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% 泓熠 (HY).
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\newcommand{\heitisection}[1]{\section{\heiti #1}}
\renewcommand{\refname}{\heiti 参考资料}

\title{
	\heiti \textbf{
	试验设计与分析快速回顾 \\
	Trial Design and Analysis Quick Review
	}
}
\author{\heiti 泓熠 (HY)}
\date{}

\begin{document}
	\maketitle
	\noindent Copyright \copyright\ 2026, 泓熠 (HY). \\
	Permission is granted to copy, distribute and/or modify this document under the terms of the GNU Free Documentation License, Version 1.3 (\url{https://www.gnu.org/licenses/fdl-1.3.html}) or any later version published by the Free Software Foundation (\url{https://www.fsf.org}); with no Invariant Sections, no Front-Cover Texts, and no Back-Cover Texts.
	\vfill
	本文对应教材：《试验设计方法》（科学出版社） \cite{9787030176271}
	\heitisection{简答}
	\begin{enumerate}
		\item 试验设计的四个发展阶段(P4)
		\item 什么是因素？水平？响应？(P6)
		\item 方差分析的基本思想(P13)
		\item 什么是交互作用？(P23)
		\item 什么是回归直线？(P32)
		\item 正交试验设计的基本方法(步骤)(P66)
		\item 什么是并列法？(P89)拟水平法？(P92)拟因素法？(P94)赋闲列？(P95)
		\item 什么是直和法？(P100)直积法？(P108)
		\item 产品三次设计的三个阶段(P123)
		\item 什么是望目特性？(P127)望小望大？(P129)信噪比？(P128)
		\item 什么是稳健设计？(P130)灵敏度设计？(P141)
		\item 稳健设计的基本步骤(P134)
		\item 什么是动态特性？(P151)
		\item 均匀设计的特点(P172)
	\end{enumerate}
	\heitisection{公式}
		\begin{equation}
			Q
			=
			\sum_{i=1}^{r} \frac{1}{n_{i} } (\sum_{j=1}^{n_{i} } y_{ij} )^{2}
			;
			S_{A}^{2}
			=
			Q-P
			;
			f_{A}
			=
			r-1
		\end{equation}
		\begin{equation}
			P
			=
			\frac{1}{n}(
				\sum_{i=1}^{r}\sum_{j=1}^{n_{i}}y_{ij}
			)^{2}
			;
			S_{e}^{2}
			=
			R-Q
			;
			f_{e}
			=
			n-r
		\end{equation}
		\begin{equation}
			R
			=
			\sum_{i=1}^{r}\sum_{j=1}^{n_{i}}y_{ij}^{2}
			;
			S_{T}^{2}
			=
			R-P
			;
			f_{T}
			=
			n-1
		\end{equation}
		\begin{equation}
			F
			=
			\frac{S_{A}^{2}/f_{A}}{S_{e}^{2}/f_{e}}
			;
			\mbox{标准}
			F_{\alpha}(f_{A},f_{e})
			;
			\alpha
			=
			0.05
			\mbox{(一个*)}
			;
			\alpha =0.1
			\mbox{(两个*)}
		\end{equation}
		\begin{equation}
			Q: \mbox{各水平下所有数据和的平方, 除以数据个数商的加和}
		\end{equation}
		\begin{equation}
			P: \mbox{所有数据和的平方除以数据个数}; R: \mbox{所有数据平方和}
		\end{equation}
		\begin{equation}
			D_{ij(\alpha)}=\sqrt{\left(\frac{1}{n_{i}}+\frac{1}{n_{j}}\right)\frac{S_{e}^{2} }{f_{e} }f_{A}F_{\alpha}(f_{A},f_{e})}
		\end{equation}
		\begin{equation}
			\mbox{i指行，j指列，同一水平在一行，同一次试验在一列}
		\end{equation}
		\begin{equation}
			l_{xx}=\sum_{i=1}^{n}(x_{i}-\bar{x}^{2})=\sum_{i=1}^{n} x_{i}^{2}-n\bar{x}^{2}
		\end{equation}
		\begin{equation}
			l_{yy}=\sum_{i=1}^{n}(y_{i}-\bar{y}^{2})=\sum_{i=1}^{n} y_{i}^{2}-n\bar{y}^{2}
		\end{equation}
		\begin{equation}
			l_{xy} =\sum_{i=1}^{n} (x_{j}-\bar{x}  )(y_{j}-\bar{y} )=\sum_{i=1}^{n}x_{i}y_{i}-n\bar{x}\bar{y}
		\end{equation}
		\begin{equation}
			\hat{\beta}=\frac{l_{xy} }{l_{xx}};\hat{\alpha } =\bar{y}-\hat{\beta }\bar{x};Q=l_{yy} -l_{xy}\hat{\beta}
		\end{equation}
		\begin{equation}
			u=l_{xy}\hat{\beta};l_{yy}=Q+U;f_{T}=n-1;f_{Q}=n-2
		\end{equation}
		\begin{equation}
			f_{U}=1;F=\frac{U/f_{U} }{Q/f_{Q} };r=\frac{l_{xy}}{\sqrt{l_{xx} l_{yy}}}
		\end{equation}
		\begin{equation}
			\mbox{标准}F_{\alpha}(f_{U},f_{Q});r_{\alpha}(f_{Q})
		\end{equation}
		\begin{equation}
			S_{y}=\sqrt{\frac{Q}{n-2}};y_{0} \in (\hat{y}\mp 2S_{y})\Rightarrow 95\%;y_{0}\in(\hat{y}\mp 3S_{y})\Rightarrow 99\%
		\end{equation}
		\begin{equation}
			L_{n}(t^{q});\mbox{n次试验q因素t水平；n行q列t个数码}
		\end{equation}
		\begin{equation}
			\mbox{二水平}S_{i}^{2}=\frac{(I_{i}-II_{i})^{2}}{\mbox{数据总个数}};
			\mbox{多水平}S_{i}^{2}=\frac{I_{i}^{2}+II_{i}^{2}+III_{i}^{2}+\cdots}{\mbox{水平重复数}}-\frac{T^{2}}{\mbox{数据总个数}}
		\end{equation}
		\begin{equation}
			f_{i}：\mbox{第i列（第i因素）的水平数}-1;S_{T}^{2}=\sum S_{i}^{2};f_{T}=\sum f_{i}
		\end{equation}
		\begin{equation}
			S_{T}=\sum_{i=1}^{n}y_{i}^{2}-\frac{T^{2} }{n};T=\sum y_{i}
		\end{equation}
		\begin{equation}
			\mbox{控制：}x_{1}=\frac{y_{1}- \hat{\alpha}+2S_{y}}{\hat{\beta}}；x_{2}=\frac{y_{2}-\hat{\alpha}+2S_{y}}{\hat{\beta}}\Rightarrow 95\%
		\end{equation}
		\begin{equation}
			x_{1}=\frac{y_{1}- \hat{\alpha}+3S_{y}}{\hat{\beta}}；x_{2}=\frac{y_{2}-\hat{\alpha}+3S_{y}}{\hat{\beta}}\Rightarrow 99\%
		\end{equation}

	\begin{thebibliography}{9999}
		\bibitem{9787030176271} 赵选民.试验设计方法[M].北京:科学出版社,2006.8,ISBN 9787030176271.
	\end{thebibliography}
\end{document}
