# A Simple Estimation Method of Weibull Modulus and Verification with Strength Data
## 5 Discussion
### Estimation of m from Standard Deviation or from Coefficient of Variation
\begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline
**Materials** & **\textless{}\textless{}\textgreater{}** & **S** & **CV** & **M\({}_{\text{abs}}\)** & **M\({}_{\text{est}}\)** & **N** & **Note** & **Ref** \\ \hline Mid-Hudson Bridge & 1635.55 & 65.27 & & & 27.56 & \textgreater{}10 & 61-62 & [43] \\ Mid-Hudson Bridge & 1637.76 & 77.14 & & & 23.35 & \textgreater{}10 & 90-91s & [43] \\ Mid-Hudson Bridge & 1599.07 & 59.80 & & 29.42 & \textgreater{}10 & 136-137s & [43] \\ Bridge W & 1695.00 & & 0.026 & 42.31 & 17 & Corrosion Stage 2 & [122] \\ Bridge W & 1695.00 & & 0.026 & 42.31 & 17 & Stage 3 & [122] \\ Bridge W & 1661.10 & & 0.038 & 28.95 & 35 & Stage 4 & [122] \\ Bridge W & 1508.55 & & 0.128 & 8.59 & 11 & Stage 4 + Cr & [122] \\ Bridge X & 1647.06 & & 0.018 & 61.11 & 30 & Stage 2 & [122] \\ Bridge X & 1625.52 & & 0.024 & 45.83 & 18 & Stage 3 & [122] \\ Bridge X & 1592.38 & & 0.038 & 28.95 & 10 & Stage 4 & [122] \\ Bridge X & 1381.94 & & 0.131 & 8.40 & 15 & Stage 4 + Cracks & [122] \\ Bridge Z & 1644.00 & & 0.021 & 52.38 & 20 & Stage 1 & [122] \\ Bridge Z & 1620.98 & & 0.029 & 37.93 & 29 & Stage 2 & [122] \\ Bridge Z & 1553.58 & & 0.039 & 28.21 & 22 & Stage 3 & [122] \\ Bridge Z & 1551.94 & & 0.041 & 26.83 & 33 & Stage 4 & [122] \\ Bridge Z & 1144.22 & & 0.263 & 4.18 & 6 & Stage 4 + Cracks & [122] \\ Al-Cu casting & & & 4 & 36 & & [123] \\ Al-Cu casting & & & 4 & 36 & & [123] \\ White cast iron & & & 2 & 26 & & [123] \\ White cast iron & & & 2 & 21 & & [123] \\ Gray cast iron & & & 6 & 17 & & [123] \\ Al casting A357-T6 & 357 & & 47.5 & 354 & & [124] \\ Al casting A357-T6 & 361 & & 30.6 & 388 & & [124] \\ [PERSON] casting & & 10.79 & 45 & & [125] \\ [PERSON]Si casting & & 19.71 & 40 & & [125] \\ Al?Si casting & & 37.74 & 36 & & [125] \\ Al?Si casting & & 20.87 & 80 & & [125] \\ Al?Si casting & & 2.5 & 30 & & [126] \\ Al?Si casting & & 6.4 & 30 & & [126] \\ Al?Si casting & 13.7 & 30 & Bimodal, low & [126] \\ Al?Si casting & 20 & 30 & Bimodal, high & [126] \\ AM60B Mg casting & 7.69 & 18 & As cast & [127] \\ AM60B Mg casting & 13.52 & 18 & T6 heat treatment & [127] \\ \hline \hline \end{tabular} Ref. reference number: Note 7-1: N.A. not available, but expected to be above 30 for [107]: Note 7-2: N.A. not available, but expected to be above 50 for [108]: Note 7-3: N.A. = not available for [110]: Note 7-4: N.A. = not available for [114]: Note 7-5: N.A. = not available for [115]: CNT. = carbon nanotubes.  
\end{table} 
Table 7: _Cont._Two groups of steel in Table 3 have lower m values of 15 to 29, but these were sintered materials that were expected to contain numerous voids. The following six rows in Table 7 are the data from laser-sintered maraging steel [51]. The first row was listed in Table 3 as it included nine strength values. Its m\({}_{\text{obs}}\) value was calculated as 99.2, which agreed reasonably with the m\({}_{\text{est}}\) of 113.5 with the modified Robinson relation. Other m\({}_{\text{est}}\) values given here were between 25-179, reflecting the variability of the selective laser melting process used. However, the last row with an m value of 179 is clearly out of the range. The estimated m values should lead to a better selection of process parameters, since normally sintered medium carbon steel showed m values within the range of 15 to 27 [52], as shown in Table 3. The seven datasets that follow are from dual-phase steel with ferrite and martensite phases [109]. The carbon level is low (0.11-0.12%), producing a uniform strain of more than 10%. Estimated m values ranged from about 20 to 113, and most were in the 30 to 50 range. The case of the highest m value was for quasi-static loading, and the yield strength also showed a low scatter, making the high m value plausible (one dataset was not included since only a one-digit S value was given). The next 15 rows in Table 7 covered various alloys with a wide range of m values.