Formulas: 9-5-4-7-2

MIL-HDBK-5J, Metallic Materials and Elements for Aerospace Vehicle Structures

Last Updated 29 Oct 2026

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Formula 1

That is, the calculations in this section are performed based on $Z_{(1)}$ , $\ldots, Z_{(n)}$ , where $Z_{(\mathrm{i})}=X_{(\mathrm{i})}-\tau$ , with $\tau$ estimated as in Section 9.5.4.7.1.

Z_{(\mathrm{i})}=X_{(\mathrm{i})}-\tau

Formula 2

The assumption is made here that if the data are censored, then only the $r$ smallest observations in the sample are observed $(1 \leq r \leq n)$ , where $r$ is some pre-specified number (often based on a percentage); this is called Type II censoring.

(1 \leq r \leq n)

Formula 3

Let $S_{y}$ denote the standard deviation of $Y_{1}, \ldots, Y_{r}$ where $Y_{i}=\ln \left(Z_{i}\right)$ for $i=1, \ldots, r$ .

Y_{i}=\ln \left(Z_{i}\right)

Formula 4

i=1, \ldots, r

Formula 5

Calculate $I=1.28 / S_{y}$ as an initial guess at the solution and calculate $g(I)$ .

I=1.28 / S_{y}

Formula 6

If $g(I)>0$ , then find the smallest positive integer $k$ such that $g\left(I / 2^{k}\right)<0$ and let $L=I / 2^{k}$ and $H=I / 2^{k-1}$ .

g(I)>0

Formula 7

g\left(I / 2^{k}\right)<0

Formula 8

L=I / 2^{k}

Formula 9

H=I / 2^{k-1}

Formula 10

If $g(I)<0$ , then find the smallest positive integer $k$ such that $g\left(2^{k} I\right)>0$ and let $L=2^{k-1} I$ , and $H=2^{k} I$ .

g(I)<0

Formula 11

g\left(2^{k} I\right)>0

Formula 12

L=2^{k-1} I

Formula 13

H=2^{k} I

Formula 14

Reduce the (L,H) interval by calculating $M=(L+H) / 2$ and setting

M=(L+H) / 2