# 品質工程

## 田口方法

### 品質損失

${\displaystyle {1 \over n}\textstyle \sum _{i=1}^{n}\displaystyle k(y_{i}-m)^{2}=k\times MSD}$ （式1）

${\displaystyle {1 \over n}\textstyle \sum _{i=1}^{n}\displaystyle (y_{i}-m)^{2}=MSD}$ （式2）

#### 望目型（英文：nominal-the-best，NTB）

${\displaystyle {1 \over n}\textstyle \sum _{k=1}^{n}\displaystyle k(y_{i}-m)^{2}=k\times MSD=k\times [({\bar {y}}-m)^{2}+S^{2}]}$ （式3）

#### 望小型（英文：smaller-the-better ，STB）

${\displaystyle y_{i}}$ 越小品質損失越小，亦即目標值m=0，改寫式1為：

${\displaystyle {1 \over n}\textstyle \sum _{k=1}^{n}\displaystyle ky_{i}^{2}=k\times MSD=k\times ({\bar {y}}^{2}+S^{2})}$ （式4）

#### 望大型（英文：larger-the-better ，LTB）

${\displaystyle y_{i}}$ 越大品質損失越小，相當求1/${\displaystyle y_{i}}$ 越大品質損失越小，此時m=0，亦即

${\displaystyle {1 \over n}\textstyle \sum _{k=1}^{n}\displaystyle k({1 \over y_{i}}-m)^{2}={1 \over n}\textstyle \sum _{k=1}^{n}\displaystyle k({1 \over y_{i}})^{2}}$ （式5）

### 訊號／雜訊比

SN比${\displaystyle \eta }$  是以直交表中各因子的各水準為計算組，例如當控制因子${\displaystyle C_{A}}$ 有兩種水準，則需分別計算第一水準${\displaystyle C_{A}}$ 的SN比${\displaystyle \eta _{1}}$ 與第二水準${\displaystyle C_{A}}$ 的SN比${\displaystyle \eta _{2}}$ ，較大的SN比代表該水準的品質損失越小，為理想的水準。

### ${\displaystyle L_{9}(3^{4})}$ 直交表

${\displaystyle C_{A}}$  ${\displaystyle C_{B}}$  ${\displaystyle C_{C}}$  ${\displaystyle C_{D}}$  ${\displaystyle N_{A}}$  ${\displaystyle N_{B}}$
1 1 1 1 1 ${\displaystyle y_{1}}$  ${\displaystyle y_{2}}$  ${\displaystyle y_{3}}$  ${\displaystyle y_{4}}$
2 1 2 2 2 ${\displaystyle y_{1}}$  ${\displaystyle y_{2}}$  ${\displaystyle y_{3}}$  ${\displaystyle y_{4}}$
3 1 3 3 3 ${\displaystyle y_{1}}$  ${\displaystyle y_{2}}$  ${\displaystyle y_{3}}$  ${\displaystyle y_{4}}$
4 2 1 2 3 ${\displaystyle y_{1}}$  ${\displaystyle y_{2}}$  ${\displaystyle y_{3}}$  ${\displaystyle y_{4}}$
5 2 2 3 1 ${\displaystyle y_{1}}$  ${\displaystyle y_{2}}$  ${\displaystyle y_{3}}$  ${\displaystyle y_{4}}$
6 2 3 1 2 ${\displaystyle y_{1}}$  ${\displaystyle y_{2}}$  ${\displaystyle y_{3}}$  ${\displaystyle y_{4}}$
7 3 1 3 2 ${\displaystyle y_{1}}$  ${\displaystyle y_{2}}$  ${\displaystyle y_{3}}$  ${\displaystyle y_{4}}$
8 3 2 1 3 ${\displaystyle y_{1}}$  ${\displaystyle y_{2}}$  ${\displaystyle y_{3}}$  ${\displaystyle y_{4}}$
9 3 3 2 1 ${\displaystyle y_{1}}$  ${\displaystyle y_{2}}$  ${\displaystyle y_{3}}$  ${\displaystyle y_{4}}$

#### ${\displaystyle L_{8}(2^{6})}$ 直交表

${\displaystyle C_{A}}$  ${\displaystyle C_{B}}$  ${\displaystyle C_{C}}$  ${\displaystyle C_{D}}$  ${\displaystyle C_{E}}$  ${\displaystyle C_{F}}$  ${\displaystyle N_{A}}$  ${\displaystyle N_{B}}$
1 1 1 1 1 1 1 ${\displaystyle y_{1}}$  ${\displaystyle y_{2}}$  ${\displaystyle y_{3}}$  ${\displaystyle y_{4}}$
2 1 1 1 2 2 2 ${\displaystyle y_{1}}$  ${\displaystyle y_{2}}$  ${\displaystyle y_{3}}$  ${\displaystyle y_{4}}$
3 1 2 2 1 1 2 ${\displaystyle y_{1}}$  ${\displaystyle y_{2}}$  ${\displaystyle y_{3}}$  ${\displaystyle y_{4}}$
4 1 2 2 2 2 1 ${\displaystyle y_{1}}$  ${\displaystyle y_{2}}$  ${\displaystyle y_{3}}$  ${\displaystyle y_{4}}$
5 2 1 2 1 2 1 ${\displaystyle y_{1}}$  ${\displaystyle y_{2}}$  ${\displaystyle y_{3}}$  ${\displaystyle y_{4}}$
6 2 1 2 2 1 2 ${\displaystyle y_{1}}$  ${\displaystyle y_{2}}$  ${\displaystyle y_{3}}$  ${\displaystyle y_{4}}$
7 2 2 1 1 2 2 ${\displaystyle y_{1}}$  ${\displaystyle y_{2}}$  ${\displaystyle y_{3}}$  ${\displaystyle y_{4}}$
8 2 2 1 2 1 1 ${\displaystyle y_{1}}$  ${\displaystyle y_{2}}$  ${\displaystyle y_{3}}$  ${\displaystyle y_{4}}$

### 數據分析

（1）將設計因素分為控制，信號和弱因素三類。控制因素是影響過程可變性並且可能會或可能不會影響過程平均響應的因素。信號因子顯著影響平均響應（英文：mean response），但對響應的變異性沒有（或微不足道）影響。弱因素對響應的均值或變異性沒有影響。

（2）藉由選用控制因素的水準來減少過程的可變性。

（3）藉由選用信號因子的水準將平均響應移向理想目標m。

#### 水準選擇

SN比 控制因子
${\displaystyle C_{A}}$  ${\displaystyle C_{B}}$  ${\displaystyle C_{C}}$  ${\displaystyle C_{D}}$

(Max-min)

0.12 0.42 3.20 2.00

4 3 1 2

## 參考資料

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