田口方法

??????? ??? 2003.10.24 ?????? ???? ????????????(Taguchi Genichi)??? 1950??? ?????????????????????????????? ?????????????????????????????? ?????????(Quality Engineering)???? 1962?????? ?????????????(Deming)??1951?1953?1984??? ???????1980?????? AT?T?Ford?Xerox?Motorola? Kodak????????????????????(Taguchi Method)? ???????????????????????????? ?????????????????????????????? ????????????????????????????(1)? ?????????????(2)???????????(3)S/N?? (4)?????? ????????????????? 1. ?????? 2. ??????????? 3. ?????????????? 4. ????????? 5. ????????? 6. ????????????????????? 7. ??????????????????? 8. ??????????? 9. ???? 10. ???? ?????????????????????。 ???????????????? (1)???(trial-and-error) (2)?????? ????????????????????????????? ??????????????????? 7? 2????? y?? ?????? y?????? 1?????????? 2??? A? ?? 2?????????? A???? 0.3??? 3??? B??? 2???????? 2????? B???? 0.5? Exp A B C D E F G y 1 1 1 1 1 1 1 1 1.2 2 2 1 1 1 1 1 1 1.5 3 2 2 1 1 1 1 1 2.0 4 2 2 2 1 1 1 1 1.1 5 2 2 2 2 1 1 1 1.8 6 2 2 2 2 2 1 1 2.2 7 2 2 2 2 2 2 1 1.6 8 2 2 2 2 2 2 2 1.7 Effect 0.3 0.5 -0.9 0.7 0.4 -0.6 0.1 ?????????????? y????????????? ??????????????? y?????????????? ???????? A1 B1 C2 D1 E1 F2 G1? ???????????????????? A??????? ???????????????? A????????????? ?????? A????????? (3)???? ???????????????????????????? ?????????????????????????????? ????? 2??? 4?????? 24?16??????????? y??????? 3????? A1 B1 C2 D1? Exp. A B C D y 1 1 1 1 1 1.1 3 0 8 0 1 5 1 3 2 6 7 8 0 5 3 2 1 1 1 2 1. 3 1 1 2 1 1. 4 1 1 2 2 1. 5 1 2 1 1 2. 6 1 2 1 2 2. 7 1 2 2 1 1. 8 1 2 2 2 1. 9 2 1 1 1 2. 10 2 1 1 2 2. 11 2 1 2 1 1. 12 2 1 2 2 1. 13 2 2 1 1 1. 14 2 2 1 2 2. 15 2 2 2 1 1. 16 2 2 2 2 1. Level 1 1.49 1.63 1.85 1.60 Level 2 1.80 1.66 1.44 1.69 Effect 0.31 0.04 -0.41 0.09 ?????????? 16????????????????? ?????????????????????????????? ?? 1.2 1.4 1.6 1.8 2.0 A1 A2 B1 B2 C1 C2 D1 D2 (4)????? ?????? La(bc×de)??????? a?????????? ? b?????? c??d?????? e??? L?? Latin square? ????? L18(21×37)???? 18??????????? 2???? ?? 1??3?????? 7?(????????? 21×37?4,374? ??)????? L8(27)????? 8??????????? 2?? ???? 7?(????????? 27?128???)? ????????????????? Exp A B C D E F G y 1 1 1 1 1 1 1 1 1.2 2 1 1 1 2 2 2 2 1.8 3 1 2 2 1 1 2 2 2.0 4 1 2 2 2 2 1 1 2.2 5 2 1 2 1 2 1 2 1.5 6 2 1 2 2 1 2 1 1.7 7 2 2 1 1 2 2 1 1.3 8 2 2 1 2 1 1 2 2.1 Ave. 1.725 A B C D E F G Level 1 1.80 1.55 1.60 1.50 1.75 1.75 1.60 Level 2 1.65 1.90 1.85 1.95 1.70 1.70 1.85 Effect -0.15 0.35 0.25 0.45 -0.05 -0.05 0.25 1.4 1.5 1.6 1.7 1.8 1.9 2.0 A1 A2 B1 B2 C1 C2 D1 D2 E1 E2 F1 F2 G1 G2 ?????? y?????????????????? A2 B1 C1 D1 E2 F2 G1??????? 8????????????????? ?????????????????????? 95.0 )1()2()2()1()1()1()2( = −+−+−+−+−+−+−+ yGyFyEyDyCyByAy ???????? ???????????????????????????? ?????????????????????????????? ?????????????????? ???????????????????????????? ?????????????????????????????? ????????????????????????????? m ??????? 0??????????? m?????????? ???????? m 品質特性 y 品 質 損 失 L (y ) 2)()( mykyL −= ?? n???????????? ∑ = −= n i i myk 1 2)(????? ??????? Q? [ ] deviation squaremean:MSD MSDk n my k n myk Q n i i n i i =         − = − = ∑∑ == 1 2 1 2 )()( ? ( ) 22 22 1 222 1 2 22 1 2 11 2 2222 1 2 2 1 2 1 2 11 2 1 22 1 2 )()( )2()2( )2(2 22 2 2 )2( )( Smy myyy n 1 mymyyyyy n 1 mymyy n 1yy n 1y n 1 mymyyyy n 1 mymy n 1 m n 1my n 1y n 1 mmyy n 1 n my MSD n i i i n i i n i n i i n i i n i i n i i n i n i i n i i n i ii n i i +−= −+−= +−++−= +−++−= +−++−= +−= +−= +−= − = ∑ ∑ ∑∑∑ ∑ ∑ ∑∑∑ ∑ ∑ = = === = = === = = ??????????? ( )[ ]221 2)( Smyk n my kQ n i i +−= − = ∑ = ?????????? Q????????? ( )2my − ???? S2? ????????? ( ) 22 SmyMSD +−= ???????????? ?????????? 1. ??? ????????? m? ( ) 22 SmyMSD +−= 2. ??? ?????????????? m=0? 22 SyMSD += 3. ??? ???????????? 1/y???????? m=0??? n y 1 n m y 1 MSD n i i n i i ∑∑ ==       =     − = 1 2 1 2 ?MSD????????? S/N?????? [ ]MSDNS log10/ −= ?? ( ) 22 SmyMSD +−= ?? my → ??????????S→0?? ??????MSD?????????????????????? ????????? S/N??????? ????????? ???????????????????????? 80??? ?????????????????????????????? ?????????????????????????????? ???????????? 1. ?????? ?????????????????????????? 2. ??????? ?????????????????????????????? ?????????????????????????????? ????????????? ???????????? ????????????????? 1. ???? ??????????????????????????? ????????????????????????????? ????? 2. ???? ??????????????????????????? ???????? 3. ????(??????) ??????????????????????????? ?????? 例子 使用階段的 外部干擾因子 使用環境（溫度、濕度）、使用者 干擾因子 內部干擾因子 材料磨耗、材料老化 製造階段的 外部干擾因子 製造環境（溫度、濕度）、製造者 干擾因子 內部干擾因子 材料變異、製程參數變異 品質特性量測時的 量測干擾因子 量測的位置、量測的時間 干擾因子 干擾因子類別 ??????????????????????????? ????????????????????????????? ???????????? ???????????????????????? (1) ???? ??????????????????????????? ??????? (2) ???? ??????????????????????????? ?????????????????? L18(21×37)????? ??? 2??? L8(27)????? p 1 1 1 1 2 2 2 2 q 1 1 2 2 1 1 2 2 r 1 1 2 2 2 2 1 1 s 1 2 1 2 1 2 1 2 t 1 2 1 2 2 1 2 1 u 1 2 2 1 1 2 2 1 v 1 2 2 1 2 1 1 2 Exp A B C D E F G H 1 2 3 4 5 6 7 8 1 1 1 1 1 1 1 1 1 2 1 1 2 2 2 2 2 2 3 1 1 3 3 3 3 3 3 4 1 2 1 1 2 2 3 3 5 1 2 2 2 3 3 1 1 6 1 2 3 3 1 1 2 2 7 1 3 1 2 1 3 2 3 8 1 3 2 3 2 1 3 1 9 1 3 3 1 3 2 1 2 10 2 1 1 3 3 2 2 1 11 2 1 2 1 1 3 3 2 12 2 1 3 2 2 1 1 3 13 2 2 1 2 3 1 3 2 14 2 2 2 3 1 2 1 3 15 2 2 3 1 2 3 2 1 16 2 3 1 3 2 3 1 2 17 2 3 2 1 3 1 2 3 18 2 3 3 2 1 2 3 1 (3) ???? ??????????????????? 18×8?144?? ???????????????????????????? ???????????????????????????? ???(????????)?? 2????????????? ??????????????????????????? 4 ? 2??????? a?b?c?d????????? a1 a2 b1 b2 c1 c2 d1 d2 ?????????????????????????? a2 b1 c2 d1???????? a1 b2 c1 d2?????????? ???????? 2?????? N? N1(???????)?a2 b1 c2 d1 N2(???????)?a1 b2 c1 d2 ??????????????????????? N1?N2???? ?????????????????????????????? ?????????????????????????????? ?????????????? ????????????? 1. ?????? ???? 2. ??????????? ???????????????????? 3. ?????????????? 4. ????????? 5. ????????? 因子 說明 Level 1 Level 2 Level 3 A 石灰含量 5% 1% B 壽山石含量 43% 53% 63% C 壽山石種類 新配方加添加物 原來配方 新配方無添加物 D 燒粉含量 0% 1% 3% E 添加物粒徑 小一些 原來粒徑 大一些 F 燒成次數 一次燒成 二次燒成 三次燒成 G 長石含量 7% 4% 0% H 黏土種類 K-type 各一半 G-type 註：陰影部份為原設計值 6. ????????????????????? 7. ??????????????????? 8. ??????????? Exp A B C D E F G H P1 P2 P3 P4 P5 P6 P7 Ave. S S/N 1 1 1 1 1 1 1 1 1 10.18 10.18 10.12 10.06 10.02 9.98 10.20 10.11 0.087 41.3 2 1 1 2 2 2 2 2 2 10.03 10.01 9.98 9.96 9.91 9.89 10.12 9.99 0.078 42.2 3 1 1 3 3 3 3 3 3 9.81 9.78 9.74 9.74 9.71 9.68 9.87 9.76 0.064 43.6 4 1 2 1 1 2 2 3 3 10.09 10.08 10.07 9.99 9.92 9.88 10.14 10.02 0.096 40.3 5 1 2 2 2 3 3 1 1 10.06 10.05 10.05 9.89 9.85 9.78 10.12 9.97 0.129 37.7 6 1 2 3 3 1 1 2 2 10.20 10.19 10.18 10.17 10.14 10.13 10.22 10.18 0.032 50.0 7 1 3 1 2 1 3 2 3 9.91 9.88 9.88 9.84 9.82 9.80 9.93 9.87 0.048 46.3 8 1 3 2 3 2 1 3 1 10.32 10.28 10.25 10.20 10.18 10.18 10.36 10.25 0.071 43.2 9 1 3 3 1 3 2 1 2 10.04 10.02 10.01 9.98 9.95 9.89 10.11 10.00 0.070 43.1 10 2 1 1 3 3 2 2 1 10.00 9.98 9.93 9.80 9.77 9.70 10.15 9.90 0.156 36.0 11 2 1 2 1 1 3 3 2 9.97 9.97 9.91 9.88 9.87 9.85 10.05 9.93 0.071 42.9 12 2 1 3 2 2 1 1 3 10.06 9.94 9.90 9.88 9.80 9.72 10.12 9.92 0.139 37.1 13 2 2 1 2 3 1 3 2 10.15 10.08 10.04 9.98 9.91 9.90 10.22 10.04 0.120 38.5 14 2 2 2 3 1 2 1 3 9.91 9.87 9.86 9.87 9.85 9.80 10.02 9.88 0.069 43.2 15 2 2 3 1 2 3 2 1 10.02 10.00 9.95 9.92 9.78 9.71 10.06 9.92 0.129 37.7 16 2 3 1 3 2 3 1 2 10.08 10.00 9.99 9.95 9.92 9.85 10.14 9.99 0.097 40.2 17 2 3 2 1 3 1 2 3 10.07 10.02 9.89 9.89 9.85 9.76 10.19 9.95 0.147 36.6 18 2 3 3 2 1 2 3 1 10.10 10.08 10.05 9.99 9.97 9.95 10.12 10.04 0.067 43.5 Ave = 41.3 9. ???? ?S/N????????? A B C D E F G H Level 1 43.1 40.5 40.5 40.3 44.5 41.1 40.4 39.9 Level 2 39.5 41.2 41.0 40.9 40.1 41.4 41.5 42.8 Level 3 42.2 42.5 42.7 39.3 41.4 42.0 41.2 Effect 3.6 1.6 2.1 2.4 5.3 0.3 1.6 2.9 Rank 2 6 5 4 1 8 7 3 39 40 41 42 43 44 45 A1 A2 B1 B2 B3 C1 C2 C3 D1 D2 D3 E1 E2 E3 F1 F2 F3 G1 G2 G3 H1 H2 H3 S/ N R at io ????????????? A B C D E F G H Level 1 10.02 9.93 9.99 9.99 10.00 10.07 9.98 10.03 Level 2 9.95 10.00 10.00 9.97 10.02 9.97 9.97 10.02 Level 3 10.02 9.97 9.99 9.94 9.91 10.01 9.90 Effect 0.06 0.08 0.03 0.03 0.08 0.17 0.04 0.13 Rank 5 3 7 8 4 1 6 2 9.85 9.90 9.95 10.00 10.05 10.10 A1 A2 B1 B2 B3 C1 C2 C3 D1 D2 D3 E1 E2 E3 F1 F2 F3 G1 G2 G3 H1 H2 H3 品 質 特 性 ?? S/N ???????????????????????? ???????? S/N ???????????????????? ???????????????????????????? ???????? 4??c???? S/N??????d???? ???(??????)?e??? S/N??f??????????? ?????????????????????????????? ?????????????????????????????? ????? 8???????? 有影響 有影響 類別 S/N？ 品質特性？ 控制因子 用途 1 是 是 A、E、H 用來縮小變異 2 否 是 B、F 用來調整品質特性至目標值 3 是 否 C、D 用來縮小變異 4 否 否 G 用來降低成本 1. ????? ?? S/N??????????? A1 B? C3 D3 E1 F? G? H2 2. ??????? ????????????????? A1 (B) C3 D3 E1 F2 G? H2 ?? B??????????????????? G?????? ??????????????????? ????? B ???????????????????????? ??????????? S/N??????? S/N??????? A? C?D?E?H???????????????? 2? ???? S/N = 41.3 + (39.5 - 41.3) + (41.0 - 41.3)+ (40.9 - 41.3) + (40.1 - 41.3) + (42.8 - 41.3)= 41.3 - 1.8 - 0.3 - 0.4 - 1.2 + 1.5 = 39.1 ?????????????? ???? S/N = 41.3 + (43.1 - 41.3) + (42.5 - 41.3)+ (42.7 - 41.3) + (44.5 - 41.3) + (42.8 - 41.3)= 41.3 + 1.8 + 1.2 + 1.4 + 3.2 + 1.5 = 50.4 S/N?? 11.3???????????????????? 10. ???? Calculated Predicted P1 P2 P3 P4 P5 P6 P7 Ave. S S/N S/N Original 10.15 10.11 10.02 9.96 9.89 9.86 10.18 10.02 0.12 38.6 39.1 10.14 10.12 10.01 9.94 9.91 9.88 10.17 Optimal 10.08 10.06 10.03 10.02 10.03 10.01 10.09 10.04 0.03 50.1 50.4 10.07 10.05 10.04 10.02 10.02 9.99 10.09 ???? ????? 80???????20?????????????? ??????????????????? ?? 1. ?????????????????????????? 2. ?????????? 3. ??????? ?? 1. ???? 2. ???????? 3. S/N? ?? ????????????????????????????? ??? ???? 1. ????2000??????????????????????? ??? 2. ????1993??????????????????? 3. ????1992?????????????????