NIST Guidelines for Evaluating and Expressing Measurement Uncertainty

Eq A1 
$Y = f(X_1, ~X_2, ~\ldots, ~X_N) ~ .$


Eq A2 
$y = f(x_1, ~x_2, ~\ldots, ~x_N) ~ .$


Eq A3 
\begin{eqnarray*}
u_c^2(y) &=& \sum_{i=1}^N ~ \left( {{\partial f}\over{\partial x_i}} \right)^2 
   ~ u^2(x_i)\\
&~& + 2 \sum_{i=1}^{N-1} ~  \sum_{j=i+1}^N ~ 
{{\partial f}\over{\partial x_i}} ~ {{\partial f}\over{\partial x_j}} 
   ~ u(x_i,x_j) ~ .
\end{eqnarray*}


Eq A4
$$ x_i = \bar{X}_i = {1\over n} ~ \sum_{k=1}^n ~ X_{i,k} ~ ,$$


Eq A5
\begin{eqnarray*}
u(x_i) &=& s(\bar{X}_i)\\
       &=& \left( {1\over{n(n-1)}} ~ \sum_{k=1}^n ~ (X_{i,k} - \bar{X}_i)^2
       \right)^{1/2} ~ .\end{eqnarray*}


Eq A6
$ x_i = (a_+ + a_-)/2 ~ ,$


Eq A7
$u(x_i) = a/\sqrt{3} ~ , $


Eq B1
$$\nu_{\rm eff} = {\textstyle{u_c^4(y)}\over{\sum_{i=1}^N ~ 
{\textstyle{c_i^4 \, u^4(x_i)}\over{\textstyle\nu_i}}}} ~ , $$


Eq B2
$$\nu_{\rm eff} \leq \sum_{i=1}^N ~ \nu_i. $$


Eq D1.1
$$u_c^2 = \sum_{i=1}^N ~ [c_i \, u(x_i)]^2 \equiv \sum_{i=1}^N ~ 
u_i^2(y) ~ , $$


Eq D3.1
\begin{eqnarray*}
x_1 &=& g_1(w_1, ~w_2. ~..., ~w_K)\\
x_2 &=& g_2(z_1, ~z_2. ~..., ~z_L)\\
 &~& {\rm etc.}\end{eqnarray*}


Eq D3.2
$y = x + C_1 + C_2 + \ldots + C_M ~ ,$


Eq D5.1 
$$1 - \alpha = \int_{-\infty}^{\textstyle{t_{1-\alpha}}}  f(t,\nu) 
{\rm d}t $$