Likewise, 16 10 = 6. To use Weibull distribution, we need to have three values, which are X, Alpha, And Beta. Description:Adds user-defined labels for accessing object parameters via control logic. How is this connected with modulo? 1 mod 2 is a situation where the divisor, 2, is larger than the dividend, 1, so the remainder you get is equal to the dividend, 1. In the number theory, scholars analyze the properties of natural Thats 16 (mod 10). Weibull Modulus Calculation Mean Strength Strength Diameter Gauge Length Lot MPa Distribution Distribution Dependence A0168 3080 10.9 2.7 - A0180 3030 11.2 2.6 - A0184 3500 12.1 4.0 - The value of the samples from the standard Weibull distribution is scaled by the factor: var element = document.getElementById("moose-equation-f2337f75-096c-4b18-8b63-ec1cf7ce33b5");katex.render("\\biggl[\\frac{\\bar{V}}{V}\\biggr]^{1/k}", element, {displayMode:true,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,. In his early 20s in 1801, he published Disquisitiones Arithmeticae, which laid the foundation for todays number theory and showed the first proof of the law of quadratic reciprocity. Continuous distributions show the relationship between failure percentage and time. \frac{k}{\lambda}\left(\frac{x-x_0}{\lambda}\right)^{k-1}e^{-((x-x_0)/\lambda)^{k}} & x\geq x_0 ,\\ 340 mod 60340 60 = 280280 60 = 220220 60 = 160160 60 = 100100 60 = 40. 6. Step#5 - A dialog box appears for the "Function Arguments.". This calculator performs a basic Weibull analysis. Consider strength measurements made on many small samples of a brittle ceramic material. This is why the 12-hour standard time uses modulo. WEIBULL.DIST(x, , , cum) = the pdf of the Weibull distribution f(x) when cum = FALSE and the cdf F(x) when cum = TRUE In fact, some values of the shape parameter will cause the distribution equations to . Calculate Modulo. Parameters Calculator. short 6 minute step by step tutorial for using excel to determine weibull modulus for test data. (2015), and using it to describe local strength for fracture models minimizes mesh size dependence. Books are Seed value for the random number generator. Thus, there should be some external factor strong enough to cause random failure irrespective of whether the section is strong or weak. Explore modular arithmetic and modulo operations further including a mod b for negative numbers. For 1 divided by 2, 2 goes into 1 zero times with a remainder of 1. Kahn Academy, What is Modular Arithmetic? For ceramics and other brittle materials, the maximum stress that a sample can be measured to withstand before failure may vary from specimen to specimen, even under identical testing conditions. You need to write a piece of software that tells a user whether a number they input is a multiple of 4. For instance, if we add the sum of 2, 4, 3 and 7, the sum is congruent to 6 (mod 10). And its X scale type and Y scale type are Log10 and Double Log Reciprocal respectively. horizontal line segments both signify equality and definition. The case where = 0 and = 1 is called the standard Weibull distribution. For instance, when pilots report that a plane will reach a base at 2100Z, it means it will arrive at 9PM GMT. The value at which to evaluate the function. In this paper, a simple method was established for the determination of the Weibull parameters, Weibull modulus m and scale parameter 0, based on Monte Carlo simulation. By using this calculator, users may find the failure rate probability P(x), expected life-time or mean (), variance ( 2), median and mode values of Weibull . The Weibull factors were estimated using six different methods. Calculations happen automatically when . Most people havent heard of modular arithmetic or mod outside of math class. An optional suffix parameter that can be appended to any attempt to retrieve/get material properties. tracked using modular arithmetic to calculate checksums for international standard https://www.calculatorsoup.com/calculators/math/modulo-calculator.php. It has CDF and PDF and other key formulas given by: with the scale parameter (the Characteristic Life ), (gamma) the Shape Parameter, and is the Gamma function with for integer . Step#2 - Now, we give a parameter to the function: Alpha and Beta. ","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});, the shape parameter, var element = document.getElementById("moose-equation-cd5b2f66-9bc0-4f3b-bd02-a24b3658c23c");katex.render("\\lambda", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,. To help you visualize, the number line below shows the difference in value. The same function (e.g., the Weibull model) may exhibit transitions from sub-exponential to super-exponential by changing the value of a key parameter; in the Weibull case this is the modulus m: m < 1 leads to a sub-exponential and m > 1 to a super-exponential tail. ","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}}); as: var element = document.getElementById("moose-equation-c606de3d-4856-4d9b-b440-a8ff5f447b03");katex.render("\\lambda=\\bar{\\eta}\\biggl[\\frac{-1}{\\ln(0.5)}\\biggr]^{1/k}", element, {displayMode:true,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,. If a number is a multiple of 4, when you divide it by 4 the remainder will be 0. Worksheet Functions. Go to the Line tab, set Color to Red, Transparency to 80%, then check Fill Area Under Curve check box and select Fill to next data plot - One . The list of blocks (ids or names) that this object will be applied, The list of boundaries (ids or names) from the mesh where this boundary condition applies. number M, which is between 0 and N 1. A parameter to the distribution. Beta Required. Calculate distribution-specific P-Values - if checked, the P-Values will be based on tables or formulas specifically developed for the Weibull distribution . 8 shows the corresponding standardized representations of strength data in sequence. Lets do it with the example below: -340 mod 60-340/60 = 5.6, when we take the decimal part, it becomes the integer -6= -340 -(-6) * 60= -340 -(-360)= 20. with time. ","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}}); is a uniform random number on the interval from 0 to 1, and var element = document.getElementById("moose-equation-2afb89b2-2b28-4579-b0a0-cd3ecfcc09d4");katex.render("k", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,. value. objective is to discover unexpected mathematical patterns and interactions Different values of the shape parameter can have marked effects on the behavior of the distribution. . Uniaxial Tension Search: Weibull Calculator Excel. Mod is a mathematical function that allows us to measure the remainder in a sum. ","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});, and the location parameter, var element = document.getElementById("moose-equation-fab0e98b-5b08-44c4-bfc5-06f5fc033caf");katex.render("\\theta", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,. In cryptography, W eibull distribution (1) probability density f(x,a,b) = a b(x b)a1e(x b)a (2) lower cumulative distribution P (x,a,b)= x 0 f(t,a,b)dt= 1e(x b)a (3) upper cumulative distribution Q(x,a,b)= x f(t,a,b)dt = e(x b)a W e i b u l l d i s t r i b u t i o n ( 1) p r o b a b i l i t y d e n s i t y f . Corin is an ardent researcher and writer of financial topicsstudying economic trends, how they affect populations, as well as how to help consumers make wiser financial decisions. Results The calculation result by SAS was identical with that in literature. The Weibull modulus of a material is the exponent m in equation 4. (Select Help: Learning Center menu or press F11 key , and then open Graph Sample: Statistical Graphs and search "weibull"). ","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}}); where var element = document.getElementById("moose-equation-0469723d-fa40-447a-b8e5-06457642a617");katex.render("\\bar{\\eta}", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,. Adds user-defined labels for accessing object parameters via control logic. Using a level of strength at which the failure probability becomes 63.2 % (0), the Weibull modulus (m) becomes a measure of the distribution of strengths. For practical applications, mod is especially useful for dealing The shape parameter, namely the Weibull modulus, is an indicator of variation in the material strength. 24-hour digital clock, which resets itself to 0 at midnight. For positive numbers, whenever the divisor (modulus) is greater than the dividend, the remainder is the same as the dividend. JavaScript is turned off in your web browser. 226 mod 4 = 2, so no, 226 is not a multiple of 4. However, if youve ever estimated lunch for 10 people, and found that theres a lot of food leftover, youre actually dealing with a mod problem. number greater than 1, which is the mod, is reached. clock to avoid confusion while traveling between time zones. The modelled Weibull plot is displayed in Figure 5 and the highest material reliability (Weibull modulus m) was found for the composite materials and the lowest results were obtained for compomers. Is 226 a multiple of 4? In terms of mod, 496 mod 4 = 0, so yes, 496 is a multiple of 4. This is related to the distribution of physical flaws present in the surface or body of the brittle specimen, since brittle failure processes originate at these weak points. Search: Weibull Calculator Excel. You would divide 496 by 4, so 496 / 4 = 124 with no remainder. Take natural log of data. The decreasing order of m is: TEC > TECB > VD > SDR > DY > CGF with very high coefficients of determination (R 2 ) being greater than 0.940 except . In this section, youll learn about modulo, its basic operation, and its uses in real life. To set a standard, pilots and the military use the Greenwich Mean Time (GMT) which they also call Zulu time (Z). For example you would have to calculate "is 496 a multiple of 4?". Their If all the scatter points are close to the reference line, we can say that the dataset follows the Weibull distribution. For people staying Set the enabled status of the MooseObject. The concept of modular arithmetic has been used by ancient All rights reserved. This is the principle behind the military time system, beginning In 2007, a 13-digit ISBN number system volume of books. ","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}}); is the reference volume, which is the volume of a test specimen that has a median strength equal to var element = document.getElementById("moose-equation-21a88592-b05f-49d5-95ea-edb84125c984");katex.render("\\bar{\\eta}", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,. mean 4 in the afternoon. Instead of saying 1600 hours, we just say 4 oclock. Alpha Required. If k=1, the rate of failure remains constant. For many years, artists have been using mathematical shapes based on formulas to create designs. ceramics must be extended by the reliability analysis, which often uses the Weibull distribution. The values of m and x o are obtained by fitting the experimental data to Eq. Cryptographers use mod in the Diffie-Hellman Unless specified otherwise, a 4am meeting is absurd, The randomized value of a given variable var element = document.getElementById("moose-equation-46e2f77e-d9ec-4609-bbdf-53d1efbfff71");katex.render("\\eta", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,. Test procedures for determining the Weibull modulus are specified in DIN EN 843-5 and DIN 51 110-3. Description:Determines whether or not the legacy generator (deprecated) should be used. The modulo operation finds the remainder, so if you were dividing a by b and there was a remainder of n, you would say a mod b = n. The modulo operation finds the remainder of a divided by b. between natural numbers. (CV) for the crushing force together with an equation to calculate Weibull modulus from CV. Today, the same concept is applied to computer graphics, as well as sculptures and modern paintings. But it was introduced into Western The higher the Weibull modulus is, the more consistent the material (which means that uniform "defects" are evenly distributed throughout the entire volume) and also the narrower the . 535 Log-gamma 1. Her other feature articles can be read on Inquirer.net and Manileno.com. Figure 2 - Chart of Weibull distribution by beta parameter. The VolumeWeightedWeibull class generates a spatially randomized distribution of a variable following a Weibull distribution, but weighted by the element volume to account for the fact that larger volumes are more likely to contain defects, and would thus have a reduced strength. WEIBULL (x,alpha,beta,cumulative) The WEIBULL function syntax has the following arguments: X Required. Cumulative Required. ","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}}); and var element = document.getElementById("moose-equation-f2d6c3b8-af05-463c-93da-c40d0a5b61c5");katex.render("k", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,. The modulo operation finds the remainder of a divided by b.To do this by hand just divide two numbers and note . Using this approach, the Weibull modulus, m, can be determined by plotting log of mean strength as a function of log of gauge length. This class follows the approach documented in Strack et al. ","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}}); is the median value of the strength variable, var element = document.getElementById("moose-equation-c014f1b0-90f0-4644-b0e4-911f24753914");katex.render("\\bar{V}", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,. A further method to determine the strength of brittle materials has been described by the Wikibook contribution Weakest link determination by use of three parameter Weibull statistics. Klein, C.A (2009) "Characteristic strength, Weibull modulus, and failure probability of fused silica glass". This Weibull distribution is defined by two parameters: the Weibull modulus, var element = document.getElementById("moose-equation-608ee2ea-3599-412b-a243-5004f884eb74");katex.render("k", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,. of the most influential figures in modern mathematics. This diminishes the sum to a The variable this initial condition is supposed to provide values for. Step 4 - Click on "Calculate" button to get Weibull distribution probabilities. The suffix will be prepended with a '_' character. In each case, all the standardized strength distribution fall onto a master curve. Description:Reference volume (of a test specimen). O.E. Description:An optional suffix parameter that can be appended to any attempt to retrieve/get material properties. mathematics by German scientist Carl Friedrich Gauss, who also developed the The data sample is fitted to a Weibull distribution using "Weibull analysis." Once the data is fitted to a Weibull distribution, the probability of survival can be estimated for any point in time. Description:When set to true, a UserObject retrieved by this IC will not be executed before the this IC. The ","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}}); is the Weibull modulus. Description:Seed value for the random number generator. She holds a Masters degree in Creative Writing from the University of the Philippines, one of the top academic institutions in the world, and a Bachelors in Communication Arts from Miriam College. Step 2 - Enter the value of x. Scale ( > 0) : Shape (k > 0) : How to Input Interpret the Output. calculation that involves a number that resets itself to zero each time a whole The Weibull modulus is a shape parameter for the Weibull distribution model which, in this case, maps the probability of failure of a component at varying stresses. Intro to Statistics, A Teachers Aide 1 Considering one surface moving over the other in a rolling motion, the rolling element produces subsurface stresses To compute the maximum likelihood estimates of the parameters of a 2-parameter Weibull distribution Johnson, N The probability P ( X 0 and the shape, k > 0 The probability P ( X 0 and the shape, k > 0. This implies that the weak and defective parts fail in the beginning, with the harder sections surviving. For each case, the maximum likelihood method is applied to estimate Weibull modulus m 0 as shown in Fig. Enter two numbers, with the first number a being the dividend while the second smaller number n is the divisor. Step 2 - Enter the scale parameter . It can therefore be said that the . It can also fit a huge range of data from many other fields like economics, hydrology, biology, engineering sciences. ","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}}); is typically greater than 1). Open QI Macros Weibull Analysis template by clicking on QI Macros Menu, then Capability Templates, then Histogram with Cp and Cpk. S j is the survival probability of j sample (j ranging from 1 to 30). Likewise, 13 12 = 1. Mathforum.org explains, with a positive number like 340, the multiple subtracted is less than the absolute value, which results in 40. (5) b. Calculate a mod b which, for positive numbers, is the remainder of a divided by b in a division problem. Other commonly used life distributions include the exponential, lognormal and normal distributions. It is an extreme value of probability distribution . 9.. Download : Download high-res image (678KB) Download : Download full-size image If k<1, then the failure rate decreases with time. Weibull Distribution Definition. codes are written to protect secret data. . Description:The variable this initial condition is supposed to provide values for. Modular arithmetic has other applications in the field of cryptography, art and graphics design. The Weibull modulus is a shape parameter for the Weibull distribution model which, in this case, maps the probability of failure of a component at varying stresses. numbers, which are whole numbers like -1, -2, 0, 1, 2, and so on. The standard format for mod is: a mod n Where a is the value that is divided by n. For example, youre calculating 15 mod 4. The logic for this part of your program would be: If you did not use the mod operator you would have to do the math in your code. Calculations happen automatically when you click out of any form fields. different time zones. The suffix will be prepended with a '_' character. Instead of saying 9 oclock PM, they say 2100 hours. Another example, 13 1 (mod 12). at midnight with 0000 hours, and ending the hour at 11PM with 2300 hours. Results of 30 samples tested by uniaxial compressive strength (r c ) were used to calculate the Weibull modulus (m). Step 1 - Enter the location parameter . all the numbers (0, 1, 2, , N 1,) are known as residues modulo N. The Inverse Cosine Calculator. ","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});, var element = document.getElementById("moose-equation-9e79c2ae-99ee-429a-a426-953d324ef960");katex.render("R", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,. subtracted from the sum as many times as possible. Afferrante L. et al. When we make appointments, its generally understood people (which was previously 10) was introduced to help manufacturers identify a large Encryption is important because it allows users to safeguard information. Enter two numbers, with the first number a being the dividend while the second smaller number n is the divisor. The Weibull Distribution is a continuous probability distribution used to analyse life data, model failure times and access product reliability. Initialize a variable with randomly generated numbers following a volume-weighted Weibull distribution. Strack, R.B. Paste your sorted data into column B of the worksheet - it will create a histogram and calculate Weibull and . where is the shape and . Modulo is also referred to as mod.. In Figure 3 (above), the shape =1, and the scale =2000. A parameter to the distribution. Divide 226 by 4, so 226 / 4 = 56 with a remainder of 2. You can refer to this graph in Learning Center. When flaws are consistent and evenly distributed, samples will behave more uniformly than when flaws are clustered inconsistently. Note that as the Weibull modulus increases, there is less scatter in the breaking strength; we have more confidence that the specimens will survive at loads near the breaking strength. Returns the individual term binomial distribution probability. Products made from components of low Weibull modulus will exhibit low reliability and their strengths will be broadly distributed. The slope of the log-log gauge length plot is equal to 1/ m. Figure 2 shows a log-log plot of tensile strength as a function of gauge length for Nextel 610fiber. The Weibull shape parameter, , is also known as the Weibull slope. . Probabilities for the Weibull distribution are easily computed taking into account that the random variable Z=[(X-x0)/b]a has a standard negative exponential scale: the scale parameter of weibull distribution where: > 0 is the scale parameter; and; k > 0 is the shape parameter 957 Log-logistic 1 There is more info on this topic below the form There is more . Since we have 24 hours in a day, it makes sense to refer to This is actually not the case. Define the Weibull variable by setting the scale ( > 0) and the shape (k > 0) in the fields below. The value for var element = document.getElementById("moose-equation-76a65bc9-d811-4116-9b50-6081b113f46e");katex.render("\\lambda", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,. People use modular arithmetic all the time, especially with anything involving remainders, time and calendar schedules. Cite this content, page or calculator as: Furey, Edward "Modulo Calculator" at https://www.calculatorsoup.com/calculators/math/modulo-calculator.php from CalculatorSoup, Weibull modulus, a key parameter in Weibull statistics, was observed to decrease with increasing porosity from 17 to 56 vol.%, based on eight sets of compacts at different porosity levels, each set containing 50 samples, a total of 407 tests. basis for the number theory. Step#1 - We will again give a value to the function, i.e.190, for this case. This implies that there is random failure occurring. This means 13 divided by 12 leaves a remainder of 1. Now to calculate the value for at least 105 we can use the probability mass distribution formula by changing the cumulative argument. If you needed to find 27 mod 6, divide 27 by 6. Calculate a mod b which, for positive numbers, is the remainder of a divided by b in a division problem. Better Explained, Fun with Modular Arithmetic, Wikipedia, Applications of Modular Arithmetic. When you divide 15 by 4, theres a remainder.15 / 4 = 3.75. which is read as is congruent to. Instead of the usual = symbol, the three It . The Weibull modulus is a dimensionless parameter of the Weibull distribution which is used to describe variability in measured material strength of brittle materials.. For ceramics and other brittle materials, the maximum stress that a sample can be measured to withstand before failure may vary from specimen to specimen, even under identical testing conditions. This in contrast to the standard version, which has three parameters: the Weibull modulus, var element = document.getElementById("moose-equation-cf8e5f9c-9dd5-4d93-8013-999a4b11686c");katex.render("k", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,. in one time zone, its more important to tell time by separating night and day. Age Under 20 years old 20 years old level 30 years old level 40 years old level 50 years old level 60 years old level or over Occupation Elementary school/ Junior high-school student ","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});. Real-world uses for mod include organizing ISBN and bank information, resetting ARM rates, computer graphics design, and cryptography which helps protect private data. 1-Standard deviation method (STDM) [15], [16], [17] (10) k = v 1. Fig. The case where = 0 is called the 2-parameter Weibull distribution. This must be taken into account when describing the strength of the material, so strength is best represented as a distribution of values rather than as one specific value. The value for for the standard set of parameters in a Weibull distribution can be computed from and as: 2. Median value of property measured in a specimen of volume equal to reference_volume. The Weibull probability plot is used to test whether or not a dataset follows Weibull distribution. It is commonly used to analyze data representing lifetimes or times until failure. The value of k shows the kind of failure being experienced. 2006 - 2022 CalculatorSoup For this example, 15 / 4 = remainder 3, which is also 15 = (4 * 3) + 3. where is the shape parameter , is the location parameter and is the scale parameter. The cumulative hazard function for the Weibull is the integral of the failure rate or. Weibull distribution calculator, formulas & example work with steps to estimate the reliability or failure rate or life-time testing of component or product by using the probability density function (pdf) in the statistcal experiments. To improve this 'Weibull distribution (chart) Calculator', please fill in questionnaire. Weibull distribution. In this dialog, change Distribution to Weibull and then click the OK button to create a Weibull probability plot with column A. Double-click on the Lower Percentiles line to open the Plot Details dialog. When it comes to housing loans, mod is used to reset calculations for a new period. This has two important differences from using the standard Weibull distribution, which can also be used to define a randomized strength in MOOSE using a combination of the WeibullDistribution object in the stochastic_tools module and the MOOSE RandomIC object: 1. military uses this to coordinate with bases and other personnel located in Calculate the Weibull modulus for a material that has an 80% probability of fracture when placed under a 200MPa load, will not fracture with a load less than 40MPa, and has a scaling parameter of 150MPa. 086 (11) c = v 1 + 1 k. Maximum likelihood estimation has been the most widely used method for estimating the parameters of the Weibull distribution. The same principle is also used by banks to identify errors on international bank account numbers (IBAN) when they track transactions from other countries. Britannica notes that in modular arithmetic, where mod is N, Why does this happen? If the value of k>1, the rate of failure increases over time. [math]\displaystyle{ f(x; x_0,\lambda,k) = \begin{cases} Plot (on a single set of axes) survival probability (Ps) versus applied stress (a) for three different ceramics, one with a high Weibull modulus (e.g., m 20), one with a medium Weibull modulus (eg, m = 10), and one with a low Weibull modulus (m-5). Example of Weibull modulus calculation As-tested.
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