ก ก ก (FORECASTING FOR PRODUCTION)
. ! ! ! "# $ # #ก %&' ( )ก " *# #ก % ( %) # + , -ก. (
/0ก # 12 02 *"#3"'%ก - 45 -670 8&1 6 *% ก 9:1"# % 8&1ก ;&1( 0"8 2 *3 ก +<=" #> 4*-ก ;:?0/0$>#1 * *-# )0:=1/0&0 " +<=ก5 )0 @#8 +,?10<?กA - B=&4*@ 84, - < %6C44, +<=45 -670 >&ก @#8/)8 8&% 2 *-670@6& > 16 *) , ก ก 03, -670;,?0 &02 ก/0ก *3#0ก # 12 02 *"#3"'%ก D:=1 +,=#E@62 8#4*+ ก "# % 8&1ก /0$>#1 * *-# 1 6G;8 1)08 - 4*-)A0 @ 8#> ก ก %<"# %(5 ",H% ก/0ก *3#0ก ,10,?0- 4*% :ก. # I<ก ก /0233 > 1E
ก ก ก ก "B& ก " ก 9:1( =1/ ( =1)0:1= +<=4*-ก ;:?0 /0$>#1-# /0&0 " 2 *05 "> ก +<=@ 80,?0% /$8 6 * $0 - B=&ก , ( 0/4/ E ก ก 4*%< "# %(5 ",H/0 8 0 > 1E ,10<? ก /$8/0ก , ( 0/4-ก<= #ก,3;0 ;&1 2 * ,ก. *;&1 ก /$84 , +5 -670 1-# ก 2 *ก "#3"'% #,( '"1" ,1- B&= &3(0&1 >&"# % 8&1ก ;&1 Jก"8 /0 " +<= -)% *(%
ก -1 02 *ก 3,H$< /$8/0ก # 12 0ก >#1)08 -ก<= #ก,3 ก 4, ( 136 *% -1 0 1+'0 ก5 )0 ,3 4> /02 > *$>#1-# - B=&/)83 .+, 5 1& J>/0(9 0*(! " >&1 2 * 5 -0 01 0@6& > 1%<6 *( +I !
6 *-!+;&1ก ก 1. * *(,?0 (3-12 - B&0) ก ก ">&0;8 12%>0 5 ก -6 <= 026 1+ 1 8 0(! #* - .Nก 4 (,1"% ก -%B&1 %< ก *+308& - B=&# 12 0ก 6O 3, 1 0 2. * * # (3 6G, 5 6G, ) B& 10 6G) ก ก 2%>0 5 08& 1 ก -6 <= 026 1+ 1 8 0(! #* - .Nก 4 (,1"% ก -%B&1 4*%< % ก - B=&# 1+ + 1) B&-6S )% + 1I' ก 4 * * 1 - 3 6G - B=&# 12 0 , ( 0/4 - ,?1"&% #- & - ,?1-" B=&14,ก 11 0 * *-# 3 6G;:?0@6 - , ( 0/4-ก<= #ก,32 0;&1&1" ก - + + 1ก ; 11 0 ก ,?1 11 0/)%>
# I<ก ก 1. REGRESSIVE METHOD /$8;8&%J 2 * ,#- ;/0& < -670 ,#$<?&0 " /$8-+"0 "-$ 16 % /0ก ก ( Quantitative Forecasting ) -)% *(5 ) ,3( 0"8 ) ,ก+<@= 86J @#8 < &(%"# 2 8# > # I<04<? * 8&1%<;8&%J +<=-$B=&9B&@ 82 *%<;8&%J 8&% < 2. PROGRESSIVE METHOD @%>%<) B&@%>( % 9/$8;8&%J /0& < -67020#+ 1 (! #*- .Nก 4 (,1"% 2 *ก -%B&12 *(! 26 6 #0% ก -670( 0"8 $0 /)%> /$8-+"0 "ก ก -$ 1"' ! ( Qualitative Forecasting ) > # I<0<?4*+5 ก -กA3;8&%J , +5 market Research , +5 233(&39 % <
-+"0 "ก ก -$ 16 % 1. ก # -" *) &0'ก %-# (TIME SERIES ANALYSIS) - ก # -" *) &0'ก %-# 4* J"# % >&-0B=&1+<= > 0% /0& < D:=1-670# I<+<=/$8ก,0& > 12 >) /06C44'30, %<# I< 1, 0<? 1.1 DECOMPOSITION METHOD 1.2 TIME SERIES MODELS 1.2.1 TREND MODELS 1.2.2 MOVING - AVERAGE MODELS 1.2.3 EXPONENTIAL MODELS 1.2.4 BOX-JENKINS METHODS
2. REGRESSION ANALYSIS CAUSAL MODELS (ก # -" *) -$ 19 9& ) 2.1 SIMPLE LINEAR REGRESSION 2.2 MULTIPLE REGRESSION 2.3 ECONOMETRIC MODELS
> # I<ก 0<?-670ก # -" *) 6C44, +<=% < 2 6C44, ;:?0@6D:=1-670ก # -" *) +<=D,3D8&0-)% *(5 ) ,33 .,+/)H>E- * 8&1%&1 ก *+3) ,# <
-+"0 "ก ก -$ 1"' ! 1. # I<- $q (Delphi Method) (&39 % J8-$<= #$ H)%'0-#< 0 >&-0B=&1 2. # I< Panel Consensus #%ก '>% J8-$<= #$ H&! 6 3. Gross-Root Forecasting (&39 % J8/ก 8$ 6CH) -$>0 J82+0; 4. # I<# 4, (Marketing Research) #3 #%;8&%J # -" *) + (&3
Forecasting
Quantity
Patterns of Demand
Time Figure 12.1
(a) Horizontal: Data cluster about a horizontal line.
Quantity
Patterns of Demand
Time Figure 12.1
(b) Trend: Data consistently increase or decrease.
Patterns of Demand
Quantity
Year 1
Figure 12.1
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|
|
|
|
|
|
J
F
M
A
M
J
J
A
S
O
N
D
Months
(c) Seasonal: Data consistently show peaks and valleys.
Patterns of Demand
Quantity
Year 1
Year 2
Figure 12.1
|
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|
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|
|
|
|
|
|
|
J
F
M
A
M
J
J
A
S
O
N
D
Months
(c) Seasonal: Data consistently show peaks and valleys.
Quantity
Patterns of Demand
Figure 12.1
|
|
|
|
|
|
1
2
3
4
5
6
Years
(c) Cyclical: Data reveal gradual increases and decreases over extended periods.
Demand Forecast Applications Time Horizon
Application
Short Term (0â&#x20AC;&#x201C;3 months)
Forecast quantity
Individual products or services
Decision area
Inventory management Final assembly scheduling Workforce scheduling Master production scheduling Time series Causal Judgment
Forecasting technique
Table 12.1
Medium Term (3 monthsâ&#x20AC;&#x201C; 2 years)
Long Term (more than 2 years)
Total sales Groups or families of products or services Staff planning Production planning Master production scheduling Purchasing Distribution
Total sales
Causal Judgment
Causal Judgment
Facility location Capacity planning Process management
Causal Methods Linear Regression Dependent variable
Y
X Figure 12.2
Independent variable
Causal Methods Linear Regression Regression equation: Y = a + bX
Dependent variable
Y
X Figure 12.2
Independent variable
Causal Methods Linear Regression Regression equation: Y = a + bX
Dependent variable
Y
Actual value of Y Value of X used to estimate Y
X Figure 12.2
Independent variable
Causal Methods Linear Regression Dependent variable
Y
Deviation, Estimate of or error Y from regression equation
{
Regression equation: Y = a + bX Actual value of Y Value of X used to estimate Y
X Figure 12.2
Independent variable
TIME-SERIES ANALYSIS : DECOMPOSITION METHOD &1" 6 *ก&3;&1&0'ก %-# (COMPONENT OF TIME SERIES)) 1. TREND (20# 08%) - ก -6 <= 026 1;&1 & ; #> @6+ 1@)0 2. SEASONAL (u Jก ) - -) 'ก +<=-ก ;:?0D?5 E/02 > * &36G 3. CYCLICAL (#,O4,ก ) 4. RANDOM ORIRREGULAR ("# %@%>20>0&0)
Demand
Seasonal Patterns
| 0 Figure 12.7
| | | | | | | | | | | | | | | 2 4 5 8 10 12 14 16 Period
Seasonal Patterns
Y = T X S X CX R Y = TIME SERIES FORECASE
Demand
(a) Multiplicative pattern
| 0
| | | | | | | | | | | | | | | 2 4 5 8 10 12 14 16 Period
Seasonal Patterns
Y = T + S + C+ R Y = TIME SERIES FORECASE
Demand
(b) Additive pattern
| 0 Figure 12.8
| | | | | | | | | | | | | | | 2 4 5 8 10 12 14 16 Period
ก ก * *(,?0 (SHORT-RANGE FORECASE) C 2 * R -670& +I /0 * * # 2 >ก ก - B=&ก # 12 0ก -670ก ก /0 * *(,?0 C 2 * R 4:1%<& +I >& ก ก - < 1- Aก08& ,10,?0 ,# 233ก ก 4:1( % 9 4, J6@ 8 ,10<?
Y=TXS
ภ6 *% "> 20# 08% Linear Model
Exponential Model Y = abt
Y = a+bt
Y = a+bt+ct2 Quadralic Model
Quadralic Model
ก 6 *% "> 20# 08% # I<ก5 ,1(&108& +<=(' (Least Squares Technique) ก <20# 08%-(80 1%<"# %$,0
y(t) = a + b(t)
ก 6 *% "> 20# 08% # I<ก5 ,1(&108& +<=(' (Least Squares Technique) ก <20# 08%-(80 1%<"# %$,0 Q Y(t) = a + b (t) ∴ e(t) = y (t) − Y(t) = y (t) − (a + b( t ) ) n [ e 2 ( t )] = n [ y ( t ) − ( a + b ( t ))] 2 t =1 t =1 d [
e2 (t) ] da
= 0
d [
e2 (t) ] db
= 0
e(t) == e(t)
"# %" -" B=&=&0$> 0$>##1-# 1-# tt/ / EE "# %" -" B
y(t) == y(t)
& ; 4 11$>$>##1-# 1-# tt/ / EE & ; 4
Y(t) == Y(t)
ก $$>#>#1-# 1-# tt/ / EE ">"> ก
nn
0#0$>##1-# 1-# 4545 0#0$>
==
ก n
∑ a =
y (t
t =1
n
n
)
b
∑
−
t
t =1
n
n
n
n
t =1
t =1 n
t =1
n ∑ t y(t) − ∑ y(t) ∑ t b=
n 2
n ∑ t − ( ∑ t) t =1
t =1
2
ภภ!
y(t)
1
7
2
8
3
10
4
12
5
13
6
14
7
16
80
12( 1 & ; 6G;&13 .+, Generox ()0># )
1+<= 3.1 : & ; 6G;&13 .,+ Generox ()0># ) 1 2 3 4 5 6 7
y(t) 7 8 10 12 13 14 16 80
t 1 2 3 4 5 6 7 28
t2 1 4 9 16 25 36 49 140
t y(t) 7 16 30 48 65 84 112 362
( 7 )( 362 ) − ( 80 )( 28 ) b = 7 ( 140 ) − ( 28 ) 2 = 1 .5 80 1 . 5 ( 28 ) a = − 7 7 = 5 .4 y ( t ) = 5 .4 + (1 .5 ) t
t
Y(t)
t
Y(t)
t
Y(t)
1
6.9
4
11.4
7
15.9
2
8.4
5
12,9
8
17.4
3
9.9
6
14.4
ภ" # $%&' !( &) ! *) +&) # I<9,#-Â&#x201A; <= -" B=&0+<=& > 11> (Sample Moving Average) N
Y (t) =
â&#x2C6;&#x2018; y(t-1)
i=1
N N = 45 0#04' ;&1;8&%J +<=/$8/0ภ9,#-Â&#x201A; <= > -$>0 1 6G %< 4 @ % ( , N = 4 <
N
Y(t) =
y(t-1) + y(t-2) +Â&#x192;Â&#x192;. y(t-N)
12( 1 & ; @ % ( 6 +&)
6G
1
2
3
4
2546
500
1050
250
1800
2547
525
1090
200
2000
,#& > 1ก "5 0# Y(5) =
y(4) + y(3) + y(2) + y(1) N
Y(5) =
500+1050+250+1800 4
Y(6) = Y(6) =
y(5) + y(4) + y(3) + y(2) N 1050+250+1800 +525 4
= 900
= 906.25
"< 2546
2547
Y(5) = 2548
6
t 1 1 2 2 3 3 4 4 1 5 2 6 3 7 500+1050+250+1800 4 4 8 1 9 2 10 3 11 4 12
# y(t) 500 1050 250 1800 525 1090 200 = 900 2000
Y(t)
900.00
"< 2546
2547
2548Y(6)
=
6
t # y(t) Y(t) 1 1 500 2 2 1050 3 3 250 4 4 1800 1 5 525 900.00 2 6 1090 906.25 3 7 200 4 1050+250+1800 8 + 525 2000 = 906.25 1 4 9 2 10 3 11 4 12
"< 2546
2547
2548
6
1 2 3 4 1 2 3 4 1 2 3 4
t 1 2 3 4 5 6 7 8 9 10 11 12
# y(t) 500 1050 250 1800 525 1090 200 2000
Y(t)
900.00 906.25 916.25 903.75 953.75
# I<9,#- <= -" B=&0+<=2339>#10?5 )0,ก (Weight Moving Average) " 8 ก,3# I<9,#- <= -" B=&0+<=& > 11> 2 >@ 8/$8 #, 9>#10?5 )0,ก+<= -)% *(%- B=&6 ,3"> /)8/ก 8-"< 1ก,3;8&%J 4 1% ก 1= ;:?0 Y (t) =
N
∑ W(N-k+1) y(t-1)
i=1
W(t-k) "B& "> 9>#10?5 )0,ก(5 ) ,3$>#1-# (t-k) %< #% -+> ก,3 1 /0+ 1I' ก 44*/)8"# %(5 ",Hก,3;8&%J $' > (' % กก#> ;8&%J -ก>
ก 12( 1 & ; @ % ( 6 +&)
6G
1
2
3
4
2546
500
1050
250
1800
2547
525
1090
200
2000
(%% "> 9>#10?5 )0,ก = 1/6 , 1/3 , 1/3 , 1/6
( #%ก,0 = 1)
ก Y(5) = W(4)y(4) +W(3) y(3) +W(2) y(2) +W(1) y(1) Y(5) = (1/6)500+(1/3)1050+(1/3)250+(1/6)1800 = 816.66 Y(6) = W(4)y(5) +W(3) y(4) +W(2) y(3) +W(1) y(2) Y(6) = (1/6)1025+(1/3)250+(1/3)1800+(1/6)525 = 945.83
"< 2546
2547
2548
6
1 2 3 4 1 2 3 4 1 2 3 4
t 1 2 3 4 5 6 7 8 9 10 11 12
# y(t) 500 1050 250 1800 525 1090 200 2000
Y(t)
816.66 945.83 998.32 904.99 850.82
ก "5 0# "> ก # I&< 0'ก %-# 2332 ก&1" 6 *ก&3 ก <%<&1" 6 *ก&320# 08%2 *u Jก
TREND AND SEASONAL
1+<= 3.7 2( 1;8&%J & ; @ % (;&13 .,+2)>1)0:=1 /0& < 4 6G+<= > 0% (2539-2542) . .
1
@ % (+<= 2
2539
56
2540
3
4
50
60 ) 6 +&
67
62
56
65
71
2541
65
60
70
77
2542
73
66
75
85
Y(t) = b
53.2+1.52 t
(16)(9510) (1058)(136) = = 1.52 (16)(1496) (136)2
2 * a
=
1058 (1.52)(136) 16 16
= 53.2
1+<= 3.8 2( 1"> 20# 08%233-(80 1%<"# %$,0 @ % ( (Trend) @ % (+<= . .
1
2
3
4
2539
54.72
56.24
57.76
59.28
2540
60.80
62.32
63.84
65.36
2541
66.89
68.41
69.93
71.45
2542
72.97
74.49
76.01
77.53
ก ) "> ,$0<u Jก # I<&, (>#0 >&"> 20# 08% -%B=&
y(t)
=
Y(t) = t
=
y(t) / Y(t) & ; 4 1/0$>#1-# t (4 ก 1+<= 3.7) "> ก 20# 08%/0$>#1-# t ( 1+<= 3.8) 1,2,3, ,16
ก "5 0# 2( 1/0 1+<= 3.9
1+<= 3.9 2( 1&, (>#0 & ; 4 1 >&"> 20# 08%;&12 > *@ % (
@ % (+<= . . 2539 2540 2541 2542 #% - <= ) "> - <=
1 1.023 1.020 0.972 1.000 4.015 1.004
2 0.889 0.899 0.877 0.886 3.551 0.888 ,$0<u Jก
3 1.039 1.018 1.001 0.987 4.045 1.011
4 1.130 1.086 1.078 1.096 4.390 1.097
ก "5 0# "> ก +<= 4 "> 20# 08%2 *u Jก T = 53.2 + 1.52 t 6G+<= @ % (+<= $>#1-# +<= "> 20# 08% ,$0<u Jก "> ก 1
2
T
S
Y=TxS
1
1
54.72
1.004
54.9
2
2
56.24
0.888
49.9
3
3
57.76
1.011
58.4
4
4
59.28
1.097
65.10
1
5
60.80
1.004
61.0
2
6
62.32
0.888
55.3
1+<= 3.15 12( 1"> ก +<= 4 "> 20# 08%2 *u Jก /0 *)#> 16G 2539 2542 @ % (+<= . .
1
2
3
4
2539
54.9
49.9
58.4
65.10
2540
61.0
55.3
64.6
71.7
2541
67.1
60.7
70.7
78.4
2542
73.2
66.1
76.9
85.1
1+<= 3.10
12( 1"> ก 6G 2543 2 * 2544 4 &1" 6 *ก&320# 08%2 *u Jก (1) (2) (3) (4) (5) . . @ % ( T "> 20# 08% ,$0<u Jก "> ก 2543 1 17 79.04 1.004 79.36 2 18 80.56 0.888 71.54 3 19 82.08 1.011 82.98 4 20 83.60 1.097 91.71 2544 1 21 85.12 1.004 85.46 2 22 86.64 0.888 76.94 3 23 88.16 1.011 89.13 4 24 89.68 1.097 98.38
ก # -" *) "# %" -" B=&0;&1ก ก 1. ) "> - <= ;&1"# %-3<= 1-30(%3J (Mean Absolute Deviation, MAD) #, 2 >;0 ;&1"> -3<= 1-30
N
∑ MAD =
y(t) − Y(t)
t =1
N
2. "> - <= "# %" -" B=&0ก5 ,1(&1 (Mean Sauared Error, MSE) N
∑ {y(t) − Y(t) } MAD =
2
t =1
N
3. "> - <= -6& -DA0 ;&1"# %" -" B=&0(%3J (Mean Absolute Percent Error, MAP)
100 MAD = N
∑ t =1
[y(t) − Y(t) ] y(t)
> -670ก #, "' ! ;&1ก ก
2( 1ก "5 0# "# %" -" B=&0;&1ก ก +,?1 3 # I<
$>#1-#
& ; 4 1
"> ก
"# %" -" B=&0 (%3J
"# %" 2 %"# %" -" B=&0 -" B=&0ก5 ,1 (%3J (&1
1
20
18
2
4
10.00 %
2
30
25
5
25
16.67 %
3
10
15
5
25
4
40
30
10
100
50.00 % 25.00 %
5
30
35
5
25
16.67 %
"> - <= ;&1"# %-3<= 1-30(%3J =
"> - <= "# %" -" B=&0ก5 ,1(&1 =
2+5+5+10+5 5 4+25+25+100+25 5
= 5.4
= 35.8
"> - <= -6& -DA0 "# %" -" B=&0(%3J = 10 + 16.67+50+25+16.67 = 23.6 5
1+<= 3.11 12( 1"> -3<= 1-30(%3J *)#> 1 & ; 4 12 *"> ก /0 *)#> 16G 2539-2542 Y − y ( t ) (t) @ % (+<= . . 1 2 3 4 2539 1.1 0.1 1.6 1.9 2540 1.0 0.7 0.4 0.7 2541 2.1 0.7 0.7 1.4 N 2542 0.2 0.1 1.9 0.1 ∑ y(t) − Y (t) #%"> -3<= 1-30(%3J = 14.7 t = 1 "> - <= -3<= 1-30(%3J = 14.7 = .919 16
MAD
1+<= 3.12 12( 1"> "# %" -" B=&0ก5 ,1(&1 . . 2539 2540 2541 2542
1 1.21 1.0 4.41 0.04
@ % (+<= 2 3 0.01 2.56 0.49 0.16 0.49 0.49 0.01 3.61
4 3.61 0.49 1.96 0.01
#%"# %" -" B=&0ก5 ,1(&1 = 20.55 "> - <= "# %" -" B=&0ก5 ,1(&1 = 20.55 = 1.28 16
1+<= 3.13 12( 1"> &, (>#0"# %" -" B=&0 >& & ; 4 1 @ % (+<= . . 1 2 3 4 2539 0.019 0.002 0.027 0.028 2540 0.016 0.012 0.006 0.009 2541 0.032 0.012 0.01 0.018 2542 0.003 0.002 0.025 0.001 #%&, (>#0"# %" -" B=&0 >& & ; 4 1 = 0.222 "> - <= -6& -DA0 "# %" -" B=&0(%3J = 1.39
ภภ" ! & ! ?ภ@ "! !A& (Exponential Smoothing) 6 ,3- < 3-&Aภ6 -080-$< & > 11> (Simple Exponential Smoothing) Y(t)
= Îą y(t) + (1- Îą)Y(t-1)
Y(t) = "> ภ6 ,3- < 3-&AภD 6-00-$< $>#1-# t Îą = "> 9>#10?5 )0,ภ6 ,3- < 39,#-Â&#x201A; <= ( ภ5 )0 "> *)#> 1 0.1-0.3)
y(t) = & ; 4 1 $>#1-# t
Y(t)
= α y(t) + (1- α)Y(t-1)
+<= t = 1 Y(1)
ก "5 0# "> - =% 80 = α y(1) + (1- α)Y(0)
Y(0) = X(1) - (L/2) T(0)
> /03 1ก < Y(0) = & ; 4 1;&1 period +<= 1 กA@ 8
# T(O) ' 6# Q ก T(0) = [X(m) - X(1) ]/(m-1)L
X(1) = "> - <= >&$>#1-# ;&16G+<= 1 L = 45 0#0$>#1-# /0 1 6G ( -$>0 1 6G %< 4 @ % ( L= 4 ) X(m) = "> - <= >&$>#1-# ;&16G+<= m m = 45 0#06G+,?1)% ;&1;8&%J 4 1 T(0) = "> 20# 08%(5 ) ,3$>#1-# +B= 0
ก ก " ! & ! ?ก@ "! !A& 1;8&%J & ; @ % ( 5 6G > (' @ % (+<= .
6G+<=
1
2
3
4
2543
1
107
84
68
135
2544
2
115
96
49
162
2545
3
109
102
67
140
2546
4
102
75
58
151
2547
5
99
74
42
125
m = 5 , L = 4 , α = 0.2
ก ! $ ) 1;8&%J & ; @ % ( 5 6G > (' @ % (+<= .
6G+X(1) <= "> - <= =1 (107+84+68+135)/4 2 3 4 = 98.5
2543
1
107
84
68
135
2544
2
115
96
49
162
2545
3
109
102
67
140
2546
4
102
75
58
151
2547
5
99
74
42
125
98.5
ก ! $) 1;8&%J & ; @ % ( 5 6G > (' @ % (+<= .
6G+<=
1
2
3
4
"> - <=
2543
1
107
84
68
135
98.5
2544
2
115
96
49
162
2545
3
109
102
67
140
2546
4
102
75
58
151
2547
5
99
74
42
125
85
X(m) = X(5) = (99+74+42+125)/4 = 85
ก ! $)
1;8&%J & ; @ % ( 5 6G > (' @ % (+<= .
6G+<=
1
2
3
4
"> - <=
2543
1
107
84
68
135
98.5
2544
2
115
96
49
162
422
2545
3
109
102
67
140
104.5
2546
4
102
75
58
151
96.5
2547
5
99
74
42
125
85
T(0) =
85 - 98.5 (5-1)/4
= -0.8438
Y(0) = 98.5 – (4/2)(-0.8438) = 100.1876
1ก "5 0# "> ก 233 Simple Exponential Smoothinh 6G+<=
@ % (+<=
t
1
1
1
Y(1) = 0.2(107) + (1-0.2)100.1876 = 101.55
2
2
Y(2) = 0.2(84) + (1-0.2)101.55
= 98.04
3
3
Y(3) = 0.2(68) + (1-0.2)98.04
= 92.03
4
4
Y(4) = 0.2(135) + (1-0.2)92.03
= 100.63
1
5
Y(5) = 0.2(115) + (1-0.2)100.63 = 103.50
2
6
Y(6) = 0.2(96) + (1-0.2)103.50
2
Y(t) = α y(t) + (1- α)Y(t-1)
= 102.00
Trick ' !ภ$#+ Q 'U "<+&) t = 20 "<+&) 5 ภQ 6# Y(20) = ιy(20)+(1- ι)Y(19) Y(21) = ιy(21)+(1- ι)Y(20) , Y(21) = ι y(20)+(1- ι)Y(20) Y(22) = ιy(22)+(1- ι)Y(21) , Y(22) = ι y(20)+(1- ι)Y(21) Y(23) = ιy(23)+(1- ι)Y(22) , Y(23) = ι y(20)+(1- ι)Y(22) @U) ! Q 6 ' y(21),y(22),y(23) 6# # Y ! Q A y(20) + y(21),y(22),y(23) !A
ก ก " ! & ! ?ก@ "! !A& # $Q " ก Y(t) = α y(t) + (1- α)Y(t-1) T(t) = β[Y(t) Y(t-1)]+(1- β) T(t-1) E(t+1) = Y(t) + 1-β β T(t) + T(t) β
= "> 9>#10?5 )0,ก6 ,3- < 320# 08%
T(t)
= "> 20# 08%(5 ) ,3$>#1-# t
Y(t) = "> ก & ; 6 ,3- < 39,#- <= $>#1-# t E(t+1) = "> ก 2336 ,3- < 3-&Aก 6-080-$< 4 &1" 6 *ก&320# 08%(5 ) ,3$>#1-# t+1
ก ก " ! & ! ?ก@ "! !A& # $Q " ก 1;8&%J & ; @ % ( 5 6G > ('
@ % (+<= .
6G+<=
1
2
3
4
2543
1
107
84
68
135
2544
2
115
96
49
162
2545
3
109
102
67
140
2546
4
102
75
58
151
2547
5
99
74
42
125
m=5
, L = 4 , α = 0.2 , β = 0.1
ภ"5 0# Y(1)
= 0.2(107) + (1-0.2)100.1876 = 101.55
T(1)
= 0.1(101.55-100.1876) +(1-0.1)(-0.8438) = -0.623
E(1+1) = 101.55 + 1-0.1 (-0.623) + (-0.623) = 95.32 0.1 Y(1) = 0.2(84) + (1-0.2)101.55 = 98.04 T(2)
= 0.1(98.04 -101.55) + (1-0.1)(-0.623) 1-0.1 E(1+1) = 98.04 + (-0.912) + (-0.912) 0.1
> +5 9:1 period +<= 20 Y(t) "1+<=+<= 20
= - 0.912 = 88.923
264*@ 8-670-(80 1 - *
ก ก 2336 ,3- < 3 -&AกD 6-00-$< 4 &1" 6 *ก&320# 08%2 *u Jก Y(t) = T(t) = I(t)
=
E(t+k) =
y(t) α I(t-L) + (1- α)[Y(t-1) + T(t-1)] β[Y(t) Y(t-1)]+(1- β) T(t-1) y(t) γ + (1-γ) I(t-L) Y(t) [Y(t) + {k x T(t)}] x I(t-L+k)
I(t) = ,$0<u Jก $>#1-# t Y(t) = "> ก 4 &1" 6 *ก&320# 08%2 *u Jก (5 ) ,3$>#1-# t E(t+k) = "> ก 2336 ,3- < 3-&Aก 6-080-$< 4 &1" 6 *ก&320# 08%2 *u Jก (5 ) ,3$>#1-# t+1
ก ก " ! & ! ?ก@ "! !A& # $Q " ก Z# ก 1;8&%J & ; @ % ( 5 6G > ('
@ % (+<= .
6G+<=
1
2
3
4
2543
1
107
84
68
135
2544
2
115
96
49
162
2545
3
109
102
67
140
2546
4
102
75
58
151
2547
5
99
74
42
125
m=5
, L = 4 , α = 0.2 , β = 0.1 , γ = 0.3
ก # A &Z# ก ! $) "> u Jก /02 > *$>#1-# ( % 9"5 0# @ 8 1, 0<? I(t) =
y(t) X (i) [(L + 1)/2-j]T(0)
I(t) = ,$0<u Jก ;&1$>#1-# t j = 5 2)0>1;&1$>#1-# t /0 &36G+<= i
, t = 1,2,3 ., ml
12( 1ก ) "> u Jก /02 > *$>#1-# "<+&) (i)
A ! (t)
ก
1
1
I(1) = 107/ 98.5 [(4+1)/2-1](-0.8438) = 1.0725
1
2
I(2) = 84/ 98.5 [(4+1)/2-2](-0.8438) = 0.849
1
3
I(3) = 68/ 98.5 [(4+1)/2-3](-0.8438) = 0.693
1
4
I(4) = 135/ 98.5 [(4+1)/2-4](-0.8438) = 1.388
2
5
I(5) = 107/ 105.5 [(4+1)/2-1](-0.8438) = 1.077
2
6
I(6) = 115/ 105.5 [(4+1)/2-2](-0.8438) = 0.906
2
7
I(7) = 96/ 105.5 [(4+1)/2-3](-0.8438) = 0.466
2
8
I(8) = 49/ 105.5 [(4+1)/2-4](-0.8438) = 1.554
X1
ก "5 0# ,$0<u Jก 6 +&) "< 2543 2544 2545 2546 2547 #% - <=
1 1.0725 1.077 1.03 1.043 1.147 5.3695 1.0739
,$0<u Jก - =% 80 I(1)
2 0.849 0.906 0.972 0.774 0.866 4.367 0.8734
3 0.693 0.466 0.644 0.604 0.496 2.903 0.5806
4 1.388 1.554 1.356 1.586 1.493 7.377 1.4754
I(2)
I(3)
I(4)
ก ก " ! & ! ?ก@ "! !A& # $Q " ก Z# ก 107 ]+ 0.8{100.1876 + (-0.8438)} Y(1) = 0.2 [ 1.074
= 99.42
T(1) = 0.1(99.72 100.1876) + 0.9 (-0.8438) 107 ] + 0.7(1.074) I(1) = 0.3[ 1.074
= - 0.836 = 1.074
E(2) = [ 99.42 + {1 x (-0.836)}] x 0.8734
= 86.103
ก ก " ! & ! ?ก@ "! !A& # $Q " ก Z# ก
84 ]+ 0.8{99.42 + (-0.836)} Y(2) = 0.2 [0.8734
= 98.12
T(2) = 0.1(98.12 99.42) + 0.9 (-0.836) 84 ] + 0.7(0.8734) I(2) = 0.3[ 98.12
= - 0.883
E(3) = [ 98.12 + {1 x (-0.833)}] x 0.58
= 56.39
= 0.868
68 ] + 0.8{98.12 + (-0.883)} Y(3) = 0.2 [ 0.58
= 101.24
T(3) = 0.1(101.24 98.12) + 0.9 (-0.883) 68 ] + 0.7(0.58) I(3) = 0.3[101.24
= - 0.483
E(4) = [ 101.24 + {1 x (-0.483)}] x 1.475
= 148.52
= 0.608
ก ก " ! & ! ?ก@ "! !A& # $Q " ก Z# ก
135 ] + 0.8{101.24 + (-0.483)} Y(4) = 0.2 [ 1.475
= 98.92
T(4) = 0.1(98.12 101.24) + 0.9 (-0.483) 135 ] + 0.7(1.475) I(4) = 0.3[ 98.92
= - 0.483 = 1.44
E(5) = [ 98.92 + {1 x (-1.0267)}] x 1.074 = 105.14 115 Y(5) = 0.2 [ 1.074 ] + 0.8{98.92 + (-1.0267)} = 99.73 T(5) = 0.1(99.73-98.92) + 0.9 (-1.0267) 115 ] + 0.7(1.074) I(5) = 0.3[ 99.73
= - 0.843 = 1.098
E(6) = [ 99.73 + {1 x (-0.843)}] x 0.868
= 85.834
ก ก " ! & ! ?ก@ "! !A& # $Q " ก Z# ก
2 *(5 ) ,3"> ก /06G+<= 5 t
y(t)
Y(t)
T(t)
I(t)
E(t+1)
17
99
95.03
-0.63
1.066
84.45
18
74
92.26
-0.844
0.859
54.45
19 20
42 125
87.11 85.45
-1.27 -1.309
0.565 1.48
127.9 89.69
ก ก " ! & ! ?ก@ "! !A& # $Q " ก Z# ก
4 ก ก "5 0# 6G(' +8 +5 /)8- @ 8"> ,#233 +<=4*/$8-670N 0 (5 ) ,3ก ก /0&0 " ,10<? t= 20
Y(20) = 85.45
T(20) = - 1.309
I(17) = 1.066 (@ % (+<= 1) I(18) = 0,859 (@ % (+<= 2)
α = 0.2 , β = 0.1 , γ = 0.3
I(19) = 0.565 (@ % (+<= 3) I(20) = 1.48 (@ % (+<= 4)
E(t+k) = [Y(t) + {k x T(t)}] x I(t-L+k)
ก ก " ! & ! ?ก@ "! !A& # $Q " ก Z# ก
/$8 ,#233+<=-670N 0/0ก ก ก 2+0"> k = 1,2,3 %$>#1-# +<= 8&1ก ก @6;8 1)08 6G+<= @ % (+<= t k E(t+k) 6 6 6 6 7 7 7 7
1 2 3 4 1 2 3 4
20 20 20 20 20 20 20 20
1 2 3 4 5 6 7 8
E(21) E(22) E(23) E(24) E(24) E(24) E(24) E(24)
[Y(t) + {k x T(t)}] x I(t-L+k) [85.45 + {1 x (-1.309)}] x 1.066 [85.45 + {2 x (-1.309)}] x 1.066 [85.45 + {3 x (-1.309)}] x 1.066 [85.45 + {4 x (-1.309)}] x 1.066 [85.45 + {5 x (-1.309)}] x 1.066 [85.45 + {6 x (-1.309)}] x 1.066 [85.45 + {7 x (-1.309)}] x 1.066 [85.45 + {8 x (-1.309)}] x 1.066
= = = = = = = =
89.96 71.15 46.06 118.72 84.11 66.65 43.10 110.96
[" > $%& sample Moving Average ! ภ+&)6 " " ภ> $%& Weight Moving Average ภ$%& sample Moving Average &ภA ' Y ภQU &ภ" ภ! & ภQ $ ภUY > $%& Exponential Smoothing (6 & Trend & Seasonal) ! A ŕ¸
+&) & +&) ( c Q ภ$%& Weight Moving Average ) > $%& Exponential Smoothing ( $Q Trend & Seasonal) !"d $%&+&) $ A ภ+& ) [#! & ! & # ŕ¸
ก !ef $# ก [ ก ก CFE Tracking signal = MAD
CFE = #%"# %" -" B=&0;&1ก ก $>#1-# +<= n MAD = "> -3<= 1-30(%3J - <= $#1-# +<= n
σ = MAD = 0,8 σ
Σ(yt – Yt )2 n–1
or
σ = 1.25 MAD
Tracking Signals ( "#! $!#)
> /$8 J#> model ,1/$8@ 8& J> :-6 > - *;8&%J -6 <= 0+5 /)8 model ,#- %/$8@%>@ 8 > /$8 control chart % -670 ,#"#3"'%"' ! " &98 &&ก% 0&ก control 4* 6ก 6 *% + 2 σ 2 8#-& "> Tracking Signal % Plot 98 &&ก;8 10&ก2( 1#> model @%> <2 8#
Tracking Signals Percentage of the Area of the Normal Probability Distribution within the Control Limits of the Tracking Signal Control Limit Spread (number of MAD) ± 1.0 ± 1.5 ± 2.0 ± 2.5 ± 3.0 ± 3.5 ± 4.0 Table 12.2
Equivalent Number of σ
Percentage of Area within Control Limits
Tracking Signals
Percentage of the Area of the Normal Probability Distribution within the Control Limits of the Tracking Signal Control Limit Spread (number of MAD)
Equivalent Number of σ
± 1.0 ± 1.5 ± 2.0 ± 2.5 ± 3.0 ± 3.5 ± 4.0
± 0.80 ± 1.20 ± 1.60 ± 2.00 ± 2.40 ± 2.80 ± 3.20
Table 12.2
Percentage of Area within Control Limits
Tracking Signals
Percentage of the Area of the Normal Probability Distribution within the Control Limits of the Tracking Signal Control Limit Spread (number of MAD)
Equivalent Number of σ
Percentage of Area within Control Limits
± 1.0 ± 1.5 ± 2.0 ± 2.5 ± 3.0 ± 3.5 ± 4.0
± 0.80 ± 1.20 ± 1.60 ± 2.00 ± 2.40 ± 2.80 ± 3.20
57.62 76.98 89.04 95.44 98.36 99.48 99.86
Table 12.2
Tracking Signals Control Limits
=
0 ± 2σ
Tracking Signals
CFE Tracking signal = MAD Control limit
+2.0 — +1.5 — +1.0 — Tracking signal
+0.5 — 0— –0.5 — –1.0 — –1.5 — Control limit
--2.0 — 0 Figure 12.9
| 5
| | | 10 15 20 Observation number
| 25
Tracking Signals
CFE Tracking signal = MAD
Out of control Control limit
+2.0 — +1.5 — +1.0 — Tracking signal
+0.5 — 0— –0.5 — –1.0 — –1.5 —
Control limit
--2.0 — 0 Figure 12.9
| 5
| | | 10 15 20 Observation number
| 25
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ก # 12 0ก ;
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6 * $0 8 0ก # 12 0ก ,1? 136 *%
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6C44, +<=%<& +I >&&'6(1" #14 + 1I' ก 4 (THE BUSINESS CYCLE)
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