WT CDF parameters and main sizes, the regression model of the WT average used power (AUP) in specific wind conditions has been built. The area of existence of possible values of main sizes P and D is defined. The presence of local maxima in the distribution of AUP by nameplate capacity at fixed values of the rotor diameters has been revealed. An analytical relationship was found between the optimal values of WT main sizes in different wind conditions. Certain restrictions were obtained for the maximum rotor diameter depending on the values of the nameplate capacity. The average starting wind speed of 3.37 m per s, at which the wind turbine starts working, has been determined theoretically.

A new simulation framework to evaluate the suitability of eDNA for marine and aquatic Environmental Impact Assessments

AbstractA model was developed to forecast and compare changes in species presence assessed with either eDNA or traditional observations. We use it to explore how ecosystem conditions could affect the suitability of eDNA for Environmental Impact Assessment. First, a deterministic model simulated the dynamics of the impacted population (called “receptor” in EIA) and their shed DNA fragment concentrations. Second, random distributions of receptor organisms and eDNA fragment quantities at steady state were simulated within the impacted spatial domain (called “project area”). Then, simple random samplings were performed for both the receptor and eDNA. Third, post‐sampling processes (eDNA extraction, amplification, and analysis) were simulated to estimate the taxon detection probability. Fourth, we simulated an impact by modifying the growth, mortality, and mobility (null, passive, and active) parameters of the receptor taxon. eDNA detection probability curves were then estimated for a range of environmental sample volumes by fitting a Weibull cumulative distribution function. A F‐like statistic compared detection curves before and after impact. Statistically significant differences were detected with eDNA in impact scenarios where receptor taxon growth rate decreased and receptor mobility was null or passive. In scenarios where the project area accumulates DNA shed from multiple categories of the same taxon (e.g., from dead organisms if mortality increased or when individuals can cross project area boundaries), it is difficult to assess impact. Our study shows that results obtained from eDNA sampling will not always agree with an impact classically assessed on a receptor population. One reason is that sources of the total eDNA pool are not identified. The modeling highlights the need: to do preliminary testing of sample sizes, to develop new approaches that will identify sources from the pool of extracted DNA, and to improve descriptions of the ecogeochemical processes required to forecast shed DNA reactivity.

Pointwise Modelling and Prediction for Ground Surface Uplifts in Abandoned Coal Mines from InSAR Observations

Interferometric synthetic aperture radar (InSAR) is a useful tool for monitoring surface uplifts due to groundwater rebound in abandoned coal mines. However, InSAR-based prediction for surface uplifts has rarely been focused on so far, hindering the scientifical assessment and controlling of uplift-related geohazards in a wide area. In this study, we firstly revealed that the temporal evolution of surface uplifts caused by groundwater rebound at a surface point approximately followed an exponential distribution. Following the result, a varied cumulative distribution function (CDF) of the Weibull distribution was then used to model the temporal evolution of surface uplifts on a point-by-point basis. Finally, the parameters of the varied Weibull CDF were inverted from historical InSAR observations of surface uplifts and were forward used to predict uplift trends. Two abandoned coal mines in Beipiao city, China, were chosen to test the presented method. The results suggest that the varied Weibull CDF is able to well describe the processing of time-series uplifts, and the root mean square errors of the predicted uplifts were about 1.2 mm. The presented pointwise method predicts surface uplifts based on historical uplift observations and a mathematical function (i.e., the varied Weibull CDF), without the requirement of in situ geological and hydrological information about the focused abandoned coal mines. Therefore, it offers a new tool for predicting surface uplifts in abandoned mines, especially in case they lack in situ geological and hydrological information.

UHPC-PINN-parallel micro element system for the local bond stress–slip model subjected to monotonic loading

The bond stress between Ultra-High-Performance Concrete (UHPC) and steel bars is an essential issue in designing reinforced UHPC structures. Although, to date, considerable studies have been directed on the Local Bond Stress-Slip (LBSS) relationship, not enough progress has been achieved in the parametric investigation of the Parallel Micro Element System (PMES) on the LBSS relationship at the steel bar-UHPC interface. Therefore, the presented research applied the two-parameter Weibull Cumulative Distribution Function (WCDF) and conducted a series of monotonic pullout tests on 144 specimens considering the most influential parameters on the LBSS, such as concrete cover (c), UHPC compressive strength (fUHPC′), steel bar diameter (db), and bond length (lb). The Finite Element Method (FEM), ABAQUS, calibrated the experimental results to provide a reliable database. The Genetic Algorithm (GA) and the Physics-Informed Neural Network (PINN) were adopted to solve the inverse problem of this research, predict the results, and check the accuracy of the PMES. It can be concluded that PINN's application, compared to GA, leads to more precise results. Observing the specimens R16C1L2F155 and R18C1L3F155, for instance, PINN provided more consistent values for the friction coefficient (β) [0.2549, 0.8165] and the LBSS relationship stiffness (G) [453.1250, 249.9757], while GA failed to acquire not only β and G but also the hyper-parameters of (a) [0.3016, 0.3088] and (m) [0.3035, 0.3635], respectively. This research developed the application of GA and PINN to solve an inverse problem in structural engineering.

Application of the weibull model to describe the kinetic behaviors of thiol decolorizers in chlorogenic acid-lysine solutions

Thiols (cysteine and glutathione) were explored as potential decolorization agents to mitigate green pigment formation in chlorogenic acid quinone-lysine solutions. Reparameterizations of the Weibull cumulative distribution function were applied to describe the time-dependence of greening under varying pH conditions. Repeated fitting of 3-parameter models (RMSE = 0.0111, CVRMSE = 1.55%) indicated the linear dependence of model parameters on thiol concentration. A 6-parameter Weibull model incorporating time and initial thiol concentration (RMSE = 0.0255, CVRMSE = 3.56%) accurately predicted green color development. Calculated model parameters descriptive of greening rate, terminal greening magnitude, and lag time before greening onset facilitated comparison of the relative effectiveness of each thiol based on concentration. Bayesian regression of the model yielded nearly similar predictive power (RMSE = 0.0272, CVRMSE = 3.80%). Glutathione yielded longer lag time durations at both pH 8.0 and 9.0 but yielded less green solutions only at pH 9.0.

Wind Resource Assessment: Optimizing the Weibull Distribution Curve

Abstract: In this paper, it was analyze the wind speed characteristics and provide projections of optimal wind resources by comparing data at different hub heights using wind power law. We have acquired data from an operational project site in the western part of India using data points acquired from the site from August 2017 to February 2018.Weibull distribution probability distribution function and cumulative distribution function for wind speed and other parameters involved in an accurate wind resource assessment methodology. To predict wind regimes, the Weibull probability function is commonly used. A comparison of alternative methods for estimating Weibull parameters of a wind regime is presented in this research. For the estimation, five alternative methods are discussed and employed. The study examined wind speed time series data at two sites over the course of a year. Although all five methods produce similar results when plotting error versus wind speed, the standard deviation method produces the best results.

Strength Properties of Surface-Modified Giant Cavendish (Musa acuminata) Banana Fibers

ABSTRACT This study focused on examining and comparing the strength properties of untreated and surface-modified Giant Cavendish banana fibers. The banana fibers were mercerized using 0.06 M Sodium Hydroxide (NaOH) and treated using 0.003 M Potassium Permanganate (KMnO4) solutions. The untreated and surface-modified fibers were then subjected to a tensile test and the results analyzed using the Weibull Cumulative Distribution Function. KMnO4 treated banana fibers had a mean tensile strength of 209.321 ± 22.619 MNm−2, which translated to a 65.92% gain in strength while the mercerized banana fibers had a mean tensile strength of 162.233 ± 7.976 MNm−2, which was a 28.60% gain in strength. Mercerized banana fibers recorded a Weibull modulus of 7.6096 compared to the untreated fibers (4.7042) and KMnO4 treated fibers (3.2135). The banana fiber surface-modification using KMnO4 resulted in stronger fibers. However, the lower Weibull modulus of 3.2135 can be attributed to the introduction of flaws in to the fiber structure by the KMnO4 treatment.

Reparameterization of the Weibull model for practical uses in food science.

The reparameterization of the Weibull cumulative distribution function and its survival function was performed to obtain meaningful parameters in food and biological sciences such as the lag phase (λ), the maximum rate ( ), and the maximum increase/decrease of the function (A). The application of the Lambert function was crucial in order to achieve an explicit mathematical solution. Since the reparameterized model is applicable only when the shape parameter (α) is greater than one, the Weibull model was modified with the introduction of a new parameter ( ) that represents the model rate at time β (scale parameter). All models were applied to literature data on food technology and microbiology topics: Microbial growth, thermal microbial inactivation, thermal degradation kinetics, and particle size distributions. The Weibull model and the reparameterized versions showed identical fitting performance in terms of coefficient of determination, residual mean standard error, values of residuals, and estimated values of the parameters. Some faults in the datasets used in this study permitted to re-mark the criticality of a good experimental plan when data modeling is approached. The parameter resulted in an interesting new rate parameter that is not correlated with the scale parameter ( =0.64 ± 0.37)and highly correlated with the shape parameter ( =0.90 ± 0.11). Also, the reparameterization of the Weibull probability density function was performed by using both the standard and new parameters and applied to experimental data and gave useful information from the distribution curve, such as the value of the mode ( ) and a measure of the curve skewness (λ).

Monotonic and cyclic bond responses of steel bar with steel-polypropylene hybrid fiber reinforced recycled aggregate concrete

The bond failure between steel bars and concrete is the main reason for the strength degradation and deformation increase of structures in service. In this study, the bond behavior of steel bars with steel-polypropylene hybrid fiber reinforced recycled aggregate concrete (HFRAC) under monotonic and cyclic loadings was investigated. The acoustic emission (AE) technique was applied to monitor the bond response and the inner damage evolution of specimens during the loading process, and the microstructure of HFRAC was analyzed through the scanning electron microscope (SEM). The hysteresis curves, failure modes, bond strength degradation rate, and energy dissipation capacity, were systematically investigated by considering the effects of water-cement ratio, recycled aggregate replacement ratio, steel fiber volume fraction, and polypropylene fiber volume fraction. Experimental results demonstrated that there was more obvious degradation in the bond strength for the HFRAC specimens under cyclic loading, compared with that under monotonic loading. In the case of cyclic loading, the bond strength was degraded with the increase of the number of cycles, and the degradation rate increased quickly with the increase of the displacement amplitude. Moreover, the analysis of AE parameters measured on steel bar bonded recycled aggregate concrete (RAC) and HFRAC specimens, including the AE hits, AE energy, localization of AE events, and average frequency, was performed. Results showed that the AE technique could effectively monitor the bond damage of HFRAC specimens at different stages. A good correlation between the results of AE parameters analysis and the cracking process of specimens was confirmed. Based on the Weibull cumulative distribution function, the bond-slip models of steel bars with HFRAC under monotonic and cyclic loadings were proposed by considering the coupling effect of hybrid fibers and recycled coarse aggregates.

Effect of loading frequency on the fatigue life in compression of natural hydraulic lime mortars

This paper focuses on the study of the influence of the loading frequency on the fatigue life in compression of natural hydraulic lime (NHL) mortars. For this purpose, fatigue tests were performed under three different loading frequencies: 0.05 Hz, 0.5 Hz, and 5 Hz. The maximum and minimum stresses applied in the fatigue tests were 85% and 20% of the compressive strength of the mortar, respectively, and the runout limit was set at around three days. It is observed that the NHL mortar is sensitive to the loading frequency; that is, for higher frequencies, more cycles are resisted by the specimens. Concerning the secondary strain of the fatigue creep curves, the Sparks and Menzies law was satisfied independently of the loading frequency. This law is useful to predict the number of cycles to failure of runouts if the secondary strain is known. In addition, given the high scatter of results, a probabilistic treatment is applied. Firstly, they were fitted to a two-parameter cumulative Weibull distribution function. Secondly, the results were fitted to a probabilistic fatigue model based on the initial distribution. With it, one can obtain the failure probability of the material for any given value of loading frequency. Finally, we observed an increase in the residual strength after fatigue in comparison to the static compression tests of around 40%. Through mercury intrusion porosimetry tests, it is concluded that a possible chemical curing of the material could have occurred induced by the cyclic loads.

A New Approach to Assess Wind Potential

&lt;p&gt;Weibull Cumulative Distribution Function (C.D.F.) has been employed to assess and compare wind potentials of two wind stations Europlatform and Stavenisse of The Netherland. Weibull distribution has been used for accurate estimation of wind energy potential for a long time. The Weibull distribution with two parameters is suitable for modeling wind data if wind distribution is unimodal. Whereas wind distribution is generally unimodal, random weather changes can make the distribution bimodal. It is always desirable to find a method that accurately represents actual statistical data. Some well-known statistical methods are Method of Moment (MoM), Linear Least Square Method (LLSM), Maximum Likelihood Method (M.L.M.), Modified Maximum Likelihood Method (MMLM), Energy Pattern Factor Method (EPFM), and Empirical Method (E.M.), etc. All these methods employ Probability Density Function (PDF) of Weibull distribution, except LLSM, which uses Cumulative Distribution Function (C.D.F.). In this communication, we are presenting a newly proposed method of evaluating Weibull parameters. Unlike most methods, this new method employs a cumulative distribution function. A MATLAB® GUI-based simulation is developed to estimate Weibull parameters using the C.D.F. approach. It is found that the Mean Square Error (M.S.E.) is the lowest when using the new method. The new method, therefore, estimates wind power density with reasonable accuracy. Wind Power (W.P.) is estimated by considering four different Wind Turbine (W.T.) models for two sites, and maximum W.P. is found using Evance R9000.&lt;/p&gt;&#x0D;

A scaling approach to size effect modeling of Jc CDF for 20MnMoNi55 reactor steel in transition temperature region

Ever since the 1980s there is a sustained interest in the size effect, as one of the most pronounced consequences of fracture mechanics. In the present study, the investigation of the size effect is focused on estimation of the Weibull cumulative distribution function (CDF) of the critical value of the J-integral (Jc) in the transition temperature region under constraint of a small statistical sample size. Specifically, the Jc experimental data correspond to the C(T) specimen testing of the reactor pressure-vessel steel 20MnMoNi55 at only two geometrically-similar sizes. Thus, a simple approximate scaling algorithm has been developed to tackle the effect of the C(T) specimen size on the Jc CDF under these circumstances. Due to the specific form of the two-parameter Weibull CDF, F(Jc|β,η), the scaling procedure is applied according to a two-step scheme. First, the Jc-scaling is performed to ensure the approximate overlap of the points that correspond to the CDF value F(Jc = η) = 1 − 1/e ≈ 0.632 for different C(T) specimen widths (W), which assumes η·Wκ = const. Second, the F-scaling is performed to ensure the equality of the slopes of the CDF in the scaled (F·Wξ vs. Jc·Wκ) space. The objective of the sketched approach is to obtain a size-dependent Jc CDF that encapsulates a reasonably conservative data extrapolation.

Probabilistic Assessment of Fracture Toughness of Epoxy Resin EPOLAM 2025 Including the Notch Radii Effect.

Many design scenarios of components made of polymer materials are concerned with notches as representative constructive details. The failure hazard assessment of these components using models based on the assumption of cracked components leads to over-conservative failure estimations. Among the different alternative approaches proposed that are based on the apparent fracture toughness, is considered. In so doing, the current deterministic underlying concept must be replaced by a probabilistic one to take into account the variability observed in the failure results in order to ensure a reliable design. In this paper, an approach based on the critical distance principle is proposed for the failure assessment of notched EPOLAM 2025 CT samples with each different notch radii () including a probabilistic assessment of the failure prediction. First, each apparent fracture toughness is transformed into the equivalent fracture toughness for based on the critical distances theory. Then, once all results are normalized to the same basic conditions, a Weibull cumulative distribution function is fitted, allowing the probability of failure to be predicted for different notch radii. In this way, the total number of the specimens tested in the experimental campaign is reduced, whereas the reliability of the material characterization improves. Finally, the applicability of the proposed methodology is illustrated by an example using the own experimental campaign performed on EPOLAM 2025 CT specimens with different notch radii ().

An approach for predicting failure mechanism in rough surface rolling contact fatigue

A finite element model was developed to investigate the influence of near surface orthogonal shear stress (OSS) on the competitive failure mechanism between surface originated pitting (SOP) and subsurface originated spalling (SOS), which is intrinsic to rolling contact fatigue (RCF). Surface roughness in heavily loaded non-conformal contacts causes competition between SOS and SOP. In this investigation, tribo-surface roughness has been represented as sinusoidal waveform based on surface measurements of rolling element bearings. These measurements outlined the range of roughness frequency and amplitude. The effects of these surfaces on the contact were investigated and the resulting pressure distributions were used in a finite element model in order to quantify the effects of pressure distribution on near surface orthogonal shear stress concentration. The resulting pressure distributions obtained from rough surfaces were also used in a continuum damage mechanics finite element model (CDM-FEM). The results indicate that a contact with a low frequency surface roughness (pressure distribution) is more susceptible to surface failure, whereas the contact with high frequency surface roughness frequency will resist surface failure. To quantify surface originated failure for a given surface roughness, the probability of surface failure parameter (πsf), which is defined as the ratio of contacts exhibiting SOP characteristics to the total tested is proposed. The near surface stress analysis and failure mechanism results were used to establish a relation between the near surface OSS concentration and πsf. This relation is described by a 2-parameter Weibull cumulative distribution function (CDF). The results indicate that roughness frequency and half contact width are the main parameters controlling the probability of surface failure.

Appropriate search techniques to estimate Weibull function parameters in a Pinus spp. plantation

The Weibull function, a continuous probability distribution, is widely used for diameter distribution modelling, in which parameter estimation performance is affected by stand attributes and fitting methods. The Weibull cumulative distribution function is nonlinear, and classical fitting methods may provide a not optimal solution. Invoking the use of artificial intelligence by metaheuristics is reasonable for this optimisation task. Therefore, aimed and compared (1) the metaheuristics genetic algorithm and simulated annealing performance over the moment and percentile methods; (2) the hybrid strategy merging the metaheuristics tested and the percentile method and, (3) the metaheuristics fitness functions under basal area and density errors. A long-term experiment in a Pinus taeda stand subjected to crown thinning was used. According to our findings, all methods have a similar performance, independent of the thinning regimes and age. The pattern of the estimated parameters tends to be acceptable, as b increases over time and c increases after thinning. Overall, our findings suggest that methods based on metaheuristics have a higher precision than classical methods for estimating Weibull parameters. According to the classification test, the methods that involved simulated annealing stood out. The hybrid method involving this metaheuristic also stood out, with accurate estimates. Classical methods showed the poorest performance, and we therefore suggest the use of simulated annealing due to its faster processing time and high-quality solution.

Effect of pilot-scale UV-C light treatment assisted by mild heat on E. coli, L. plantarum and S. cerevisiae inactivation in clear and turbid fruit juices. Storage study of surviving populations

Consumer growing demands for high-quality and safe food and beverages have stimulated the interest in alternative preservation technologies. Short-wavelength ultraviolet light (UV-C, 254 nm) has proven to be useful for the decontamination of a great variety of clear juices while improving their quality compared to traditional thermal treatments. Suspended solids and coloured compounds in turbid juices, diminish light transmission. The use of UV-C under a hurdle approach, may be a promising strategy for their treatment. The purpose of this study was to analyse Escherichia coli ATCC 25922, Saccharomyces cerevisiae KE 162 and Lactobacillus plantarum ATCC 8014 inactivation in clear pear juice (PJ), turbid orange-tangerine (OT) and orange-banana-mango-kiwi-strawberry (OBMKS) juices processed by single UV-C (390 mJ/cm2, 20 °C) and UV-C assisted by mild heat (UV-C/H, 50 °C) at pilot-scale in a coiled tubing unit and stored under refrigeration (5 °C). Inactivation studies were also conducted in peptone water (PW) and model solution (MS). The adequacy of the Coroller, Weibull and Biphasic Plus Shoulder models was studied. UV-C was highly effective in PW, MS and PJ, achieving up to 5.5-6.3-4.7, 4.8-5.1-4.6 and 4.4-5.5 log reductions for L. plantarum, E. coli,and S. cerevisiae, respectively. Whereas, a moderate inactivation by single UV-C was recorded in the turbid blends, reducing up to 2.4-3.8-1.6 and 3.6-3.7-1.3 log-cycles in OT and OBMKS, respectively. When the UV-C/H treatment was applied, high bacterial inactivation was observed achieving 5.2-5.6, 6.3-6.6 and 5.5-6.7 log reductions in OT, OBMKS and PJ, respectively, while 4.6-4.9 log reductions were determined for the yeast in OBMKS and OT, respectively. Thus, additive inactivation effects between UV-C and H were observed. All the models tested gave useful information regarding the existence of microbial subpopulations with varying resistances. However, the cumulative Weibull distribution function was the most versatile one, fitting inactivation curves with different shapes. Additionally, the frequency distributions of resistances showed that UV-C/H not only increased the UV-C microbicidal effect but changed the distribution of inactivation times. Principal component analysis revealed that UV-C effectiveness was associated to low particle size, a⃰, turbidity and high UV-C transmittance. An increase on the inactivation of treated bacterial populations was recorded along storage, while no yeast recovery was observed, thus emphasizing the contribution of refrigerated storage to microbial inactivation. Microbial inactivation in clear and turbid juices achieved by UV-C (390 mJ/cm2) assisted by mild heat (50 °C) and subsequent refrigerated storage may represent an useful alternative for multiple applications in the juice industry.

Statistical Size Effect in Fatigue Properties for Mini-Specimens.

The study verifies the sensitivity of selected construction materials (S235JR structural steel and 1.4301 stainless steel) to the statistical size effect. The P–S–N curves were determined experimentally under high-cycle fatigue conditions for two specimen sizes (mini-specimen and standard specimen). The results were analyzed using a probabilistic model of the three-parameter Weibull cumulative distribution function. The analysis included the evaluation of the technological process effects on the results based on the material microstructure near the surface layer and the macro-fractography. The differences in the susceptibility to the size effect validated the applicability of the test method to mini-specimen and showed different populations of the distribution of critical material defects.