x_i = μ + ε_i

x_{pt} = x_{char} + δ_{hom} + δ_{trans} + δ_{stab}

u(x_{pt}) = \sqrt{u_{char}^2 + u_{hom}^2 + u_{trans}^2 + u_{stab}^2}

x_{pt} = x_{CRM} + \bar{d}

u_{char} = \sqrt{u_{CRM}^2 + u_d^2}

u(x_{pt}) = 1.25 \cdot (s \cdot / \sqrt{p})

u_{diff} = \sqrt{u^2(x_{ref}) + u^2(x_{pt})}

sigma_R = 0.22 \cdot c if c < 1.2e-7; sigma_R = 0.02 \cdot c^0.8495 if 1.2e-7 < = c < = 0.138; sigma_R = 0.01 \cdot c^0.5 if c > 0.138

sigma_{pt} = \sqrt{sigma_R^2 - sigma_r^2 \cdot (1 - 1/m)}

u(x_{pt}) < 0.3 \cdot sigma_{pt} \text{或} u(x_{pt}) < 0.1 \cdot delta_E

D_i = x_i - x_{pt}

D_i\% = \dfrac{100 \cdot (x_i - x_{pt})}{x_{pt} \%}

P_{Ai} = (D_i / delta_E) \cdot 100\%

z_i = \dfrac{x_i - x_{pt}}{sigma_{pt}}

z'_i = \dfrac{x_i - x_{pt}}{\sqrt{sigma_{pt}^2 + u^2(x_{pt})}}

delta_E' = \sqrt{delta_E^2 + U^2(x_{pt})}

zeta_i = \dfrac{x_i - x_{pt}}{\sqrt{u^2(x_i) + u^2(x_{pt})}}

\dfrac{sigma_{pt}}{\sqrt{sigma_{pt}^2 + u^2(x_{pt})}}

\dfrac{x_i - x_{pt}}{\sqrt{U^2(x_i) + U^2(x_{pt})}}

q_i = \dfrac{q_{min} + (i-1) \cdot (q_{nk} - q_1)}{n_k - 1}

h_i = (1/(p \cdot sigma_k)) \cdot \sum_{j=1}^{p} phi((x_j - q_i)/sigma_k)

(\sqrt{m} \cdot (x_i - x \cdot )/w \cdot )^2 + [\sqrt{2 \cdot (m-1)} \cdot ln(s_i/w \cdot )]^2

s = w \cdot \cdot exp{±(1/\sqrt{2 \cdot (m-1)}) \cdot \sqrt{chi2_{2:0.99}^2 - (\sqrt{m} \cdot (x - x \cdot )/w \cdot )^2}}

x \cdot - w \cdot \cdot \sqrt{\dfrac{chi2_{2:0.99}^2}{m}} < = x < = x \cdot + w \cdot \cdot \sqrt{\dfrac{chi2_{2:0.99}^2}{m}}

s_s < = 0.3 \cdot sigma_{pt}

s_s < = 0.1 \cdot delta_E

sigma_{allow}^2 = (0.3 \cdot sigma_{pt})^2

c = F1 \cdot sigma_{allow}^2 + F2 \cdot s_w^2

F_m = \dfrac{F_{g-1, g(m-1), 0.95}}{m}

sigma_{pt}' = \sqrt{sigma_{pt}^2 + s_s^2}

\bar{x}_{t} = (1/m) \cdot \sum_{k=1}^{m} x_{t,k}

s_t^2 = (1/m) \cdot \sum_{k=1}^{m} (x_{t,k} - \bar{x}_{t})^2

w_t^2 = (1/(m-1)) \cdot \sum_{k=1}^{m} (x_{t,k} - \bar{x}_{t})^2

\bar{x} = (1/g) \cdot \sum_{t=1}^{g} \bar{x}_{t}

\bar{s}_{x}^2 = (1/(g-1)) \cdot \sum_{t=1}^{g} (\bar{x}_{t} - \bar{x})^2

s_w^2 = (1/g) \cdot \sum_{t=1}^{g} w_t^2

s_{s,w}^2 = (1/(g-1)) \cdot \sum_{t=1}^{g} (\bar{x}_{t} - \bar{x})^2 + (1 - 1/m) \cdot s_w^2

s_s^2 = s_{s,w}^2 - s_w^2

\bar{x}_{t} = \dfrac{x_{t,1} + x_{t,2}}{2}

w_t = |x_{t,1} - x_{t,2}|

\bar{x} = (1/g) \cdot \sum_{i=1}^{g} \bar{x}_{i}

s_x = \sqrt{\dfrac{\sum_{i=1}^{g} (\bar{x}_{i} - \bar{x})^2}{g-1}}

s_w = \sqrt{\dfrac{\sum_{i=1}^{g} w_i^2}{2g}}

s_s = max(0, \sqrt{s_x^2 - (s_w^2 / 2)})

abs(y1_{bar} - y2_{bar}) < = 0.3 \cdot sigma_{pt} \text{或} < = 0.1 \cdot delta_E

abs(y1_{bar} - y2_{bar}) < = 0.3 \cdot sigma_{pt} + 2 \cdot \sqrt{u^2(y1_{bar}) + u^2(y2_{bar})}

med(x) = { x((p+1)/2) if p odd; (x(p/2)+x(p/2+1))/2 if p even }

MADe(x) = 1.483 \cdot med(d)

nIQR(x) = 0.7413 \cdot (Q3(x) - Q1(x))

x \cdot = med{x_i}

s \cdot = 1.483 \cdot med{|x_i - x \cdot |}

delta = 1.5 \cdot s \cdot ; x_i \cdot = { x \cdot - delta if x_i < x \cdot - delta; x \cdot + delta if x_i > x \cdot + delta; x_i otherwise }; x \cdot = \dfrac{sum(x_i \cdot )}{p; s \cdot } = 1.134 \cdot \sqrt{\dfrac{sum((x_i \cdot - x \cdot )^2)}{p-1}}

w \cdot = med{w_i}

ψ = η × w \cdot

w_i \cdot = ψ (\text{若} w_i > ψ) \text{否则} w_i

w \cdot = ξ \cdot \sqrt{\dfrac{\sum_{j=1}^{p} (w_j \cdot )^2}{p}}

d_{ij} = |x_i - x_j|

k = \dfrac{h(h-1)}{2}

h = \dfrac{p}{\dfrac{2 (p\text{为偶数}) \text{或} (p-1)}{2 (p\text{为奇数})}}

Q_n = 2.2219 \cdot d_(k) \cdot b_p

b_p = \dfrac{1}{r_p + 1}

r_p = (1/p) \cdot [1.6019 + (1/p) \cdot (-2.128 - 5.172/p)]

r_p = (1/p) \cdot {3.6756 + (1/p) \cdot [1.965 + (1/p) \cdot (6.987 - 77/p)]}

H_1(x) = (2/(p(p-1))) \cdot \sum_{1≤i<j≤p} (1/(n_i n_j)) \cdot \sum_{k=1}^{n_i} \sum_{m=1}^{n_j} I(|y_{ik} - y_{jm}| ≤ x)

G_1(x_i) = 0.5 \cdot (H_1(x_i)+H_1(x_{i-1})) (\text{若}i≥2) \text{或} 0.5 \cdot H_1(x_1) (\text{若}i=1\text{且}x_1>0)

s \cdot = \dfrac{G_1^{-1}[0.25+0.75 \cdot H_1(0)]}{\sqrt{2} \cdot Φ^{-1}[0.625+0.375 \cdot H_1(0)]}

w_i = \dfrac{0 if |q_i| > 4.5; (4.5 - q_i)}{q_i if 3 < |q_i| <} = \dfrac{4.5; 1.5}{q_i if 1.5 < |q_i| <} = 3.0; 1 if |q_i| < = 1.5

x \cdot = \dfrac{sum(w_i \cdot x_i)}{sum(w_i)}

|x \cdot _{new} - x \cdot _{old}| < 0.01 \cdot s \cdot \cdot \sqrt{p}

w_t = \dfrac{0 if |q| > c; a \cdot (c - q)}{(q \cdot (c - b)) if b < |q| <} = \dfrac{c; a}{q if a < |q| <} = b; 1 if |q| < = a

\sum_{i=1}^{p} psi((y_i - x \cdot )/s \cdot ) = 0

psi(q) = 0 if q < = -4.5; -4.5 - q if -4.5 < q < = -3; -1.5 if -3 < q < = -1.5; q if -1.5 < q < = 1.5; 1.5 if 1.5 < q < = 3; 4.5 - q if 3 < q < = 4.5; 0 if q > 4.5

d_{6(i-1)+j} = y_i + c_j \cdot s \cdot \text{其中} c_j \text{为} -4.5, -3, -1.5, 1.5, 3, 4.5

P_m = \sum_{i=1}^{p} psi((y_i - d_{(m)})/s \cdot )

x_m = \dfrac{d_{(m)} - P_m}{\dfrac{P_{m+1} - P_m}{d_{(m+1)} - d_{(m)}}}

|x \cdot - med(y_1,...,y_p)| = min{|x - med(y_1,...,y_p)|; x in S}

s \cdot = (1/(0.798 \cdot p)) \cdot \sum_{i=1}^{p} |x_i - med(x)|

x_{pt} = 21.62 + 1.73

u(x_{pt}) = \sqrt{0.26^2 + 0.24^2}

u(x \cdot ) = 1.25 \cdot (s \cdot / \sqrt{n})

u_{diff} = \sqrt{u^2(x_{ref}) + u^2(x \cdot )}

x_{diff} = x_{ref} - x \cdot

0.02 \cdot c^0.8495

\sqrt{σ_R^2 - σ_r^2 \cdot (1 - 1/m)}

\sqrt{σ_R^2 - σ_r^2}