Brinell hardness tests were made on a random sample of 10 steel parts during processing. The

results were HB values of 230, 232(2), 234, 235(3), 236(2), and 239. Estimate the mean and

standard deviation of the ultimate strength in kpsi.

Question

Brinell hardness tests were made on a random sample of 10 steel parts during processing. The

results were HB values of 230, 232(2), 234, 235(3), 236(2), and 239. Estimate the mean and

standard deviation of the ultimate strength in kpsi.

Accepted Answer

[latex] \text { For the data given, converting } H_{B} \text { to } S_{u} \text { using Eq. (2-21) }\[/latex]

[latex]\begin{array}{|ccc|} \hline H_{B} & S_{u}(\mathrm{kpsi}) & S_{u}^{2}(\mathrm{kpsi}) \ 230 & 115 & 13225 \ 232 & 116 & 13456 \ 232 & 116 & 13456 \ 234 & 117 & 13689 \ 235 & 117.5 & 13806.25 \ 235 & 117.5 & 13806.25 \ 235 & 117.5 & 13806.25 \ 236 & 118 & 13924 \ 236 & 118 & 13924 \ 239 & 119.5 & 14280.25 \ \Sigma S_{u}= & 1172 & \Sigma S_{u}^{2}=137373 \ \hline \end{array}\[/latex]

[latex]\ \bar{S}_{u}=\frac{\sum S_{u}}{N}=\frac{1172}{10}=117.2 \doteq 117 \mathrm{kpsi} \quad \text { . }\[/latex]

Eq. (20-8),

[latex]s_{S_{u}}=\sqrt{\frac{\sum_{i=1}^{10} S_{u}^{2}-N \bar{S}_{u}^{2}}{N-1}}=\sqrt{\frac{137373-10(117.2)^{2}}{9}}=1.27 \mathrm{kpsi} \quad \text { . }[/latex]

Eq. (2-21),

[latex]S_{u}= \begin{cases}0.5 H_{B} & \text { kpsi } \ 3.4 H_{B} & \mathrm{MPa}\end{cases}[/latex]

Eq. (20-8),:

[latex]s_{x}=\sqrt{\frac{\sum_{i=1}^{N} x_{i}^{2}-\left(\sum_{i=1}^{N} x_{i}\right)^{2} / N}{N-1}}=\sqrt{\frac{\sum_{i=1}^{N} x_{i}^{2}-N \bar{x}^{2}}{N-1}}[/latex]

Question 2.15: Brinell hardness tests were made on a random sample of 10 s...

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