LES ERREURS DE PRÉVISION LES ERREURS DE PRÉVISION e e t t = X = X t t - P - P t t X X 1 X X 2 X X 3 X X 4 X X 5 X X 6 … … P P 5 P P 6 e e 5 e e 6
Jan 29, 2016
LES ERREURS DE PRVISIONet = Xt - PtX1X2X3X4 X5 X6P5P6e5e6
LES ERREURS DE PRVISION: UNE SOURCE DINFORMATION UTILEPour lajustement des mthodes de prvision et de leurs paramtres
Pour lvaluation des prvisions
Pour lestimation de lcart-type de la demande
Pour la dtermination du stock de scurit
Pour les intervalles de confiance sur les prvisions
EM, EMA ET EMAtMesure du biaisMesure de la distance (amplitude) moyenneentre une prvision et la demanderelle de la priode correspondante
]|Expr|[#>`b___}) b'4" *|: ;bP8&c0!"EMA ,]
PRVISIONS NON BIAISESPrvisions biaisesCaractristiques desprvisions non biaises- il ny a pas dallure distinctive dans les erreurs de prvision
- les erreurs sont centres 0
- il y a peu prs autant de termes derreurs positifs que de ngatifs
Graph1
10911050
10061054.1
11051049.29
10341054.861
10951052.7749
10811056.99741
11361059.397669
11161067.0579021
11091071.95211189
11991075.656900701
12091087.9912106309
12321100.0920895678
11911113.282880611
12391121.0545925499
12351132.8491332949
13301143.0642199654
13421161.7577979689
13321179.782018172
13741195.0038163548
14021212.9034347193
15041231.8130912474
15021259.0317821226
15881283.3286039104
16071313.7957435194
16901343.1161691674
17621377.8045522507
17571416.2240970256
18391450.301687323
18481489.1715185907
19041525.0543667317
19751562.9489300585
20611604.1540370526
21531649.8386333474
22131700.1547700126
22381751.4392930114
23661800.0953637102
371856.6858273392
LES
a=0.1
tXtPtet
190100.00-10.00
210599.006.00
39599.60-4.60
411099.1410.86
595100.23-5.23
69099.70-9.70
710598.736.27
812099.3620.64
9120101.4218.58
10115103.2811.72
11125104.4520.55
12115106.518.49
13115107.367.64
14125108.1216.88
15115109.815.19
16120110.339.67
17120111.308.70
18105112.17-7.17
1990111.45-21.45
2095109.30-14.30
21110107.872.13
2295108.09-13.09
23105106.78-1.78
2490106.60-16.60
25104.94
LES
LESA
b=0.2
tXtPtetabs(et)EtMtat
19095.00-5.005.00-5.005.000.40
210593.0012.0012.00-1.606.400.25
39596.00-1.001.00-1.485.320.28
411095.7214.2814.281.677.110.24
59599.08-4.084.080.526.500.08
69098.75-8.758.75-1.336.950.19
710597.077.937.930.527.150.07
812097.6522.3522.354.8910.190.48
9120108.3711.6311.636.2410.480.60
10115115.29-0.290.294.938.440.58
11125115.129.889.885.928.730.68
12115121.82-6.826.823.378.350.40
13115119.07-4.074.071.887.490.25
14125118.046.966.962.907.380.39
15115120.77-5.775.771.167.060.16
16120119.820.180.180.975.690.17
17120119.850.150.150.804.580.18
18105119.88-14.8814.88-2.336.640.35
1990114.65-24.6524.65-6.8010.240.66
209598.29-3.293.29-6.098.850.69
2111096.0213.9813.98-2.089.870.21
229598.97-3.973.97-2.468.690.28
2310597.857.157.15-0.548.390.06
249098.30-8.308.30-2.098.370.25
2596.23
LESA
demande
prvisions
priodes
demande et prvisions
LETS
priodes
valeurs de at
LESAIS
a=0.5
g=0.5
b=0.5
tXtStbtItPt
13620.9526
23851.0132
34321.1368
4341380.00009.75000.8974
5382395.372212.56110.9594371.2882
6409405.810811.49991.0105413.3009
7498427.683116.68611.1506474.4164
8387437.815113.40900.8907398.7629
9473472.119123.85650.9806432.9066
10513501.820426.77891.0164501.1874
11582517.205121.08181.1380608.2211
12474535.240819.55870.8881479.4261
13544.0560
14583.7738
15675.8498
16544.8383
LESAIS
demande
prvisions
priodes
demande
LETO2
a=0.5L=4
b=0.5X bar=380
tXtStItPt
13620.9526
23851.0132
34321.1368
4341380.00000.8974
5382390.49720.9654362.0000
6409397.09281.0216395.6354
7445394.26401.1328451.4318
8335383.78890.8851353.8000
9360378.33870.9585370.5235
10375372.71001.0139386.5002
11440380.57031.1445422.1924
12355390.82240.8967336.8512
13374.5963
14396.2385
15447.2813
16350.4628
LETO2
demande
prvisions
priodes
demande
LETO1
a=0.3
XtS'tS''tStbtPt
110911091109110910
21006106610831048-8
31105107710821073-21040
41034106410761052-51071
51095107410761072-11047
6108110761076107601071
7113610941081110751076
8111611001087111461112
9110911031092111451120
101199113211041160121119
111209115511191191151172
121232117811371219181206
131191118211501214141237
141239119911651233151227
151235121011781241131248
161330124611991293201255
171342127512211328231313
181332129212431341211351
191374131712651368221362
201402134212881396231390
211504139113191463311420
221502142413501498321493
231588147313871559371529
241607151314251602381596
251640
261677
271715
LETO1
observations
S't
S''t
prvisions
priodes
demande
MMP
a=0.3
g=0.4
tXtStbtPt
110911091.0010.00
211011101.0010.001101.00
311051109.209.281111.00
410341093.14-0.861118.48
510951093.09-0.531092.28
610811089.09-1.921092.56
711361101.823.941087.18
811161108.835.171105.76
911091112.504.571114.00
1011991141.6514.401117.07
1112091171.9320.751156.05
1212321204.4825.471192.69
1311911218.2720.801229.95
1412391239.0420.791239.06
1512351252.3817.811259.83
1613301288.1424.991270.19
1713421321.7828.451313.12
1813321344.7726.261350.24
1913741371.9226.621371.03
2014021399.5827.031398.54
2115041449.8336.321426.61
2215021490.9138.221486.15
2315881546.7945.291529.13
2416071596.5547.081592.08
251643.63
261690.71
271737.79
MMP
Erreurs
w1=0.5w1=0.1
w2=0.3w2=0.2
w3=0.2w3=0.3
w4=0.4
tXtPtPt
190
2105
395
411097.00
595104.5097.50
69099.50102.00
710595.5099.00
812098.50101.00
9120109.5098.00
10115117.00103.50
11125117.50113.50
12115121.00119.50
13115118.00119.00
14125117.00118.00
15115120.00120.00
16120118.00117.00
17120119.50118.50
18105119.00120.50
1990112.50116.50
2095100.50114.00
2111095.50107.00
2295101.5099.00
2310599.5096.00
2490103.00100.50
2595.50102.50
Erreurs
Feuil1
a=0.1
tXtPtetabs(et)
110911050.00
210061054.1048.1048.1
311051049.29-55.7155.71
410341054.8620.8620.86
510951052.77-42.2342.23
610811057.00-24.0024.00
711361059.40-76.6076.60
811161067.06-48.9448.94
911091071.95-37.0537.05
1011991075.66-123.34123.34
1112091087.99-121.01121.01
1212321100.09-131.91131.91
1311911113.28-77.7277.72
1412391121.05-117.95117.95
1512351132.85-102.15102.15
1613301143.06-186.94186.94
1713421161.76-180.24180.24
1813321179.78-152.22152.22
1913741195.00-179.00179.00
2014021212.90-189.10189.10
2115041231.81-272.19272.19
2215021259.03-242.97242.97
2315881283.33-304.67304.67
2416071313.80-293.20293.20
2516901343.12-346.88346.88
2617621377.80-384.20384.20
2717571416.22-340.78340.78
2818391450.30-388.70388.70
2918481489.17-358.83358.83
3019041525.05-378.95378.95
3119751562.95-412.05412.05
3220611604.15-456.85456.85
3321531649.84-503.16503.16
3422131700.15-512.85512.85
3522381751.44-486.56486.56
3623661800.10-565.90565.90
371856.69
-229.31233.25
EMEMA
Feuil1
MM
moisdemande
Aug-971115
sept.-971125
oct.-971115
nov.-971120
dc.-971120
jan.-981105
fv.-981090
Mar-981095
Apr-981110
May-981095
Jun-981105
juil.-981090
MM
demande
mois
demande
Demande mensuelle
MM3MM5MM7
tXtPtPtPt
190
2105
395
411096.67
595103.33
690100.0099.00
710598.3399.00
812096.6799.0098.57
9120105.00104.00102.86
10115115.00106.00105.00
11125118.33110.00107.86
12115120.00117.00110.00
13115118.33119.00112.86
14125118.33118.00116.43
15115118.33119.00119.29
16120118.33119.00118.57
17120120.00118.00118.57
18105118.33119.00119.29
1990115.00117.00116.43
2095105.00110.00112.86
2111096.67106.00110.00
229598.33104.00107.86
23105100.0099.00105.00
2490103.3399.00102.86
2596.6799.0098.57
moy.=107.08
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
LE PMEAUne mesure relative
EM, EMA, EMAt et PMEA: ex. 1.14EM = -0,083 EMA = 4,07 PMEA = 5,15%a = 0,2
Calcul des valeurs de EM, EMA, EMAt et PMEA
mois
Demande (Xt)
Prvisions (Pt)
et
|et|
|et|/Xt
EMAt
1
75
80,0
-5,0
5,0
0,0667
5,00
2
86
79,0
7,0
7,0
0,0814
5,40
3
84
80,4
3,6
3,6
0,0429
5,04
4
78
81,1
-3,1
3,1
0,0397
4,65
5
83
80,5
2,5
2,5
0,0301
4,22
6
72
81,0
-9,0
9,0
0,1250
5,18
7
81
79,2
1,8
1,8
0,0222
4,50
8
79
79,6
-0,6
0,6
0,0076
3,72
9
75
79,4
-4,4
4,4
0,0587
3,86
10
77
78,6
-1,6
1,6
0,0208
3,41
11
77
78,2
-1,2
1,2
0,0156
2,96
12
84
78,0
9,0
9,0
0,1071
4,17
Somme
-1
48,8
0,6178
LE PMEA AJUSTUne sous-estimation dela demande a un plusgrand impact quunesurestimation quivalenteSi Pt = 50Si Pt = 200Xt = 100
LA STATISTIQUE U DE THEILU = 1
U < 1
U > 1Plus la valeur de U est basse, mieux cest ...
]|Expr|[#>`b___})%# b'4" *|: ;bP8&c0!"U ,]
LA STATISTIQUE U: ex. 1.16U = 0,9248
t
Xt
Pt
et
(et+1/Xt)2
[(Xt+1-Xt)/Xt]2
1
90
95,00
-5,00
0,0178
0,0278
2
105
93,00
12,00
0,0001
0,0091
3
95
96,00
-1,00
0,0226
0,0249
4
110
95,72
14,28
0,0014
0,0186
5
95
99,08
-4,08
0,0085
0,0028
6
90
98,75
-8,75
0,0078
0,0278
7
105
97,07
7,93
0,0453
0,0204
8
120
97,65
22,35
0,0094
0,0000
9
120
108,37
11,63
0,0000
0,0017
10
115
115,29
-0,29
0,0074
0,0076
11
125
115,12
9,88
0,0030
0,0064
12
115
121,82
-6,82
0,0013
0,0000
13
115
119,07
-4,07
0,0037
0,0076
14
125
118,04
6,96
0,0021
0,0064
15
115
120,77
-5,77
0,0000
0,0019
16
120
119,82
0,18
0,0000
0,0000
17
120
119,85
0,15
0,0154
0,0156
18
105
119,88
-14,88
0,0551
0,0204
19
90
114,65
-24,65
0,0013
0,0031
20
95
98,29
-3,29
0,0217
0,0249
21
110
96,02
13,98
0,0013
0,0186
22
95
98,97
-3,97
0,0057
0,0111
23
105
97,85
7,15
0,0062
0,0204
24
90
98,30
-8,30
Somme
0,2369
0,2770
EMQ ET EMQtPour lestimation de lcart-type
ESTIMATION DE LCART-TYPEDeux faons destimer lcart-type des erreurs de prvision
EMQ, EMQt et ET: ex. 1.17EMQ = 107,43
ET = 10,59
ET24 = 10,16
t
Xt
Pt
et
et2
EQMt
1
90
95,00
-5,00
25,00
25,00
2
105
93,00
12,00
144,00
36,90
3
95
96,00
-1,00
1,00
33,31
4
110
95,72
14,28
203,92
50,37
5
95
99,08
-4,08
16,65
47,00
6
90
98,75
-8,75
76,56
49,95
7
105
97,07
7,93
62,88
51,25
8
120
97,65
22,35
499,52
96,08
9
120
108,37
11,63
135,26
99,99
10
115
115,29
-0,29
0,08
90,00
11
125
115,12
9,88
97,61
90,76
12
115
121,82
-6,82
46,51
86,34
13
115
119,07
-4,07
16,56
79,36
14
125
118,04
6,96
48,44
76,27
15
115
120,77
-5,77
33,29
71,97
16
120
119,82
0,18
0,03
64,78
17
120
119,85
0,15
0,02
58,30
18
105
119,88
-14,88
221,41
74,61
19
90
114,65
-24,65
607,62
127,91
20
95
98,29
-3,29
10,82
116,21
21
110
96,02
13,98
195,44
124,13
22
95
98,97
-3,97
15,76
113,29
23
105
97,85
7,15
51,12
107,08
24
90
98,30
-8,30
68,89
103,26
Somme
2 578,43
LE POURCENTAGE DE PRVISIONS RUSSIESri = 1 si E est vrai et ri = 0 si E est faux
E: un vnement prdfini
PPR: ex. 1.18PPR = 62,5%
t
Xt
Pt
et
Xt 8%
Xt + 8%
rt
1
90
95,00
-5,00
82,80
97,20
1
2
105
93,00
12,00
96,60
113,40
0
3
95
96,00
-1,00
87,40
102,60
1
4
110
95,72
14,28
101,20
118,80
0
5
95
99,08
-4,08
87,40
102,60
1
6
90
98,75
-8,75
82,80
97,20
0
7
105
97,07
7,93
96,60
113,40
1
8
120
97,65
22,35
110,40
129,60
0
9
120
108,37
11,63
110,40
129,60
0
10
115
115,29
-0,29
105,80
124,20
1
11
125
115,12
9,88
115,00
135,00
1
12
115
121,82
-6,82
105,80
124,20
1
13
115
119,07
-4,07
105,80
124,20
1
14
125
118,04
6,96
115,00
135,00
1
15
115
120,77
-5,77
105,80
124,20
1
16
120
119,82
0,18
110,40
129,60
1
17
120
119,85
0,15
110,40
129,60
1
18
105
119,88
-14,88
96,60
113,40
0
19
90
114,65
-24,65
82,80
97,20
0
20
95
98,29
-3,29
87,40
102,60
1
21
110
96,02
13,98
101,20
118,80
0
22
95
98,97
-3,97
87,40
102,60
1
23
105
97,85
7,15
96,60
113,40
1
24
90
98,30
-8,30
82,80
97,20
0
Somme
15
LA DTERMINATION DE LA LONGUEUR DUN CYCLE SAISONNIERPar inspection visuelle
Graph1
362
385
432
341
382
409
498
387
473
513
582
474
L = 4
priode
demande
Feuil2
iXtMM(12) centre 7MM(12) centre 6MM(12) centreRatios saisonniersIndices sais.
10.7494
20.8452
30.9569
41540
51.1724
61.2777629.83RAPPORT DTAILL
71.3728629.83628.25629.041.16
81.2759628.25644.50636.381.19Statistiques de la rgression
91.1643644.50650.67647.580.99Coefficient de dtermination multiple0.9978859236
101643650.67666.00658.330.98Coefficient de dtermination R^20.9957763165
110.9641666.00671.42668.710.96Coefficient de dtermination R^20.9956520905
120.8588671.42681.17676.290.87Erreur-type7.11060783
130.7475681.17692.42686.790.69Observations36
140.8647692.42707.67700.040.92
150.9643707.67729.08718.380.90ANALYSE DE VARIANCE
161724729.08737.75733.420.99Degr de libertSomme des carrsMoyenne des carrsFValeur critique de F
171.1789737.75745.67741.711.06Rgression1405287.11117021405287.111170218015.84552399170
181.2894745.67759.17752.421.19Rsidus341719.065286193950.5607437116
191.3863759.17769.25764.211.13Total35407006.176456404
201.2942769.25775.33772.291.22
211.1900775.33782.67779.001.16CoefficientsErreur-typeStatistique tProbabilitLI 95%LS 95%
221747782.67792.75787.710.95Constante561.40047547553.0358405356184.92423066720555.2309092704567.5700416805
230.9736792.75810.17801.460.92Variable X 110.21376555130.114080447389.531254453409.981926341110.4456047615
240.8750810.17815.33812.750.92
250.7596815.33833.58824.460.72
260.8720833.58840.83837.210.86
270.9731840.83840.58840.710.87
281845840.58859.17849.880.99
291.1998859.17873.33866.251.15
301.2956873.33873.33873.331.09
311.31082873.33879.25876.291.231.1737793135
321.21029879.25882.00880.631.171.1936425676
331.1897882.00889.17885.581.011.0537138125
341970889.17903.42896.291.081.0024221353
350.9906903.42909.17906.291.000.9588561802
360.8750909.17929.42919.290.820.8693619579
370.7667929.42942.58936.000.710.7090424605
380.8753942.58956.75949.670.790.8590471629
390.9817956.75976.17966.460.850.8699783919
4011016976.17979.00977.581.041.0069073333
411.11067979.00982.58980.791.091.1012498324
421.21199982.58988.92985.751.221.1663868926
431.31240988.921000.5923941799
441.211991010.8061597312
451.111301021.0199252824
46110041031.2336908337
470.99491041.447456385
480.88261051.6612219362Prvisions
491061.8749874875912.2006954033
501072.0887530388932.6940493593
511082.302518591089.7783428024
521092.51628414131203.1333747647
531102.73004969261286.2098759915
541112.94381524381306.3504273707
551123.15758079511340.6486985871
561133.37134634641194.2490423489
571143.58511189761146.3550297673
581153.79887744891106.3271843261
591164.01264300011011.9483103964
601174.2264085514832.5763818707
MM(12) complte, t=T-L/2, , T
prvisions dsaisonnalises
Feuil2
demande
MM(12) centre 7
MM(12) centre 6
MM(12) centre
prvisions
Feuil3
priodedemande
1362
2385
3432
4341
5382
6409
7498
8387
9473
10513
11582
12474
Feuil3
L = 4
priode
demande
LONGUEUR DUN CYCLE SAISONNIER: LAUTOCORRLATIONCorrlation entre une sriedobservations et ces mmesobservations dcales de kpriodesk: ordre de lautocorrlation-1 rk 1rk = -1 ou rk = 1autocorrlation parfaite
rk = 0autocorrlation nulle
CYCLE DE LONGUEUR LSi les observations sont affectes par la prsence dun cycle saisonnier,lautocorrlation dordre L sera, parmi toutes les autres autocorrlations,la plus importante.Gnralement, les autocorrlations dodre k=1, , 12 sont calculespuisque la plupart du temps, la longueur des cycles saisonniers est dauplus 12 priodes.
AUTOCORRLATION: ex. 1.19-0,2669rk -0,3581-0,22160,6072
priode
demande
k=1
k=2
k=3
k=4
1
362
2
385
362
3
432
385
362
4
341
432
385
362
5
382
341
432
385
362
6
409
382
341
432
385
7
445
409
382
341
432
8
335
445
409
382
341
9
360
335
445
409
382
10
375
360
335
445
409
11
440
375
360
335
445
12
355
440
375
360
335
GRAPHIQUE DES AUTOCORRLATIONS-0,2669 -0,3581-0,22160,6072
_974525618.xls
Graph1
-0.2668829524
-0.3581085888
-0.2215549147
0.6072483911
ordre k des autocorrlations
rk
Feuil7
priodedemandek=1k=2k=3k=4r1r2r3r4err. Car.
1362532.84
23853621.920.01
3432385362-3.91-1082.992201.17
4341432385362-2068.243.671017.591943.34
5382341432385362135.92-144.660.2671.179.51
6409382341432385-73.74-1054.331122.09-1.99572.01
74454093823414321433.01-184.74-2641.332811.093590.01
8335445409382341-3000.83-1197.83154.422207.842508.34
93603354454093821256.26-1502.91-599.9177.34629.17
10375360335445409252.92505.01-604.16-241.16101.67
11440375360335445-553.74-1377.49-2750.413290.423015.84
12355440375360335-1652.08303.34754.591506.67905.01
sommes-4272.51-5732.93-3546.859721.3916008.92
moyenne385.08
somme car.16008.92rk-0.2669-0.3581-0.22160.6072
Feuil7
ordre k des autocorrlations
rk
Feuil6
exemple 5.18
tXtPtetXt 8%Xt + 8%rt
19095-582.80102.601
2105931296.60100.440
39596-187.40103.681
411095.7214.28101.20103.380
59599.08-4.0887.40107.011
69098.75-8.7582.80106.651
710597.077.9396.60104.841
812097.6522.35110.40105.460
9120108.3711.63110.40117.040
10115115.29-0.29105.80124.511
11125115.129.88115.00124.331
12115121.82-6.82105.80131.571
13115119.07-4.07105.80128.601
14125118.046.96115.00127.481
15115120.77-5.77105.80130.431
16120119.820.18110.40129.411
17120119.850.15110.40129.441
18105119.88-14.8896.60129.471
1990114.65-24.6582.80123.821
209598.29-3.2987.40106.151
2111096.0213.98101.20103.700
229598.97-3.9787.40106.891
2310597.857.1596.60105.681
249098.3-8.382.80106.161
Feuil5
exemple 5.16 et 5.17a=0.1
tXtPtet(et+1/Xt)^2((Xt+1-Xt)/Xt)^2et^2EQMt
19095-50.01780.027825.0025.00
210593120.00010.0091144.0036.90
39596-10.02260.02491.0033.31
411095.7214.280.00140.0186203.9250.37
59599.08-4.080.00850.002816.6547.00
69098.75-8.750.00780.027876.5649.95
710597.077.930.04530.020462.8851.25
812097.6522.350.00940.0000499.5296.08
9120108.3711.630.00000.0017135.2699.99
10115115.29-0.290.00740.00760.0890.00
11125115.129.880.00300.006497.6190.76
12115121.82-6.820.00130.000046.5186.34
13115119.07-4.070.00370.007616.5679.36
14125118.046.960.00210.006448.4476.27
15115120.77-5.770.00000.001933.2971.97
16120119.820.180.00000.00000.0364.78
17120119.850.150.01540.01560.0258.30
18105119.88-14.880.05510.0204221.4174.61
1990114.65-24.650.00130.0031607.62127.91
209598.29-3.290.02170.024910.82116.21
2111096.0213.980.00130.0186195.44124.13
229598.97-3.970.00570.011115.76113.29
2310597.857.150.00620.020451.12107.08
249098.3-8.368.89103.26
Total0.23690.27702578.43
U=0.9247620447EQM=107.43
Feuil4
Exemple 5.14
a=0.2
moisDemande (Xt)Prvisions (Pt)et|et|EMAt|et|/Xt
17580-555.000.0667
28679775.400.0814
38480.43.63.65.040.0429
47881.1-3.13.14.650.0397
58380.52.52.54.220.0301
67281-995.180.1250
78179.21.81.84.500.0222
87979.6-0.60.63.720.0076
97579.4-4.44.43.860.0587
107778.6-1.61.63.410.0208
117778.2-1.21.22.960.0156
128478994.170.1071
Somme-148.8
Feuil1
a=0.2Diffrenciation d'ordre 1
priodedemandeX'tP'tX''t
11091
21006-85-85.00
3110599-85.00184
41034-71-48.20-170
5109561-52.76132
61081-14-30.01-75
7113655-26.8169
81116-20-10.45-75
91109-7-12.3613
10119990-11.2897
111209108.97-80
121232239.1813
131191-4111.94-64
141239481.3589
151235-410.68-52
161330957.7599
1713421225.20-83
181332-1022.56-22
1913744216.0552
2014022821.24-14
21150410222.5974
221502-238.47-104
2315888630.3888
2416071941.50-67
2537.00
Feuil1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
demande
priode
demande
Feuil2
a=0.1Diffrenciation d'ordre 1 et 2
priodedemandeX'tX''tP''tP'tPt
11091
21006-85
31105991840.00
41034-71-17018.40
5109561132-0.44
61081-14-7512.80
7113655694.02
81116-20-7510.52
91109-7131.97
10119990973.07
11120910-8012.46
12123223133.22
131191-41-644.20
1412394889-2.62
151235-4-526.54
16133095990.69
17134212-8310.52
181332-10-221.17
1913744252-1.15
20140228-144.16
211504102742.35
221502-2-1049.51
2315888688-1.84
24160719-677.15
25-0.2718.731625.73
26-0.2718.461643.92
27-0.2718.191661.58
28-0.2717.921678.69
Feuil2
1091
1006
1105
1034
1095
1081
1136
1116
1109
1199
1209
1232
1191
1239
1235
1330
1342
1332
1374
1402
1504
1502
1588
1607
demande
priode
demande
Feuil3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
priodes
X't
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
priodes
X''t
Dcomposition par dsaisonnalisation
priodedemandeMM(4)RtIt
1362
2385
3432
4341380.000.8974
5382385.000.9922
6409391.001.0460
7445394.251.1287
8335392.750.8530
9360387.250.92960.9609
10375378.750.99011.0181
11440377.501.16561.1471
12355382.500.92810.8928
00
00
00
00
00
00
00
00
00
00
00
00
srie originale
srie dsaisonnalise
priodes
demande
LA STATISTIQUE DE DURBIN-WATSONPour sassurer que les erreurs de prvision sont indpendantesLa valeur de D-W doittre prs de 2 ...
TEST DE SIGNIFICATIVIT DE LA STATISTIQUE DE DURBIN-WATSONValeurs lues dans letableau 1.33, p. 102selon le nombre T determes derreur si dU < D-W < 4-dU, D-W nest pas significativement diffrent de 2; si D-W < dL ou D-W > 4-dL, D-W est significativement diffrent de 2; si dL < D-W < dU ou 4-dU < D-W < 4-dL, on ne peut conclure.
STATISTIQUE DE DURBIN-WATSON: ex. 1.20D-W = 0,5319T = 16dL = ?dU = ?Conclusion: ?
t
et
(et - et-1)2
(et)2
1
-63,82
4 072,99
2
-56,44
54,46
3 185,47
3
-14,79
1 734,72
218,74
4
-9,31
30,03
86,68
5
7,62
286,62
58,06
6
12,86
27,46
165,38
7
29,57
279,22
874,38
8
34,61
25,40
1 197,85
9
-27,85
3 901,25
775,62
10
-20,06
60,68
402,40
11
-17,06
9,00
291,04
12
-17,35
0,08
301,02
13
8,38
662,03
70,22
14
13,55
26,73
183,60
15
23,19
92,93
537,78
16
41,87
348,94
1 753,10
Somme
7 539,58
14 174,36
GRAPHIQUE DES ERREURS DE PRVISION: ex. 1.20Les erreurs ne sont pas centres 0 et elles ne sont pas distribuesalatoirement
Graph1
-63.82
-56.44
-14.79
-9.31
7.62
12.86
29.57
34.61
-27.85
-20.06
-17.06
-17.35
8.38
13.55
23.19
41.87
priodes
erreurs de prvision
Feuil1
1-63.82
2-56.44
3-14.79
4-9.31
57.62
612.86
729.57
834.61
9-27.85
10-20.06
11-17.06
12-17.35
138.38
1413.55
1523.19
1641.87
Feuil1
priodes
erreurs de prvision
Feuil2
Feuil3
SIGNAL DALERTEPour la dtection dun changement dans la structure des observations
Graph1
90
105
95
110
95
90
105
120
120
115
125
115
115
125
115
120
120
105
90
95
110
95
105
90
25
priodes
observations
LES
a=0.1
tXtPtet
190100.00-10.00
210599.006.00
39599.60-4.60
411099.1410.86
595100.23-5.23
69099.70-9.70
710598.736.27
812099.3620.64
9120101.4218.58
10115103.2811.72
11125104.4520.55
12115106.518.49
13115107.367.64
14125108.1216.88
15115109.815.19
16120110.339.67
17120111.308.70
18105112.17-7.17
1990111.45-21.45
2095109.30-14.30
21110107.872.13
2295108.09-13.09
23105106.78-1.78
2490106.60-16.60
25104.94
LES
priodes
observations
LESA
b=0.2
tXtPtetabs(et)EtMtat
19095.00-5.005.00-5.005.000.40
210593.0012.0012.00-1.606.400.25
39596.00-1.001.00-1.485.320.28
411095.7214.2814.281.677.110.24
59599.08-4.084.080.526.500.08
69098.75-8.758.75-1.336.950.19
710597.077.937.930.527.150.07
812097.6522.3522.354.8910.190.48
9120108.3711.6311.636.2410.480.60
10115115.29-0.290.294.938.440.58
11125115.129.889.885.928.730.68
12115121.82-6.826.823.378.350.40
13115119.07-4.074.071.887.490.25
14125118.046.966.962.907.380.39
15115120.77-5.775.771.167.060.16
16120119.820.180.180.975.690.17
17120119.850.150.150.804.580.18
18105119.88-14.8814.88-2.336.640.35
1990114.65-24.6524.65-6.8010.240.66
209598.29-3.293.29-6.098.850.69
2111096.0213.9813.98-2.089.870.21
229598.97-3.973.97-2.468.690.28
2310597.857.157.15-0.548.390.06
249098.30-8.308.30-2.098.370.25
2596.23
LESA
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
demande
prvisions
priodes
demande et prvisions
LETS
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
priodes
valeurs de at
LESAIS
a=0.5
g=0.5
b=0.5
tXtStbtItPt
13620.9526
23851.0132
34321.1368
4341380.00009.75000.8974
5382395.372212.56110.9594371.2882
6409405.810811.49991.0105413.3009
7498427.683116.68611.1506474.4164
8387437.815113.40900.8907398.7629
9473472.119123.85650.9806432.9066
10513501.820426.77891.0164501.1874
11582517.205121.08181.1380608.2211
12474535.240819.55870.8881479.4261
13544.0560
14583.7738
15675.8498
16544.8383
LESAIS
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
demande
prvisions
priodes
demande
LETO2
a=0.5L=4
b=0.5X bar=380
tXtStItPt
13620.9526
23851.0132
34321.1368
4341380.00000.8974
5382390.49720.9654362.0000
6409397.09281.0216395.6354
7445394.26401.1328451.4318
8335383.78890.8851353.8000
9360378.33870.9585370.5235
10375372.71001.0139386.5002
11440380.57031.1445422.1924
12355390.82240.8967336.8512
13374.5963
14396.2385
15447.2813
16350.4628
LETO2
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
demande
prvisions
priodes
demande
LETO1
a=0.3
XtS'tS''tStbtPt
110911091109110910
21006106610831048-8
31105107710821073-21040
41034106410761052-51071
51095107410761072-11047
6108110761076107601071
7113610941081110751076
8111611001087111461112
9110911031092111451120
101199113211041160121119
111209115511191191151172
121232117811371219181206
131191118211501214141237
141239119911651233151227
151235121011781241131248
161330124611991293201255
171342127512211328231313
181332129212431341211351
191374131712651368221362
201402134212881396231390
211504139113191463311420
221502142413501498321493
231588147313871559371529
241607151314251602381596
251640
261677
271715
LETO1
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
000
000
000
000
000
000
000
000
000
000
000
000
000
observations
S't
S''t
prvisions
priodes
demande
MMP
a=0.3
g=0.4
tXtStbtPt
110911091.0010.00
211011101.0010.001101.00
311051109.209.281111.00
410341093.14-0.861118.48
510951093.09-0.531092.28
610811089.09-1.921092.56
711361101.823.941087.18
811161108.835.171105.76
911091112.504.571114.00
1011991141.6514.401117.07
1112091171.9320.751156.05
1212321204.4825.471192.69
1311911218.2720.801229.95
1412391239.0420.791239.06
1512351252.3817.811259.83
1613301288.1424.991270.19
1713421321.7828.451313.12
1813321344.7726.261350.24
1913741371.9226.621371.03
2014021399.5827.031398.54
2115041449.8336.321426.61
2215021490.9138.221486.15
2315881546.7945.291529.13
2416071596.5547.081592.08
251643.63
261690.71
271737.79
MMP
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
Erreurs
w1=0.5w1=0.1
w2=0.3w2=0.2
w3=0.2w3=0.3
w4=0.4
tXtPtPt
190
2105
395
411097.00
595104.5097.50
69099.50102.00
710595.5099.00
812098.50101.00
9120109.5098.00
10115117.00103.50
11125117.50113.50
12115121.00119.50
13115118.00119.00
14125117.00118.00
15115120.00120.00
16120118.00117.00
17120119.50118.50
18105119.00120.50
1990112.50116.50
2095100.50114.00
2111095.50107.00
2295101.5099.00
2310599.5096.00
2490103.00100.50
2595.50102.50
Erreurs
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
Feuil1
a=0.1
tXtPtetabs(et)
110911050.00
210061054.1048.1048.1
311051049.29-55.7155.71
410341054.8620.8620.86
510951052.77-42.2342.23
610811057.00-24.0024.00
711361059.40-76.6076.60
811161067.06-48.9448.94
911091071.95-37.0537.05
1011991075.66-123.34123.34
1112091087.99-121.01121.01
1212321100.09-131.91131.91
1311911113.28-77.7277.72
1412391121.05-117.95117.95
1512351132.85-102.15102.15
1613301143.06-186.94186.94
1713421161.76-180.24180.24
1813321179.78-152.22152.22
1913741195.00-179.00179.00
2014021212.90-189.10189.10
2115041231.81-272.19272.19
2215021259.03-242.97242.97
2315881283.33-304.67304.67
2416071313.80-293.20293.20
2516901343.12-346.88346.88
2617621377.80-384.20384.20
2717571416.22-340.78340.78
2818391450.30-388.70388.70
2918481489.17-358.83358.83
3019041525.05-378.95378.95
3119751562.95-412.05412.05
3220611604.15-456.85456.85
3321531649.84-503.16503.16
3422131700.15-512.85512.85
3522381751.44-486.56486.56
3623661800.10-565.90565.90
371856.69
-229.31233.25
EMEMA
Feuil1
MM
moisdemande
Aug-971115
sept.-971125
oct.-971115
nov.-971120
dc.-971120
jan.-981105
fv.-981090
Mar-981095
Apr-981110
May-981095
Jun-981105
juil.-981090
MM
0
0
0
0
0
0
0
0
0
0
0
0
demande
mois
demande
Demande mensuelle
MM3MM5MM7
tXtPtPtPt
190
2105
395
411096.67
595103.33
690100.0099.00
710598.3399.00
812096.6799.0098.57
9120105.00104.00102.86
10115115.00106.00105.00
11125118.33110.00107.86
12115120.00117.00110.00
13115118.33119.00112.86
14125118.33118.00116.43
15115118.33119.00119.29
16120118.33119.00118.57
17120120.00118.00118.57
18105118.33119.00119.29
1990115.00117.00116.43
2095105.00110.00112.86
2111096.67106.00110.00
229598.33104.00107.86
23105100.0099.00105.00
2490103.3399.00102.86
2596.6799.0098.57
moy.=107.08
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
SIGNAL TSValeur critique: TS* = 4Si |TSt| > TS* ...
]|Expr|[#>`b___})%# b'4$(!" *|: ;bP8&c0!"TS}^t_ ,]
SIGNAL DE TRIGGSAt = |Et / Mt|
Et = bet + (1-b)Et-1
Mt = b|et| + (1-b)Mt-1
0 < b < 1LES adaptatif ...La valeur de SAt indique des erreurs de prvision non alatoires avec:
une probabilit de 95% si la valeur de SAt excde 0,51 pour une constante de lissage b=0,1; une probabilit de 95% si la valeur de SAt excde 0,74 pour une constante de lissage b=0,2
SIGNAL DALERTE: ex. 1.21Les signauxdtectent unchangementde structure
t
Xt
Pt
et
|et|
EMAt
Et
Mt
et
TSt
SAt
1
90
95,00
-5,00
5
5,00
-5,00
5,00
-5
-1,00
-1,00
2
105
93,00
12,00
12
5,70
-1,60
6,40
7
1,23
-0,25
3
95
96,00
-1,00
1
5,23
-1,48
5,32
6
1,15
-0,28
4
110
95,72
14,28
14,28
6,14
1,67
7,11
20,28
3,31
0,24
5
95
99,08
-4,08
4,08
5,93
0,52
6,51
16,2
2,73
0,08
6
90
98,75
-8,75
8,75
6,21
-1,33
6,95
7,45
1,20
-0,19
7
105
97,07
7,93
7,93
6,38
0,52
7,15
15,38
2,41
0,07
8
120
97,65
22,35
22,35
7,98
4,89
10,19
37,73
4,73
0,48
9
120
108,37
11,63
11,63
8,35
6,23
10,48
49,36
5,91
0,60
10
115
115,29
-0,29
0,29
7,54
4,93
8,44
49,07
6,51
0,58
11
125
115,12
9,88
9,88
7,77
5,92
8,73
58,95
7,58
0,68
12
115
121,82
-6,82
6,82
7,68
3,37
8,35
52,13
6,79
0,40
13
115
119,07
-4,07
4,07
7,32
1,88
7,49
48,06
6,57
0,25
14
125
118,04
6,96
6,96
7,28
2,90
7,38
55,02
7,56
0,39
15
115
120,77
-5,77
5,77
7,13
1,17
7,06
49,25
6,91
0,16
16
120
119,82
0,18
0,18
6,44
0,97
5,69
49,43
7,68
0,17
17
120
119,85
0,15
0,15
5,81
0,80
4,58
49,58
8,54
0,18
18
105
119,88
-14,88
14,88
6,71
-2,33
6,64
34,7
5,17
-0,35
19
90
114,65
-24,65
24,65
8,51
-6,80
10,24
10,05
1,18
-0,66
20
95
98,29
-3,29
3,29
7,99
-6,09
8,85
6,76
0,85
-0,69
21
110
96,02
13,98
13,98
8,59
-2,08
9,88
20,74
2,42
-0,21
22
95
98,97
-3,97
3,97
8,12
-2,46
8,70
16,77
2,06
-0,28
23
105
97,85
7,15
7,15
8,03
-0,54
8,39
23,92
2,98
-0,06
24
90
98,30
-8,30
8,3
8,05
-2,09
8,37
15,62
1,94
-0,25
CHANGEMENT DE STRUCTURE: GRAPHIQUEAugmentation du niveau moyen de 20% partir de la priode 8
Graph1
90
105
95
110
95
90
105
120
120
115
125
115
115
125
115
120
120
105
90
95
110
95
105
90
25
priodes
observations
LES
a=0.1
tXtPtet
190100.00-10.00
210599.006.00
39599.60-4.60
411099.1410.86
595100.23-5.23
69099.70-9.70
710598.736.27
812099.3620.64
9120101.4218.58
10115103.2811.72
11125104.4520.55
12115106.518.49
13115107.367.64
14125108.1216.88
15115109.815.19
16120110.339.67
17120111.308.70
18105112.17-7.17
1990111.45-21.45
2095109.30-14.30
21110107.872.13
2295108.09-13.09
23105106.78-1.78
2490106.60-16.60
25104.94
LES
priodes
observations
LESA
b=0.2
tXtPtetabs(et)EtMtat
19095.00-5.005.00-5.005.000.40
210593.0012.0012.00-1.606.400.25
39596.00-1.001.00-1.485.320.28
411095.7214.2814.281.677.110.24
59599.08-4.084.080.526.500.08
69098.75-8.758.75-1.336.950.19
710597.077.937.930.527.150.07
812097.6522.3522.354.8910.190.48
9120108.3711.6311.636.2410.480.60
10115115.29-0.290.294.938.440.58
11125115.129.889.885.928.730.68
12115121.82-6.826.823.378.350.40
13115119.07-4.074.071.887.490.25
14125118.046.966.962.907.380.39
15115120.77-5.775.771.167.060.16
16120119.820.180.180.975.690.17
17120119.850.150.150.804.580.18
18105119.88-14.8814.88-2.336.640.35
1990114.65-24.6524.65-6.8010.240.66
209598.29-3.293.29-6.098.850.69
2111096.0213.9813.98-2.089.870.21
229598.97-3.973.97-2.468.690.28
2310597.857.157.15-0.548.390.06
249098.30-8.308.30-2.098.370.25
2596.23
LESA
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
demande
prvisions
priodes
demande et prvisions
LETS
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
priodes
valeurs de at
LESAIS
a=0.5
g=0.5
b=0.5
tXtStbtItPt
13620.9526
23851.0132
34321.1368
4341380.00009.75000.8974
5382395.372212.56110.9594371.2882
6409405.810811.49991.0105413.3009
7498427.683116.68611.1506474.4164
8387437.815113.40900.8907398.7629
9473472.119123.85650.9806432.9066
10513501.820426.77891.0164501.1874
11582517.205121.08181.1380608.2211
12474535.240819.55870.8881479.4261
13544.0560
14583.7738
15675.8498
16544.8383
LESAIS
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
demande
prvisions
priodes
demande
LETO2
a=0.5L=4
b=0.5X bar=380
tXtStItPt
13620.9526
23851.0132
34321.1368
4341380.00000.8974
5382390.49720.9654362.0000
6409397.09281.0216395.6354
7445394.26401.1328451.4318
8335383.78890.8851353.8000
9360378.33870.9585370.5235
10375372.71001.0139386.5002
11440380.57031.1445422.1924
12355390.82240.8967336.8512
13374.5963
14396.2385
15447.2813
16350.4628
LETO2
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
demande
prvisions
priodes
demande
LETO1
a=0.3
XtS'tS''tStbtPt
110911091109110910
21006106610831048-8
31105107710821073-21040
41034106410761052-51071
51095107410761072-11047
6108110761076107601071
7113610941081110751076
8111611001087111461112
9110911031092111451120
101199113211041160121119
111209115511191191151172
121232117811371219181206
131191118211501214141237
141239119911651233151227
151235121011781241131248
161330124611991293201255
171342127512211328231313
181332129212431341211351
191374131712651368221362
201402134212881396231390
211504139113191463311420
221502142413501498321493
231588147313871559371529
241607151314251602381596
251640
261677
271715
LETO1
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
000
000
000
000
000
000
000
000
000
000
000
000
000
observations
S't
S''t
prvisions
priodes
demande
MMP
a=0.3
g=0.4
tXtStbtPt
110911091.0010.00
211011101.0010.001101.00
311051109.209.281111.00
410341093.14-0.861118.48
510951093.09-0.531092.28
610811089.09-1.921092.56
711361101.823.941087.18
811161108.835.171105.76
911091112.504.571114.00
1011991141.6514.401117.07
1112091171.9320.751156.05
1212321204.4825.471192.69
1311911218.2720.801229.95
1412391239.0420.791239.06
1512351252.3817.811259.83
1613301288.1424.991270.19
1713421321.7828.451313.12
1813321344.7726.261350.24
1913741371.9226.621371.03
2014021399.5827.031398.54
2115041449.8336.321426.61
2215021490.9138.221486.15
2315881546.7945.291529.13
2416071596.5547.081592.08
251643.63
261690.71
271737.79
MMP
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
Erreurs
w1=0.5w1=0.1
w2=0.3w2=0.2
w3=0.2w3=0.3
w4=0.4
tXtPtPt
190
2105
395
411097.00
595104.5097.50
69099.50102.00
710595.5099.00
812098.50101.00
9120109.5098.00
10115117.00103.50
11125117.50113.50
12115121.00119.50
13115118.00119.00
14125117.00118.00
15115120.00120.00
16120118.00117.00
17120119.50118.50
18105119.00120.50
1990112.50116.50
2095100.50114.00
2111095.50107.00
2295101.5099.00
2310599.5096.00
2490103.00100.50
2595.50102.50
Erreurs
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
Feuil1
a=0.1
tXtPtetabs(et)
110911050.00
210061054.1048.1048.1
311051049.29-55.7155.71
410341054.8620.8620.86
510951052.77-42.2342.23
610811057.00-24.0024.00
711361059.40-76.6076.60
811161067.06-48.9448.94
911091071.95-37.0537.05
1011991075.66-123.34123.34
1112091087.99-121.01121.01
1212321100.09-131.91131.91
1311911113.28-77.7277.72
1412391121.05-117.95117.95
1512351132.85-102.15102.15
1613301143.06-186.94186.94
1713421161.76-180.24180.24
1813321179.78-152.22152.22
1913741195.00-179.00179.00
2014021212.90-189.10189.10
2115041231.81-272.19272.19
2215021259.03-242.97242.97
2315881283.33-304.67304.67
2416071313.80-293.20293.20
2516901343.12-346.88346.88
2617621377.80-384.20384.20
2717571416.22-340.78340.78
2818391450.30-388.70388.70
2918481489.17-358.83358.83
3019041525.05-378.95378.95
3119751562.95-412.05412.05
3220611604.15-456.85456.85
3321531649.84-503.16503.16
3422131700.15-512.85512.85
3522381751.44-486.56486.56
3623661800.10-565.90565.90
371856.69
-229.31233.25
EMEMA
Feuil1
MM
moisdemande
Aug-971115
sept.-971125
oct.-971115
nov.-971120
dc.-971120
jan.-981105
fv.-981090
Mar-981095
Apr-981110
May-981095
Jun-981105
juil.-981090
MM
0
0
0
0
0
0
0
0
0
0
0
0
demande
mois
demande
Demande mensuelle
MM3MM5MM7
tXtPtPtPt
190
2105
395
411096.67
595103.33
690100.0099.00
710598.3399.00
812096.6799.0098.57
9120105.00104.00102.86
10115115.00106.00105.00
11125118.33110.00107.86
12115120.00117.00110.00
13115118.33119.00112.86
14125118.33118.00116.43
15115118.33119.00119.29
16120118.33119.00118.57
17120120.00118.00118.57
18105118.33119.00119.29
1990115.00117.00116.43
2095105.00110.00112.86
2111096.67106.00110.00
229598.33104.00107.86
23105100.0099.00105.00
2490103.3399.00102.86
2596.6799.0098.57
moy.=107.08
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
SLECTION DUNE MTHODE DE PRVISION POUR UN PRODUIT SANS HISTORIQUEPrvoir la demande des produits sans historique en se basant uniquement sur des tudes de march;
Utiliser, comme donnes historiques, une srie de consommation dont le niveau moyen de la demande et son comportement sont semblables;
Demander aux vendeurs des produits concerns de fournir leurs propres prvisions.
LIEN ENTRE LES ERREURS DE PRVISION ET LA DISTRIBUTION DE LA DEMANDELa distribution des erreurs de prvision sert, sous certaines conditions, estimer lcart-type de la demande des produits correspondants:- prvisions non biaises;- erreurs de prvisions distribues alatoirement autour de 0;- la meilleure mthode de prvision possible a t utilise.Conditions:
_974619502.xls
Graph2
13.3333333333
-8.3333333333
-10
6.6666666667
23.3333333333
15
0
6.6666666667
-5
-3.3333333333
6.6666666667
-3.3333333333
1.6666666667
0
-13.3333333333
-25
-10
13.3333333333
-3.3333333333
5
-13.3333333333
priode
erreurs de prvision
Feuil9
exemple 5.22
0.20.30.1
tXtmm(3)mm(4)LES(0,2)LES(0,3)LEA(0,1)e mm(3)e mm(4)e (0,2)e (0,3)e (0,1)EtMtatabs(e mm(3))abs(e mm(4))abs(e (0,2))abs(e (0,3))abs(e (0,1))% e mm(3)% e mm(4)% e (0,2)% e (0,3)% e (0,1)
19090.0090.0090.000.000.000.000.000.000.20
210590.0090.0090.0015.0015.0015.001.501.501.00
39593.0094.50105.002.000.50-10.000.352.350.15
411096.6793.4094.65103.5113.3316.6015.356.490.962.760.35
595103.33100.0096.7299.26105.77-8.33-5.00-1.72-4.26-10.77-0.213.560.06
690100.00101.2596.3897.98105.14-10.00-11.25-6.38-7.98-15.14-1.704.720.36
710598.3397.5095.1095.5899.686.677.509.909.425.32-1.004.780.21
812096.67100.0097.0898.41100.7923.3320.0022.9221.5919.211.026.220.16
9120105.00102.50101.66104.89103.9415.0017.5018.3415.1116.062.527.210.35
10115115.00108.75105.33109.42109.560.006.259.675.585.442.827.030.40
11125118.33115.00107.27111.09111.746.6710.0017.7313.9113.263.867.650.50
12115120.00120.00110.81115.27118.43-5.00-5.004.19-0.27-3.433.137.230.43
13115118.33118.75111.65115.19116.94-3.33-3.753.35-0.19-1.942.626.700.393.333.753.350.191.940.02900.03260.02910.00160.0169
14125118.33117.50112.32115.13116.186.677.5012.689.878.823.246.910.476.677.5012.689.878.820.05330.06000.10140.07900.0705
15115118.33120.00114.86118.09120.32-3.33-5.000.14-3.09-5.322.396.750.353.335.000.143.095.320.02900.04350.00130.02690.0462
16120118.33117.50114.88117.16118.441.672.505.122.841.562.306.230.371.672.505.122.841.560.01390.02080.04260.02360.0130
17120120.00118.75115.91118.01119.020.001.254.091.990.982.175.710.380.001.254.091.990.980.00000.01040.03410.01650.0082
18105118.33120.00116.73118.61119.39-13.33-15.00-11.73-13.61-14.390.526.580.0813.3315.0011.7313.6114.390.12700.14290.11170.12960.1371
1990115.00115.00114.38114.53118.26-25.00-25.00-24.38-24.53-28.26-2.368.750.2725.0025.0024.3824.5328.260.27780.27780.27090.27250.3140
2095105.00108.75109.50107.17110.63-10.00-13.75-14.50-12.17-15.63-3.699.430.3910.0013.7514.5012.1715.630.10530.14470.15270.12810.1645
2111096.67102.50106.60103.52104.5213.337.503.406.485.48-2.779.040.3113.337.503.406.485.480.12120.06820.03090.05890.0498
229598.33100.00107.28105.46106.20-3.33-5.00-12.28-10.46-11.20-3.619.260.393.335.0012.2810.4611.200.03510.05260.12930.11010.1179
23105100.0097.50104.83102.32101.835.007.500.172.683.17-2.948.650.345.007.500.172.683.170.04760.07140.00170.02550.0302
2490103.33101.25104.86103.13102.90-13.33-11.25-14.86-13.13-12.90-3.939.070.4313.3311.2514.8613.1312.900.14810.12500.16510.14590.1434
Pour les priodes 13 24EM-3.75-4.38-4.07-4.44-5.80
EMA8.198.758.898.429.14
PMEA8.238.758.928.499.27
Feuil9
priode
erreurs de prvision
Feuil8
exemple 5.21b=0.2pour Et et Mt
a=0.1pour EMAt
tXtPtet|et|EMAtEtMtsomme(et)TStSAt
19095-555.00-5.005.00-5-1.00-1.00
21059312125.70-1.606.4071.23-0.25
39596-115.23-1.485.3261.15-0.28
411095.7214.2814.286.141.677.1120.283.310.24
59599.08-4.084.085.930.526.5116.22.730.08
69098.75-8.758.756.21-1.336.957.451.20-0.19
710597.077.937.936.380.527.1515.382.410.07
812097.6522.3522.357.984.8910.1937.734.730.48
9120108.3711.6311.638.356.2310.4849.365.910.60
10115115.29-0.290.297.544.938.4449.076.510.58
11125115.129.889.887.775.928.7358.957.580.68
12115121.82-6.826.827.683.378.3552.136.790.40
13115119.07-4.074.077.321.887.4948.066.570.25
14125118.046.966.967.282.907.3855.027.560.39
15115120.77-5.775.777.131.177.0649.256.910.16
16120119.820.180.186.440.975.6949.437.680.17
17120119.850.150.155.810.804.5849.588.540.18
18105119.88-14.8814.886.71-2.336.6434.75.17-0.35
1990114.65-24.6524.658.51-6.8010.2410.051.18-0.66
209598.29-3.293.297.99-6.098.856.760.85-0.69
2111096.0213.9813.988.59-2.089.8820.742.42-0.21
229598.97-3.973.978.12-2.468.7016.772.06-0.28
2310597.857.157.158.03-0.548.3923.922.98-0.06
249098.3-8.38.38.05-2.098.3715.621.94-0.25
Feuil7
Exemple 5.19
priodedemandek=1k=2k=3k=4r1r2r3r4err. Car.
1362532.84
23853621.920.01
3432385362-3.91-1082.992201.17
4341432385362-2068.243.671017.591943.34
5382341432385362135.92-144.660.2671.179.51
6409382341432385-73.74-1054.331122.09-1.99572.01
74454093823414321433.01-184.74-2641.332811.093590.01
8335445409382341-3000.83-1197.83154.422207.842508.34
93603354454093821256.26-1502.91-599.9177.34629.17
10375360335445409252.92505.01-604.16-241.16101.67
11440375360335445-553.74-1377.49-2750.413290.423015.84
12355440375360335-1652.08303.34754.591506.67905.01
sommes-4272.51-5732.93-3546.859721.3916008.92
moyenne385.08
somme car.16008.92rk-0.2669-0.3581-0.22160.6072
Feuil7
ordre k des autocorrlations
rk
Feuil6
exemple 5.18
tXtPtetXt 8%Xt + 8%rt
19095-582.80102.601
2105931296.60100.440
39596-187.40103.681
411095.7214.28101.20103.380
59599.08-4.0887.40107.011
69098.75-8.7582.80106.651
710597.077.9396.60104.841
812097.6522.35110.40105.460
9120108.3711.63110.40117.040
10115115.29-0.29105.80124.511
11125115.129.88115.00124.331
12115121.82-6.82105.80131.571
13115119.07-4.07105.80128.601
14125118.046.96115.00127.481
15115120.77-5.77105.80130.431
16120119.820.18110.40129.411
17120119.850.15110.40129.441
18105119.88-14.8896.60129.471
1990114.65-24.6582.80123.821
209598.29-3.2987.40106.151
2111096.0213.98101.20103.700
229598.97-3.9787.40106.891
2310597.857.1596.60105.681
249098.3-8.382.80106.161
Feuil5
exemple 5.16 et 5.17a=0.1
tXtPtet(et+1/Xt)^2((Xt+1-Xt)/Xt)^2et^2EQMt
19095-50.01780.027825.0025.00
210593120.00010.0091144.0036.90
39596-10.02260.02491.0033.31
411095.7214.280.00140.0186203.9250.37
59599.08-4.080.00850.002816.6547.00
69098.75-8.750.00780.027876.5649.95
710597.077.930.04530.020462.8851.25
812097.6522.350.00940.0000499.5296.08
9120108.3711.630.00000.0017135.2699.99
10115115.29-0.290.00740.00760.0890.00
11125115.129.880.00300.006497.6190.76
12115121.82-6.820.00130.000046.5186.34
13115119.07-4.070.00370.007616.5679.36
14125118.046.960.00210.006448.4476.27
15115120.77-5.770.00000.001933.2971.97
16120119.820.180.00000.00000.0364.78
17120119.850.150.01540.01560.0258.30
18105119.88-14.880.05510.0204221.4174.61
1990114.65-24.650.00130.0031607.62127.91
209598.29-3.290.02170.024910.82116.21
2111096.0213.980.00130.0186195.44124.13
229598.97-3.970.00570.011115.76113.29
2310597.857.150.00620.020451.12107.08
249098.3-8.368.89103.26
Total0.23690.27702578.43
U=0.9247620447EQM=107.43
Feuil5
priode
erreurs de prvision
Feuil4
Exemple 5.14
a=0.2
moisDemande (Xt)Prvisions (Pt)et|et|EMAt|et|/Xt
17580-555.000.0667
28679775.400.0814
38480.43.63.65.040.0429
47881.1-3.13.14.650.0397
58380.52.52.54.220.0301
67281-995.180.1250
78179.21.81.84.500.0222
87979.6-0.60.63.720.0076
97579.4-4.44.43.860.0587
107778.6-1.61.63.410.0208
117778.2-1.21.22.960.0156
128478994.170.1071
Somme-148.8
Feuil1
a=0.2Diffrenciation d'ordre 1exemple 5.11
priodedemandeX'tP'tX''tk=1r1SC
1109126068.7934027778
21006-85-85.00109139792.751736111160741.7100694444
3110599-85.00184100636342.335069444421743.9600694444
41034-71-48.20-170110532213.501736111147724.0434027777
5109561-52.76132103434398.085069444424793.1267361111
61081-14-30.01-75109526997.543402777829397.9600694444
7113655-26.8169108119967.751736111113562.5434027778
81116-20-10.45-75113615891.710069444418620.8767361111
91109-7-12.3613111619576.085069444420580.2934027778
10119990-11.289711097669.04340277782857.7934027778
111209108.97-8011992323.21006944441888.6267361111
121232239.18131209889.0850694444418.5434027778
131191-4111.94-6412321257.33506944443777.1267361111
141239481.35891191827.1267361111181.1267361111
151235-410.68-521239234.9600694444304.7934027778
161330957.75991235-1353.74826388896012.7100694445
1713421225.20-8313306943.21006944458017.7100694445
181332-1022.56-2213427122.29340277786326.8767361111
1913744216.055213329667.626736111114772.3767361111
2014022821.24-14137418175.543402777822362.7100694445
21150410222.5974140237615.960069444563273.2100694445
221502-238.47-104150462770.126736111162271.0434027778
2315888630.3888150283731.6267361112112588.210069444
2416071941.50-671588118963.501736111125699.793402778
2537.00
somme582016.664930556667917.164930556
moyenne1252.4583333333
r1=0.871390489
Feuil1
demande
priode
demande
Feuil2
a=0.1Diffrenciation d'ordre 1 et 2
priodedemandeX'tX''tP''tP'tPt
11091
21006-85
31105991840.00
41034-71-17018.40
5109561132-0.44
61081-14-7512.80
7113655694.02
81116-20-7510.52
91109-7131.97
10119990973.07
11120910-8012.46
12123223133.22
131191-41-644.20
1412394889-2.62
151235-4-526.54
16133095990.69
17134212-8310.52
181332-10-221.17
1913744252-1.15
20140228-144.16
211504102742.35
221502-2-1049.51
2315888688-1.84
24160719-677.15
25-0.2718.731625.73
26-0.2718.461643.92
27-0.2718.191661.58
28-0.2717.921678.69
Feuil2
1091
1006
1105
1034
1095
1081
1136
1116
1109
1199
1209
1232
1191
1239
1235
1330
1342
1332
1374
1402
1504
1502
1588
1607
demande
priode
demande
Feuil3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
priodes
X't
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
priodes
X''t
Dcomposition par dsaisonnalisation
priodedemandeMM(4)RtIt
1362
2385
3432
4341380.000.8974
5382385.000.9922
6409391.001.0460
7445394.251.1287
8335392.750.8530
9360387.250.92960.9609
10375378.750.99011.0181
11440377.501.16561.1471
12355382.500.92810.8928
srie originale
srie dsaisonnalise
priodes
demande
DISTRIBUTION DE LA DEMANDEET = 1,25 EMA ou ETt = 1,25 EMAtForme de la distributionFast moversSlow moversNormalePoisson
Demande moyenne pour une priode t: Pt
cart-type de la demande pour une priode t:
ou
INTERVALLES DE CONFIANCE POUR LES PRVISIONSCas o la distribution des erreurs de prvision est connue:
- distribution Normale- distribution de Poisson
Cas o la distribution des erreurs de prvision est inconnue:
- ingalit de Chebychev- ingalit de Camp-Meidel
Cas pour la rgression linaire
- la valeur de la variable indpendante a dj t observe- la valeur de la variable indpendante na jamais t observe
INTERVALLES DE CONFIANCE PARTIR DE LA DISTRIBUTION NORMALEPt Za/2 s Xt Pt + Za/2 ss = ET
Z/2
0,001
3,100
0,005
2,575
0,010
2,327
0,025
1,960
0,050
1,645
0,075
1,439
0,100
1,281
INTERVALLES DE CONFIANCE PARTIR DE LA DISTRIBUTION DE POISONP(Xt = x | l) = (e-l lx) / x!P(Xt xinf | l) 1 - a/2P(Xt xsup | l) a/2xinf Xt xsup
INGALIT DE CHEBYCHEV
INGALIT DE CAMP-MEIDEL
INTERVALLES DE CONFIANCE: exemples ...Intervalle 90%, EQM = 1 750 et Pt = 400Ingalit de ChebychevIngalit de Camp-Meideln = 12
INTERVALLES DE CONFIANCE: exemples ...Intervalle 90%, EQM = 1 750 et Pt = 400Distribution Normalen = 12
Z/2
0,001
3,100
0,005
2,575
0,010
2,327
0,025
1,960
0,050
1,645
0,075
1,439
0,100
1,281
INTERVALLES DE CONFIANCE: exemples ...Slow mover avec l = 10, intervalle 90%?Tableau, p. 227
INTERVALLES POUR RGRESSION: VALEUR DE X DJ OBSERVE
= 6 490
INTERVALLES POUR RGRESSION: VALEUR DE X JAMAIS OBSERVE
INTERVALLES POUR RGRESSION: ex. 1.24a1 425 Y13 1 573
= 788,27 + 0,0158(45 000) = 1 499 units
= 6 490
INTERVALLES POUR RGRESSION: ex. 1.24b1 305 Y13 1 693
]|Expr|[#>`b___})0# b'4" *|: ;bP8&c0!"s"!Symbol^:!&c0 .B: &c0!" ,]:! s