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)]