I could see in some literature, comparative studies were carried out between the Weibull parameters (k & C) estimated using measured data and the models such as MLM, MMLM, AMLM, MQ, EMJ, EML, LS, etc. I would like to know, is it possible to find out k & C without any model using the measured data.
Kindly help.
Thank you Dr. Michael Uebel. Let me go through and I will come back.
My answer that Michael Uebel referred to was based on Linear Regression. I had also provided a more practical, but empirical method, loosely based on Moments.
You can take the logarithm of the Weibull equation twice and then plot the data with Excel. The slope will give you the Weibull modulus and the stress value for the y=0 will give you the characteristic strength.
I found this answer may be useful for your question
1. Sort data in ascending order
2. Assign them a rank, such that the lowest data point is 1, second lowest is 2, etc.
3. Assign each data point a probability. For beginners, i recommend (i-0.5)/n, where i and n are rank and sample size, respectively.
4. Take natural log of data.
5. Calculate ln (-ln (1-P)) for every data, where P is probabiliyy calculated in step 3.
6. Linear regression with results of Step 5 as Y and results of Step 4 as X. Altrrnatively, you can fit a trendline in Excel.
7. Slope of the regression line is the shape parameter, aka Weibull modulus. The intercept is the negative of the product of shape parameter and natural log of scale parameter.
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