Formulas: ETL – Upper Empirical Tolerance Limit

MIL-STD-810H, Environmental Engineering Considerations and Laboratory Tests

Last Updated 29 Oct 2026

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Formula 1

m_{j}=\frac{1}{N} \sum_{i=1}^{N} x_{i j} \quad j=1,2, \cdots M

\{u\}=\left\{u_{11}, u_{12}, \cdots u_{1 M} ; u_{21}, u_{22}, \cdots u_{2 M} ; u_{N 1}, u_{N 2}, \cdots u_{N M}\right\}

where

$\quad u_{i j}=\frac{x_{i j}}{m_{j}} \quad i=1,2, \cdots N ; \quad j=1,2, \cdots, M$

where : $\quad u_{i j}=\frac{x_{i j}}{m_{j}} \quad i=1,2, \cdots N ; \quad j=1,2, \cdots, M$

\quad u_{i j}=\frac{x_{i j}}{m_{j}} \quad i=1,2, \cdots N ; \quad j=1,2, \cdots, M

$u_{\beta}=u_{(k)}$ where $u_{(k)}$ is the $k^{t h}$ ordered element of set ${u}$ for $0<\beta=\frac{k}{M N} \leq 1$

u_{\beta}=u_{(k)}

0<\beta=\frac{k}{M N} \leq 1

E T L(\beta)=u_{\beta} m_{j}=x_{\beta j} \quad j=1,2, \cdots M