# A Simple Estimation Method of Weibull Modulus and Verification with Strength Data
## 5 Discussion
### Industrial Strength Data  
When one examines strength data from metal industry, the deviation of data is often given in terms of standard deviation. While the normal distribution can represent the data well, it is often useful to describe the data with Weibull distribution, as it will allow advanced data analyses, such as failure and lifetime prediction. A short list of large-scale studies of steel strength are collected and summarized in this section, providing representative m values estimated, as listed in Table 8. One notable feature is that the sample counts are high, making the outcome more reliable. Two related works are also added. \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline
**Materials** & **\textless{}\textless{}\textgreater{}** & **S** & **CV** & **M\({}_{\text{obs}}\)** & **M\({}_{\text{sat}}\)** & **N** & **Note** & **Ref** \\ \hline S355 MC steel & 497.44 & 11.31 & & & 48.38 & 703 & Hot-rolled sheet & [129] \\ ABS A steel & 408.79 & & 0.044 & & 25.00 & 33 & 1948 tests & [130] \\ ABS B steel & 420.72 & & 0.091 & 12.09 & 79 & 1948 tests & [130] \\ ABS C steel & 415.54 & & 0.051 & & 21.57 & 13 & 1948 tests & [130] \\ ABS B steel & 431.55 & & 0.044 & & 25.00 & 39 & Before 1984 & [130] \\ ABS C steel & 436.03 & & 0.047 & 23.40 & 36 & Before 1984 & [130] \\ ASTM A7 steel & 432.03 & & 0.0226 & 48.67 & 120 & Before 1984 & [130] \\ ASTM A7 steel & 443.68 & & 0.0341 & 32.26 & 58 & Before 1984 & [130] \\ ASTM A7 steel & 418.23 & & 0.0241 & 45.64 & 54 & Before 1984 & [130] \\ ASTM A7 steel & 416.65 & & 0.0719 & 15.30 & 22 & Before 1984 & [130] \\ Q235 steel & 456.87 & 21.73 & & 23.13 & 3924 & 2.5 to 16-mm thick plates & [131] \\ Q235 steel & 446.45 & 20.02 & & 24.53 & 7371 & 16 to 40 mm & [131] \\ Q235 steel & 442.33 & 22.26 & & 21.86 & 1861 & 40 to 60 mm & [131] \\ Q235 steel & 437.20 & 21.61 & & 22.25 & 718 & 60 to 100 mm & [131] \\ Q235 steel & 431.76 & 19.3 & & 24.61 & 170 & 100 to 150 mm & [131] \\ Q235 steel & 448.16 & 21.75 & & 22.67 & 14.044 & Total above & [131] \\ Q345 steel & 553.08 & 28.1 & & 21.65 & 2632 & 2.5 to 16-mm thick plates & [131] \\ Q345 steel & 539.20 & 31.05 & & 19.10 & 2230 & 16 to 40 mm & [131] \\ Q345 steel & 527.15 & 27.32 & & 21.22 & 646 & 40 to 60 mm & [131] \\ Q345 steel & 527.83 & & 20.59 & 396 & 60 to 100 mm & [121] \\ Q345 steel & 513.94 & 27.38 & & 20.65 & 36 & 100 to 150 mm & [121] \\ Q45 steel & 543.13 & 30.45 & & 19.62 & 5940 & Total above & [131] \\ S235 IR steel & 465.90 & 51.6 & & 9.93 & 120 & ASTM A235C * & [132] \\ S335j2+N steel & 569.70 & 29.1 & & 21.54 & 31 & ASTM A527-50 * & [132] \\ S550C steel & 678.10 & 37.3 & & 20.00 & 23 & ASTM A80 XL * & [132] \\ S2352N total & 316.16 & 24.46 & & 14.22 & 689 & Hot rolled & [133] \\ S2758 HS steel & 377.33 & 21.09 & & 19.68 & 290 & Hot rolled & [133] \\ S2758S steel & 310.95 & 14.34 & & 23.85 & 4095 & Hot rolled & [133] \\ S355 BS steel & 402.02 & 16.13 & & 27.42 & 1914 & Hot rolled & [133] \\ S460B8 steel & 474.64 & 20.24 & & 25.80 & 672 & Hot rolled & [133] \\ CSA A402.2450W & 450 * & & 0.035 & 31.43 & 4942 & W shapes & [134] \\ CSA A402.20 450W & 450 * & & 0.04 & 27.50 & 10.794 & W shapes & [134] \\ CSA A402.20 450W & 450 * & & 0.03 & 36.67 & 2873 & W shapes & [134] \\ CSA A402.20 450W & 450 * & & 0.047 & 23.40 & 987 & W shapes & [134] \\ \hline \hline \end{tabular}
\end{table} 
Table 8: Listing of large-scale data for estimated m values using S or CV and for observed m.