Table 1.

Approximations to the correction factor, $\phi$, for competing processes A and B with means $1/a$ and $1/b$, respectively

$\phi$	B Weibull $(\rho )$	B narrow
$\mathit{\phi }$when$\mathbf{a}\approx \mathbf{b}$	or Gamma $(C)$	$(\text{CoV}⩽30\%)$
A exponential	${\displaystyle \frac{a+b}{a}}\left(1-{\left({\displaystyle \frac{b}{b+{\mathit{aC}}^2}}\right)}^{C^{-2}}\right)$	${\displaystyle \frac{a+b}{a}}(1-e^{a/b})$
	$\mathbf{2}\left(\mathbf{1}-{\left({\displaystyle \frac{\mathbf{1}}{\mathbf{1}+{\mathbf{C}}^{\mathbf{2}}}}\right)}^{{\mathbf{C}}^{-\mathbf{2}}}\right)$	$\mathbf{2}(\mathbf{1}-{\mathit{e}}^{-\mathbf{1}})$
A, B non-exponential	$(a+b)(a^{\rho }+b^{\rho }{)}^{-1/\rho }$	${\displaystyle \frac{a+b}{\max (a,b)}}$
same shape	${\mathbf{2}}^{(\mathit{\rho }-\mathbf{1})}/\mathit{\rho }$, or
	$\mathbf{2}\left(\mathbf{1}-{\mathbf{2}}^{\mathbf{1}-\mathbf{2}\mathit{k}}{\displaystyle \frac{\mathrm{\Gamma }(\mathbf{2}\mathbf{k})}{\mathbf{k}\mathrm{\Gamma }(\mathbf{k}{)}^{\mathbf{2}}}}\right)$	2

C gives the CoV of the non-exponential distribution; for the Gamma distribution $k=1/C^2$.

Entries in bold are simplifications for the case $a=b$.