実験計画法 - lab.sdm.keio.ac.jp

1 11/29. 8.. A B . A B . B1 B2 B3 B4 xi . A1 76 77 77 74 78 79 78 75. A2 73 75 75 72 72 75 73 74. x j x = n: a:A b:B r: . B A A . B . B1. A B . A B A B B2. (1) A1 A2. xijk= ij+ ijk= +( ) +( .j- )+( ij- .j+ )+ ijk= + i+ j+( )ij+ ijk . a ij i A i =0. i =1..j b j B j =0. j =1 i. a b . ( )ij A B ( ) ij ( ) ij = 0. = 0, i =1 j =1. ijk ijk N(0, 2) . (2) . x ijk x = ( x ij x ) + ( x ijk xij ). AB . = ( xi x ) + ( x j x ) + ( xij x i x j + x ) + ( xijk xij ). A B A B . - 25 - a b r S T = ( x ijk x ) 2. i =1 j =1 k =1. a b r AB S AB = ( xij x ) 2. i =1 j =1 k =1. a b r a A S A = ( x i x ) 2 = rb ( x i x ) 2. i =1 j =1 k =1 i =1. a b r b B S B = ( x j x ) 2 = ra ( x j x ) 2. i =1 j =1 k =1 j =1. a b r a b A B S A B = ( x ij x i x j + x ) 2 = r ( x ij x i x j + x ) 2.

2 I =1 j =1 k =1 i =1 j =1. a b r S E = ( x ijk x ij ) 2. i =1 j =1 k =1. S T = S AB + S E = S A + S B + S A B + S E. ST T=n 1=abr 1. SAB AB=ab-1 ST. SA. SA A=a-1 SAB. SB. SB B=b-1. SA B A B= AB- A- B=ab-1-(a-1)-(b-1)=(a-1)(b-1) SAXB. SE. SE E=ab(r-1). T= A+ B+ A B+ E. A B A B . A B A B .. VA=SA/ A VB=SB/ B VA B=SA B/ A B VE=SE/ E. F0=VA/VE F0=VB/VE F0=VA B/VE F .. (1) . 1) . 2 4 2. S T = ( x ijk x ) 2 = i =1 j =1 k =1. 2. A S A = 2 4 ( x i x ) 2 = i =1. 4. B S B = 2 2 ( x j x ) 2 = j =1. 2 4. A B S A B = 2 ( xij x i x j + x ) 2 = i =1 j =1. - 26 - 2 4 2. S E = ( x ijk x ij ) 2 = i =1 j =1 k =1. 2) . ST T=n-1 =16-1=15. SA A=a-1 =2-1=1. SB B=b-1 =4-1=3. SA B A B=(a-1)(b-1) =3. SE E=ab(r-1) =4*2(2-1)=8. 3).

3 S V F0. **. A SA A 1 VA=SA/ A VA/VE *. B SB B 3 VB=SB/ B VB/VE A B SA B A B 3 VA B=SA B/ A B VA B/VE E SE E 8 VE=SE/ E ST T 15. A F0= F(1,8; )= F0= F(1,8; )= 1% . B F0= F(3,8; )= F0= F(3,8; )= 5% . A B F0= F(3,8; )= 5% . 4) . A B . 20% . A B F0= F(3,8; )= 20% .. xijk= + i+ j+ ijk A B . SE'=SA B+SE E'= A B+ E.. S V F0. **. A SA A 1 VA=SA/ A VA/VE *. B SB B 3 VB=SB/ B VB/VE E SE' E' 11 VE'=SE'/ E' ST T 15. - 27 - A F0= F(1,11; )= F0= F(1,11; )= 1% . B F0= F(3,11; )= F0= F(3,11; )= 5% . (2) . 1) A B .. xijk= + i+ j+( )ij+ ijk xij A1B2. ij = xij = . x ij t ( E , ) V E / r ij x ij + t ( E , ) V E / r t (8, ) / 2 12 + t (8, ) / 2. 12 2) A B .. xijk= + i+ j+ ijk A xi B x j A1, B2. ij = + i + j = + i + + j = xi + x j x = + =.

4 ( x i + x j x ) t ( E ' , ) V E ' / re ij ( x i + x j x ) + t ( E ' , ) V E ' / re re: re=n/(a+b-1) .. n n re = = =. + 1 (a 1) + (b 1) + 1 a + b 1. ) /(16 / 5) 12 + t (11, t (11, ) /(16 / 5). 12 - 28.