관리도 계수

$$ A = \frac{3}{\sqrt{n}} $$

$$ A_{2} = \frac{3}{\sqrt{n} \cdot d_{2}} $$

$$ A_{3} = \frac{3}{\sqrt{n} \cdot c_{4}} $$

$$ A_{4} = \frac{3 m_{3}}{\sqrt{n} \cdot d_{2}} $$

$$ E_{2} = \frac{3}{d_{2}} $$

$$ B_{3} = \frac{B_{5}}{c_{4}} $$

$$ B_{4} = \frac{B_{6}}{c_{4}} $$

$$ B_{5} = c_{4}-3\sqrt{1-{c_{4}}^{2}} $$

$$ B_{6} = c_{4}+3\sqrt{1-{c_{4}}^{2}} $$

$$ D_{1} = d_{2}-3d_{3} $$

$$ D_{2} = d_{2}+3d_{3} $$

$$ D_{3} = 1 -3\frac{d_{3}}{d_{2}} $$

$$ D_{4} = 1 +3\frac{d_{3}}{d_{2}} $$

$$ W=R/\sigma $$

$$ E[W]=d_{2} $$

$$ \sigma_{W}=\sqrt{V[W]}=d_{3} $$

$$ d_{2} = \int_{-\infty}^{\infty} \left[ 1- [1-\phi(x)]^{n}-\phi(x)^{n} \right] dx $$

$$ d_{3} = \sqrt{ 2 \int_{-\infty}^{\infty} \int_{-\infty}^{x^{n}} [ 1-\phi(x_{n})^{n} - [1-\phi(x_{1})]^{n} +[\phi(x_{n})-\phi(x_{1})]^{n} ] dx_{1} dx_{n} -d_{2}^{ \ 2}} $$

단, $\phi(x) = \int_{-\infty}^{x} \frac{1}{\sqrt{2 \pi}} \exp \left( - \frac{u^{2}}{2} \right) du $

$$ c_{4} = \sqrt{\frac{2}{n-1}} \frac{\Gamma(n/2)}{\Gamma[(n-1)/2]} \cong \frac{4(n-1)}{4n-3} $$

$$ c_{5} = \sqrt{1-c_{4}^{ \ 2}} $$

• 관리도 계수표 (KS A 3201)