carta cusum
DESCRIPTION
cusumTRANSCRIPT
EJEMPLO 110
No Xi CUSUM1 9.45 -0.55 -0.552 7.99 -2.01 -2.563 9.29 -0.71 -3.274 11.66 1.66 -1.615 12.16 2.16 0.556 10.18 0.18 0.737 8.04 -1.96 -1.238 11.46 1.46 0.239 9.2 -0.8 -0.57
10 10.34 0.34 -0.2311 9.03 -0.97 -1.212 11.47 1.47 0.2713 10.51 0.51 0.7814 9.4 -0.6 0.1815 10.08 0.08 0.2616 9.37 -0.63 -0.3717 10.62 0.62 0.2518 10.31 0.31 0.5619 8.52 -1.48 -0.9220 10.84 0.84 -0.0821 10.4 0.4 0.3222 8.83 -1.17 -0.8523 11.79 1.79 0.9424 11 1 1.9425 10.1 0.1 2.0426 10.58 0.58 2.6227 9.88 -0.12 2.528 11.12 1.12 3.6229 10.81 0.81 4.4330 10.02 0.02 4.45
s =25 m 0 =
Si = Xi-m 0
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30
-3
-2
-1
0
1
2
3
-0.550000000000001
-2.01
-0.710000000000001
1.662.16
0.18
-1.96
1.46
-0.800000000000001
0.34
-0.970000000000001
1.47
0.51
-0.60.0800000000000001
-0.630000000000001
0.6199999999999990.310000000000001
-1.48
0.840.4
-1.17
1.79
1
0.09999999999999960.58
-0.119999999999999
1.120.810000000000001
0.0199999999999996
CARTA CUSUM
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30
-3
-2
-1
0
1
2
3
-0.550000000000001
-2.01
-0.710000000000001
1.662.16
0.18
-1.96
1.46
-0.800000000000001
0.34
-0.970000000000001
1.47
0.51
-0.60.0800000000000001
-0.630000000000001
0.6199999999999990.310000000000001
-1.48
0.840.4
-1.17
1.79
1
0.09999999999999960.58
-0.119999999999999
1.120.810000000000001
0.0199999999999996
CARTA CUSUM
UNIVERSIDAD IBEROAMERICANA
CONTROL AVANZADO DE PROCESOS
TAREA No. 1
MARCO ANTONIO GOMEZ VELEZ
GABRIEL CAMILO ULLOA ORDOÑEZ
12-N0VIEMBRE - 199
PROBLEMA 7.1
DATOS:25
1050
No Xi CUSUM1 1045 -5 -52 1055 5 03 1037 -13 -134 1064 14 15 1095 45 466 1008 -42 47 1050 0 48 1087 37 419 1125 75 116
10 1146 96 21211 1139 89 30112 1169 119 42013 1151 101 52114 1128 78 59915 1238 188 78716 1125 75 86217 1163 113 97518 1188 138 111319 1146 96 120920 1167 117 1326
s =m 0 =
Xi-m 0
A) DISEÑAR LA MASCARILLA EN V SI SE DETECTAN CORRIMIENTOS CERCA DE 1s EN LA MEDIA DEL PROCESO.
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
0
200
400
600
800
1000
1200
1400
0 146
4 4 41116
212301
420
521599
787862
975
1113
1209
1326
CARTA CUSUM
EN LA MEDIA DEL PROCESO.
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
0
200
400
600
800
1000
1200
1400
0 146
4 4 41116
212301
420
521599
787862
975
1113
1209
1326
CARTA CUSUM
Problema 7.7Datos 950
953 985 949 937 959 948 958 952945 973 941 946 939 937 955 931972 955 966 954 948 955 947 928945 950 966 935 958 927 941 937975 948 934 941 963 940 938 950970 957 937 933 973 962 945 970959 940 946 960 949 963 963 933973 933 952 968 942 943 967 960940 965 935 959 965 950 969 934936 973 941 956 962 938 981 927
a) Estime la desviación estandar del proceso:14.0
b) Construya la grafica CUSUM usando valores estandarizados de h = 5 y k = 1/2 Interprete esta carta.
mo =
s =
950 k = 0.5s = 14 h= 5
No. Xi Xi - (mo + k) SHi NH (mo - k)-Xi SLi NL1 953 2.50 2.5 1 -3.5 0.00 02 945 -5.50 0.0 0 4.5 4.50 13 972 21.50 21.5 1 -22.5 0.00 04 945 -5.50 16.0 2 4.5 4.50 15 975 24.50 40.5 3 -25.5 0.00 06 970 19.50 60.0 4 -20.5 0.00 07 959 8.50 68.5 5 -9.5 0.00 08 973 22.50 91.0 6 -23.5 0.00 09 940 -10.50 80.5 7 9.5 9.50 1
10 936 -14.50 66.0 8 13.5 23.00 211 985 34.50 100.5 9 -35.5 0.00 012 973 22.50 123.0 10 -23.5 0.00 013 955 4.50 127.5 11 -5.5 0.00 014 950 -0.50 127.0 12 -0.5 0.00 015 948 -2.50 124.5 13 1.5 1.50 116 957 6.50 131.0 14 -7.5 0.00 017 940 -10.50 120.5 15 9.5 9.50 118 933 -17.50 103.0 16 16.5 26.00 219 965 14.50 117.5 17 -15.5 10.50 320 973 22.50 140.0 18 -23.5 0.00 021 949 -1.50 138.5 19 0.5 0.50 122 941 -9.50 129.0 20 8.5 9.00 223 966 15.50 144.5 21 -16.5 0.00 024 966 15.50 160.0 22 -16.5 0.00 025 934 -16.50 143.5 23 15.5 15.50 126 937 -13.50 130.0 24 12.5 28.00 227 946 -4.50 125.5 25 3.5 31.50 328 952 1.50 127.0 26 -2.5 29.00 429 935 -15.50 111.5 27 14.5 43.50 530 941 -9.50 102.0 28 8.5 52.00 631 937 -13.50 88.5 29 12.5 64.50 732 946 -4.50 84.0 30 3.5 68.00 833 954 3.50 87.5 31 -4.5 63.50 934 935 -15.50 72.0 32 14.5 78.00 1035 941 -9.50 62.5 33 8.5 86.50 1136 933 -17.50 45.0 34 16.5 103.00 1237 960 9.50 54.5 35 -10.5 92.50 1338 968 17.50 72.0 36 -18.5 74.00 1439 959 8.50 80.5 37 -9.5 64.50 1540 956 5.50 86.0 38 -6.5 58.00 1641 959 8.50 94.5 39 -9.5 48.50 1742 939 -11.50 83.0 40 10.5 59.00 1843 948 -2.50 80.5 41 1.5 60.50 1944 958 7.50 88.0 42 -8.5 52.00 2045 963 12.50 100.5 43 -13.5 38.50 2146 973 22.50 123.0 44 -23.5 15.00 2247 949 -1.50 121.5 45 0.5 15.50 2348 942 -8.50 113.0 46 7.5 23.00 2449 965 14.50 127.5 47 -15.5 7.50 2550 962 11.50 139.0 48 -12.5 0.00 051 948 -2.50 136.5 49 1.5 1.50 1
m o =
52 937 -13.50 123.0 50 12.5 14.00 253 955 4.50 127.5 51 -5.5 8.50 354 927 -23.50 104.0 52 22.5 31.00 455 940 -10.50 93.5 53 9.5 40.50 556 962 11.50 105.0 54 -12.5 28.00 657 963 12.50 117.5 55 -13.5 14.50 758 943 -7.50 110.0 56 6.5 21.00 859 950 -0.50 109.5 57 -0.5 20.50 960 938 -12.50 97.0 58 11.5 32.00 1061 958 7.50 104.5 59 -8.5 23.50 1162 955 4.50 109.0 60 -5.5 18.00 1263 947 -3.50 105.5 61 2.5 20.50 1364 941 -9.50 96.0 62 8.5 29.00 1465 938 -12.50 83.5 63 11.5 40.50 1566 945 -5.50 78.0 64 4.5 45.00 1667 963 12.50 90.5 65 -13.5 31.50 1768 967 16.50 107.0 66 -17.5 14.00 1869 969 18.50 125.5 67 -19.5 0.00 070 981 30.50 156.0 68 -31.5 0.00 071 952 1.50 157.5 69 -2.5 0.00 072 931 -19.50 138.0 70 18.5 18.50 173 928 -22.50 115.5 71 21.5 40.00 274 937 -13.50 102.0 72 12.5 52.50 375 950 -0.50 101.5 73 -0.5 52.00 476 970 19.50 121.0 74 -20.5 31.50 577 933 -17.50 103.5 75 16.5 48.00 678 960 9.50 113.0 76 -10.5 37.50 779 934 -16.50 96.5 77 15.5 53.00 880 927 -23.50 73.0 78 22.5 75.50 9
EJEMPLO 1950
No Xi CUSUM(Si)1 953 3 32 945 -5 -23 972 22 204 945 -5 155 975 25 406 970 20 607 959 9 698 973 23 929 940 -10 82
10 936 -14 6811 985 35 10312 973 23 12613 955 5 13114 950 0 13115 948 -2 12916 957 7 13617 940 -10 12618 933 -17 10919 965 15 12420 973 23 14721 949 -1 14622 941 -9 13723 966 16 15324 966 16 16925 934 -16 15326 937 -13 14027 946 -4 13628 952 2 13829 935 -15 12330 941 -9 11431 937 -13 10132 946 -4 9733 954 4 10134 935 -15 8635 941 -9 7736 933 -17 6037 960 10 7038 968 18 8839 959 9 9749 956 6 10341 959 9 11242 939 -11 10143 948 -2 9944 958 8 10745 963 13 12046 973 23 14347 949 -1 14248 942 -8 13449 965 15 14950 962 12 161
m o =
Xi-m 0
51 948 -2 15952 937 -13 14653 955 5 15154 927 -23 12855 940 -10 11856 962 12 13057 963 13 14358 943 -7 13659 950 0 13660 938 -12 12461 958 8 13262 955 5 13763 947 -3 13464 941 -9 12565 938 -12 11366 945 -5 10867 963 13 12168 967 17 13869 969 19 15770 981 31 18871 952 2 19072 931 -19 17173 928 -22 14974 937 -13 13675 950 0 13676 970 20 15677 933 -17 13978 960 10 14979 934 -16 13380 927 -23 110
-50
0
50
100
150
200
250
3-2
2015
40
6069
928268
103
126131131129136126109124
147146137153169153140136138
12311410197101
867760708897103
11210199
107120
143142134149161159
146151
128118130143136136
124132137134
125113108
121138
157
188190
171
149136136
156139149133
110
CARTA CUSUM
-50
0
50
100
150
200
250
3-2
2015
40
6069
928268
103
126131131129136126109124
147146137153169153140136138
12311410197101
867760708897103
11210199
107120
143142134149161159
146151
128118130143136136
124132137134
125113108
121138
157
188190
171
149136136
156139149133
110
CARTA CUSUM
Problema 7.7Datos 950
953 985 949 937 959 948 958 952945 973 941 946 939 937 955 931972 955 966 954 948 955 947 928945 950 966 935 958 927 941 937975 948 934 941 963 940 938 950970 957 937 933 973 962 945 970959 940 946 960 949 963 963 933973 933 952 968 942 943 967 960940 965 935 959 965 950 969 934936 973 941 956 962 938 981 927
a) Estime la desviación estandar del proceso:14.0
b) Construya la grafica CUSUM usando valores estandarizados. h = 5 y k = 1/2 Interprete esta carta.
Solución: para estandarizar los valores hacemos:
mo =
s =
Yi = ( Xi - mo ) / s
950 k = 0.5s = 14
No. Xi Yi Shi NH1 949 -0.07 -950.6 0 0 950.572 941 -0.64 -951.1 0 0 951.143 966 1.14 -949.4 0 0 949.364 966 1.14 -949.4 0 0 949.365 934 -1.14 -951.6 0 0 951.646 937 -0.93 -951.4 0 0 951.437 946 -0.29 -950.8 0 0 950.798 952 0.14 -950.4 0 0 950.369 935 -1.07 -951.6 0 0 951.57
10 941 -0.64 -951.1 0 0 951.1411 985 2.50 -948.0 0 0 948.0012 973 1.64 -948.9 0 0 948.8613 955 0.36 -950.1 0 0 950.1414 950 0.00 -950.5 0 0 950.5015 948 -0.14 -950.6 0 0 950.6416 957 0.50 -950.0 0 0 950.0017 940 -0.71 -951.2 0 0 951.2118 933 -1.21 -951.7 0 0 951.7119 965 1.07 -949.4 0 0 949.4320 973 1.64 -948.9 0 0 948.8621 949 -0.07 -950.6 0 0 950.5722 941 -0.64 -951.1 0 0 951.1423 966 1.14 -949.4 0 949.3624 966 1.14 -949.4 0 0 949.3625 934 -1.14 -951.6 0 0 951.6426 937 -0.93 -951.4 0 0 951.4327 946 -0.29 -950.8 0 0 950.7928 952 0.14 -950.4 0 0 950.3629 935 -1.07 -951.6 0 0 951.5730 941 -0.64 -951.1 0 0 951.1431 937 -0.93 -951.4 0 0 951.4332 946 -0.29 -950.8 0 0 950.7933 954 0.29 -950.2 0 0 950.2134 935 -1.07 -951.6 0 0 951.5735 941 -0.64 -951.1 0 0 951.1436 933 -1.21 -951.7 0 0 951.7137 960 0.71 -949.8 0 0 949.7938 968 1.29 -949.2 0 0 949.2139 959 0.64 -949.9 0 0 949.8640 956 0.43 -950.1 0 0 950.0741 959 0.64 -949.9 0 0 949.8642 939 -0.79 -951.3 0 0 951.2943 948 -0.14 -950.6 0 0 950.6444 958 0.57 -949.9 0 0 949.9345 963 0.93 -949.6 0 0 949.5746 973 1.64 -948.9 0 0 948.8647 949 -0.07 -950.6 0 0 950.57
m o =
Yi - (mo + k) (mo + k)-Yi
48 942 -0.57 -951.1 0 0 951.0749 965 1.07 -949.4 0 0 949.4350 962 0.86 -949.6 0 0 949.6451 948 -0.14 -950.6 0 0 950.6452 937 -0.93 -951.4 0 0 951.4353 955 0.36 -950.1 0 0 950.1454 927 -1.64 -952.1 0 0 952.1455 940 -0.71 -951.2 0 0 951.2156 962 0.86 -949.6 0 0 949.6457 963 0.93 -949.6 0 0 949.5758 943 -0.50 -951.0 0 0 951.0059 950 0.00 -950.5 0 0 950.5060 938 -0.86 -951.4 0 0 951.3661 958 0.57 -949.9 0 0 949.9362 955 0.36 -950.1 0 0 950.1463 947 -0.21 -950.7 0 0 950.7164 941 -0.64 -951.1 0 0 951.1465 938 -0.86 -951.4 0 0 951.3666 945 -0.36 -950.9 0 0 950.8667 963 0.93 -949.6 0 0 949.5768 967 1.21 -949.3 0 0 949.2969 969 1.36 -949.1 0 0 949.1470 981 2.21 -948.3 0 0 948.2971 952 0.14 -950.4 0 0 950.3672 931 -1.36 -951.9 0 0 951.8673 928 -1.57 -952.1 0 0 952.0774 937 -0.93 -951.4 0 0 951.4375 950 0.00 -950.5 0 0 950.5076 970 1.43 -949.1 0 0 949.0777 933 -1.21 -951.7 0 0 951.7178 960 0.71 -949.8 0 0 949.7979 934 -1.14 -951.6 0 0 951.6480 927 -1.64 -952.1 0 0 952.14
Problema 7.15
con el problema 7.125
1050
No Xi CUSUM(Si)1 1045 -5 -52 1055 5 03 1037 -13 -134 1064 14 15 1095 45 466 1008 -42 47 1050 0 48 1087 37 419 1125 75 116
10 1146 96 21211 1139 89 30112 1169 119 42013 1151 101 52114 1128 78 59915 1238 188 78716 1125 75 86217 1163 113 97518 1188 138 111319 1146 96 120920 1167 117 1326
CARTA EWMA
No Xt LICz LSCZ L= 2.71 1045 1049.5 1043.25 1056.75 0.12 1055 1050.1 1040.92 1059.08 253 1037 1048.7 1039.40 1060.604 1064 1050.3 1038.31 1061.695 1095 1054.7 1037.50 1062.506 1008 1050.1 1036.88 1063.12 CUANDO LA CARTA HA CORRIDO DURANTE7 1050 1050.1 1036.40 1063.60 VARIOS PERIODOS, LOS LÍMITES DE CONTROL8 1087 1053.8 1036.02 1063.98 SE ESTABILIZAN EN:9 1125 1060.9 1035.72 1064.28
10 1146 1069.4 1035.49 1064.51 LSCz = 1065.4855611 1139 1076.4 1035.30 1064.70 LICZ = 1034.5144412 1169 1085.6 1035.14 1064.8613 1151 1092.2 1035.02 1064.9814 1128 1095.7 1034.93 1065.0715 1238 1110.0 1034.85 1065.1516 1125 1111.5 1034.78 1065.2217 1163 1116.6 1034.73 1065.2718 1188 1123.8 1034.69 1065.31
Ahora usa la carta EWMA con l = 0.1 y L=2.7 y compara los resultados
s =m 0 =
Xi-m 0
Zt=l* Xt + (1-l)Zt-1
l=s=
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20-200
0
200
400
600
800
1000
1200
1400
1600
-5 0 -131 46 4 4 41116
212301
420521
599
787862
975
11131209
1326
CARTA CUSUM
19 1146 1126.0 1034.66 1065.3420 1167 1130.1 1034.63 1065.37
1 3 5 7 9 11 13 15 17 19980.00
1000.00
1020.00
1040.00
1060.00
1080.00
1100.00
1120.00
1140.00
CARTA EWMA
Zt=l* Xt + (1-l)Zt-1
LICz
LSCZ
CUANDO LA CARTA HA CORRIDO DURANTEVARIOS PERIODOS, LOS LÍMITES DE CONTROL
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20-200
0
200
400
600
800
1000
1200
1400
1600
-5 0 -131 46 4 4 41116
212301
420521
599
787862
975
11131209
1326
CARTA CUSUM
1 3 5 7 9 11 13 15 17 19980.00
1000.00
1020.00
1040.00
1060.00
1080.00
1100.00
1120.00
1140.00
CARTA EWMA
Zt=l* Xt + (1-l)Zt-1
LICz
LSCZ
Problema 7.17
L= 38.020.05
No Xt LICz LSCZ
1 8.00 8.0160 8.0020 8.0380 0.22 8.01 8.0148 7.9905 8.04953 8.02 8.0158 7.9831 8.0569 n= 54 8.01 8.0147 7.9784 8.06165 8.00 8.0117 7.9754 8.06466 8.01 8.0114 7.9734 8.0666 8.077 8.06 8.0211 7.9722 8.06788 8.07 8.0309 7.9714 8.0686 8.029 8.01 8.0267 7.9709 8.0691
10 8.04 8.0294 7.9706 8.0694 7.9711 8.02 8.0275 7.9704 8.069612 8.01 8.0240 7.9702 8.069813 8.05 8.0292 7.9702 8.0698 Conforme se incrementa t los límites se estabilizan14 8.04 8.0314 7.9701 8.0699 en LSC= 8.07 y LIC=7.9715 8.03 8.0311 7.9701 8.069916 8.05 8.0349 7.9700 8.070017 8.06 8.0399 7.9700 8.070018 8.04 8.0399 7.9700 8.070019 8.05 8.0419 7.9700 8.070020 8.06 8.0455 7.9700 8.070021 8.04 8.0444 7.9700 8.070022 8.02 8.0395 7.9700 8.070023 8.03 8.0376 7.9700 8.070024 8.05 8.0401 7.9700 8.0700
De los datos del ejercicio 7.4 elabore una carta EWMA con l=0.2 y L=3
m o = s=
Zt=l* Xt + (1-l)Zt-1
l=
LSC= mo +Ls *raiz( l / (2-l))
LC = mo =
LSC= mo -Ls *raiz( l / (2-l))
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24
7.9200
7.9400
7.9600
7.9800
8.0000
8.0200
8.0400
8.0600
8.0800
CARTA EWMA
Zt=l* Xt + (1-l)Zt-1
LICz
LSCZ
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24
7.9200
7.9400
7.9600
7.9800
8.0000
8.0200
8.0400
8.0600
8.0800
CARTA EWMA
Zt=l* Xt + (1-l)Zt-1
LICz
LSCZ
Conforme se incrementa t los límites se estabilizan
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24
7.9200
7.9400
7.9600
7.9800
8.0000
8.0200
8.0400
8.0600
8.0800
CARTA EWMA
Zt=l* Xt + (1-l)Zt-1
LICz
LSCZ
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24
7.9200
7.9400
7.9600
7.9800
8.0000
8.0200
8.0400
8.0600
8.0800
CARTA EWMA
Zt=l* Xt + (1-l)Zt-1
LICz
LSCZ
PROBLEMA 7.23Analiza los datos del problema 7.1 usando una carta de promedios moviles con:
w= 6
105025
No Xt Mt LICz LSCZ
1 1045.00 1045.0000 975.0000 1125.00002 1055.00 1050.0000 996.9670 1103.0330 w= 63 1035.00 1045.0000 1006.6987 1093.3013 n= 14 1064.00 1049.7500 1012.5000 1087.50005 1095.00 1058.8000 1016.4590 1083.54106 1008.00 1050.3333 1019.3814 1080.61867 1050.00 1051.1667 1019.3814 1080.61868 1087.00 1056.5000 1019.3814 1080.61869 1125.00 1071.5000 1019.3814 1080.6186 LSCx = 1080.61862
10 1146.00 1085.1667 1019.3814 1080.6186 LICx = 1019.3813811 1139.00 1092.5000 1019.3814 1080.618612 1169.00 1119.3333 1019.3814 1080.618613 1151.00 1136.1667 1019.3814 1080.618614 1128.00 1143.0000 1019.3814 1080.618615 1238.00 1161.8333 1019.3814 1080.618616 1125.00 1158.3333 1019.3814 1080.618617 1163.00 1162.3333 1019.3814 1080.618618 1188.00 1165.5000 1019.3814 1080.618619 1146.00 1164.6667 1019.3814 1080.618620 1167.00 1171.1667 1019.3814 1080.6186
m o = s=
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24
900.0000
950.0000
1000.0000
1050.0000
1100.0000
1150.0000
1200.0000
CARTA DE MEDIA MOVIL
Mt
LICz
LSCZ
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24
900.0000
950.0000
1000.0000
1050.0000
1100.0000
1150.0000
1200.0000
CARTA DE MEDIA MOVIL
Mt
LICz
LSCZ
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24
900.0000
950.0000
1000.0000
1050.0000
1100.0000
1150.0000
1200.0000
CARTA DE MEDIA MOVIL
Mt
LICz
LSCZ
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24
900.0000
950.0000
1000.0000
1050.0000
1100.0000
1150.0000
1200.0000
CARTA DE MEDIA MOVIL
Mt
LICz
LSCZ
Problema 7.24Analizar los datos del problema 7.4 usando una carta de control de media movil
8.020.05
No Xt Mt LICz LSCZ
1 8.00 8.0000 7.8700 8.17002 8.01 8.0050 7.9139 8.1261 w= 53 8.02 8.0100 7.9334 8.1066 n= 14 8.01 8.0100 7.9450 8.09505 8.00 8.0080 7.9529 8.0871 A medida que t incrementa los límites se6 8.01 8.0100 7.9529 8.0871 estabilizan en:7 8.06 8.0200 7.9529 8.0871 LSCz 8.0878 8.07 8.0300 7.9529 8.0871 LICz 7.9539 8.01 8.0300 7.9529 8.0871
10 8.04 8.0380 7.9529 8.087111 8.02 8.0400 7.9529 8.087112 8.01 8.0300 7.9529 8.087113 8.05 8.0260 7.9529 8.087114 8.04 8.0320 7.9529 8.087115 8.03 8.0300 7.9529 8.087116 8.05 8.0360 7.9529 8.087117 8.06 8.0460 7.9529 8.087118 8.04 8.0440 7.9529 8.087119 8.05 8.0460 7.9529 8.087120 8.06 8.0520 7.9529 8.087121 8.04 8.0500 7.9529 8.087122 8.02 8.0420 7.9529 8.087123 8.03 8.0400 7.9529 8.087124 8.05 8.0400 7.9529 8.0871
m o = s=
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24
7.7000
7.7500
7.8000
7.8500
7.9000
7.9500
8.0000
8.0500
8.1000
8.1500
8.2000
CARTA DE MEDIA MOVIL
Mt
LICz
LSCZ
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24
7.7000
7.7500
7.8000
7.8500
7.9000
7.9500
8.0000
8.0500
8.1000
8.1500
8.2000
CARTA DE MEDIA MOVIL
Mt
LICz
LSCZ