Problemas.Histogramas, estratificación, Ishikawa, ydiagrama de Pareto.                     Lizbeth Luévanos Martínez.     ...
La empresa “Perfumes y esencias Fraiche” elabora perfumes con diferentesconcentrados 33% y 55% de fragancia. Han recibido ...
32.93   32.97   32.97   32.94   33.02   33.11   32.88   32.72   33.04   33.05   33.18   33.01   32.95   32.98   33.08   33...
En esta tabla el mayor valore es de: 33.36 y el mínimo es de: 32.7, como es evidentese observa que en estos dos valores es...
200  180                 LSL               TV                  USL                                           media.  160  ...
Ahora hay que identificar en que maquina se presente el problema;Maquina 1: 32.9     33      33     32.9     33     33.1  ...
Los datos se agruparan en 10 intervalos.            "Reales"                                       Frecuencias            ...
200                     LSL            TV              USL  180                                       media.  160  140  12...
Maquina 2: 33.05   33.08   33.16   33.15      33   33.03   33.02   32.89   33.02   33.08 33.05   33.01   33.02   33.05    ...
Agruparemos los datos en 10 intervalos:            "Reales"                                   Frecuencias        Medidas d...
200                  LSL             TV                USL  180                                         media .  160  140 ...
Maquina 3. 33.03   32.95   33.04   32.92   33.15   33.12   33.34   32.92   33.1    33.14 32.82   33.09   33.07   32.94   3...
Datos agrupados en 10 intervalos.            "Reales"                                      Frecuencias                  Me...
200                LSL                    TV            USL  180  160                                       media.  140  1...
50                           1.200  causas      Fi        Fa         Fr           Fr a       45M.O                45      ...
descanso; esto lo resintieron los operadores y el efecto se vio en la calidad delproducto que elaboran.
Upcoming SlideShare
Loading in …5
×

Problemas inventados.

846 views
721 views

Published on

0 Comments
0 Likes
Statistics
Notes
  • Be the first to comment

  • Be the first to like this

No Downloads
Views
Total views
846
On SlideShare
0
From Embeds
0
Number of Embeds
103
Actions
Shares
0
Downloads
2
Comments
0
Likes
0
Embeds 0
No embeds

No notes for slide

Problemas inventados.

  1. 1. Problemas.Histogramas, estratificación, Ishikawa, ydiagrama de Pareto. Lizbeth Luévanos Martínez. Universidad Tecnológica de Torreón. Gerardo Edgar Mata.
  2. 2. La empresa “Perfumes y esencias Fraiche” elabora perfumes con diferentesconcentrados 33% y 55% de fragancia. Han recibido una demanda espacial para unconcurso de belleza; el cliente pide que se elaboren perfumes con un concentrado de33% de fragancia con una tolerancia de ±.19, debido a la importancia de esteconcurso se están trabajando con 3 maquinas para darle mayor rapidez. La personaencargada del departamento de calidad ha decidido tomar una muestra de 300piezas tomadas de las tres maquinas para verificar que las cosas se estén haciendobien. ¿Tomando en cuenta los resultados de la investigación crees que las cosas seestán haciendo bien? Los datos son los siguientes:Primero veremos los 1500 datos tomados de las tres maquinas y posteriormente losdatos de cada una de las máquinas para poder identificar como se desempeña laempresa:
  3. 3. 32.93 32.97 32.97 32.94 33.02 33.11 32.88 32.72 33.04 33.05 33.18 33.01 32.95 32.98 33.08 33.02 33.09 33.11 33.11 33.1133.1 33.07 32.86 33.09 33.02 33.01 33.14 33.16 32.93 33.1 33.07 33.08 33.09 33.07 33.06 32.93 33.02 33 33.08 33.0232.91 32.86 33.03 33.06 33 32.92 33.27 32.86 33.08 32.99 32.97 33.04 33.13 33.04 33.01 33.05 33.08 33 32.99 3332.99 33.06 33.14 32.93 32.87 33.06 33.1 32.93 33.06 32.99 33.11 32.97 32.95 32.97 33.06 32.98 33.03 33.01 33.05 33.0232.97 33.11 33.13 33.14 33.03 33.05 32.99 33.08 33.12 33.02 33.1 33.04 33.09 33.05 33.11 33.03 33.15 33.01 33.12 33.0333.16 32.91 33.19 32.81 33.02 33.08 32.91 33.05 32.7 32.96 33.07 33.1 33.1 33.04 33.06 32.96 33.04 32.96 33.06 33.0132.86 33.04 32.76 33.06 33.08 32.9 32.99 33.09 33.05 33.1 33.05 33.13 32.99 33.07 33.04 33.07 33.11 33.02 33.08 33.0732.9 33.06 32.97 32.99 32.92 33.06 32.97 33.06 33.16 32.95 32.94 33.1 33.11 33.05 33.08 33.04 33.13 33.07 33.05 33.0532.98 33.11 33.12 33 33.07 33.17 32.96 32.85 32.81 33.25 32.97 32.98 33.13 33.14 33.19 33.08 33.12 33.12 33.07 33.0232.88 32.98 32.88 32.93 33.02 33.03 33.09 32.88 33 33.08 33.09 33.1 33.21 33.06 33.09 33 33.04 32.96 33.04 33.0732.84 33.03 32.93 32.94 33.01 32.96 32.97 33.08 33.15 33.07 33.03 33.24 33.13 33.1 33.02 33.08 32.96 33.18 33.03 33.0932.77 32.95 32.82 33.09 33.09 33.03 33.04 33.04 33.18 32.89 32.97 33.1 33.06 33.01 33.06 33.03 33.05 33.04 33.09 33.1233.06 33.06 32.8 33.09 33.2 33.2 33.09 32.9 33.03 33.09 33.02 33.05 33.02 33.04 33.03 32.99 33.06 32.99 32.99 33.1132.96 33.17 32.89 33.05 32.86 32.74 33.03 32.97 33.02 33.16 33.05 32.95 33.09 33.01 33.13 33 33.04 33 33 33.0133.04 32.98 32.92 33.08 32.87 33 32.82 33.01 33.2 32.92 33.11 32.96 33.15 33.06 32.99 33.02 33.06 33.01 33.11 33.1232.78 32.89 32.77 33.18 33.06 32.99 33 33.06 33 32.97 33.14 33.03 33.14 32.99 32.94 33.03 33.06 33.07 33.04 33.0533.13 32.9 32.94 33.03 33.13 33.11 33.07 33.02 32.93 32.85 33.06 33.1 33.02 33.03 33.16 33.01 33.12 33.06 33.03 33.1232.79 33.08 32.96 33.06 32.9 33.13 32.98 32.9 33.1 33.15 32.99 33.04 33 32.98 32.93 33.02 33.06 33.04 33.07 32.9232.94 33.17 33.01 33.2 32.77 33.18 32.82 33.2 33 33.11 33.11 33.05 33.05 33.13 32.84 32.96 33.12 33.03 33.02 33.0732.89 32.93 32.96 32.96 32.9 32.8 32.83 33.05 33.11 33.02 33.06 33.17 33.02 32.98 33.13 33.06 33.22 33.05 33.09 33.0332.99 32.91 32.96 33.11 33.02 33.09 32.91 33.01 33.05 32.76 32.99 32.93 32.98 33.1 33.05 33.07 33 33.1 33.01 3333.01 33.11 32.96 33.02 33.05 33.04 33.03 33.09 33.16 33.05 33.04 33.08 33.03 33.06 33.05 33.07 33.11 33.09 33.16 32.9833.19 33.02 33.15 33.12 32.89 33.08 32.93 33.09 32.99 33.06 33.16 33.11 33.15 33.12 32.96 33.03 33.1 32.97 33.17 33.0332.95 33.05 32.99 32.98 32.91 33.05 33.22 32.93 32.9 33.13 33.06 32.98 33.09 33.01 32.97 33.05 33 33.03 32.98 33.1432.91 33.28 32.98 32.92 33.05 32.99 32.98 32.9 32.83 32.9 33.01 33.07 33.13 33 33.02 33.1 33.1 33 33.06 33.0232.92 32.94 32.94 33.12 33.01 33.18 33.09 33.12 32.72 33.13 33.03 32.95 33.04 32.92 33.15 33.12 33.34 32.92 33.1 33.1433.06 32.91 33.21 32.94 32.94 33.05 33.13 32.87 33.01 32.94 32.82 33.09 33.07 32.94 33.05 33.14 33.32 33.05 33.16 33.0633.14 33.13 33.09 33.06 33.01 33 32.95 32.83 33.03 32.92 33.18 33.09 33.15 33.23 33.09 33.21 33.11 33.05 33.09 33.132.84 32.97 33.26 33.06 32.9 33 32.8 33.08 33 32.81 33.06 33.17 33.06 33.08 33.11 33.14 33.02 33.09 33.11 33.1633.11 32.85 32.93 32.97 32.9 32.99 32.9 33.07 33.02 33.15 33.09 33.11 33.13 32.99 33.05 33.08 32.99 33.1 33.17 33.1233.17 33.12 33.18 32.95 33.11 32.82 33.01 33.24 33.03 32.9 33.13 33.14 32.91 33.04 33.09 32.94 32.99 33.12 33.11 32.9232.93 32.86 32.83 32.85 33.18 33.05 33.03 33.16 33.16 33.17 33.15 33.06 33.16 33.11 33.22 33.03 33.06 33.03 32.94 33.3633.01 32.96 33.06 33.22 32.93 33.02 33.1 33.14 33.01 32.87 33.1 32.99 33.15 33.13 33.02 32.97 33.21 33.07 33.13 33.1132.91 32.84 33.1 32.94 32.98 33.07 32.77 33.01 32.88 32.96 33.02 33.09 33.06 33.16 33.03 33.32 33.16 33.23 32.99 33.1533.08 32.88 33.21 33.01 33.01 32.98 32.93 33 32.85 32.86 33.06 33.05 33.08 33.03 33.21 32.97 33.13 33.26 33.11 33.0933.03 33.07 32.99 32.97 33.2 33.09 33.02 33.05 33.02 33.17 33 33.05 33.12 33.14 33.03 33.21 33.18 33.13 33.26 32.9433.01 33.01 32.94 33.31 33.06 33.14 33.02 33 33.1 33 33.14 33.01 33.23 32.97 33.08 33.02 33.18 32.94 33.11 33.1632.89 32.81 33.07 33.14 33.18 33.21 32.99 32.89 32.84 33.04 33.18 33.13 33.01 33.13 32.87 33.18 33.09 33 33.17 33.2232.97 33.22 32.96 33.1 33.02 32.86 32.97 32.81 32.93 33.11 32.96 33.25 33.1 33.16 33.22 33.1 33.2 33.21 33.03 33.1633.08 33.03 33.08 33.14 33.17 33.07 33.16 33.09 33.06 33.21 33.15 33.15 33.15 33.17 33.12 32.92 33.06 33.12 33.19 33.35 33 33.15 32.84 33.02 32.93 32.98 33.09 33.05 32.98 32.99 33.14 32.97 33.04 33.15 33.16 33.07 33.09 33.09 33.16 33.3333.11 33 32.91 33.06 32.9 32.92 32.86 33.07 32.96 32.89 33.22 33.21 33.13 33.04 33.05 33.06 32.99 33.23 33.07 33.0332.89 32.97 32.83 32.97 33.13 33.08 32.95 33.02 32.98 32.94 33.22 33.14 32.9 32.96 33.04 33.13 33.16 32.95 33.21 32.9933.08 33 32.96 32.87 33.1 33.25 32.97 32.89 32.95 33.09 33.12 33.04 33.11 33.2 33.13 33.19 33 33.09 33.14 33.233.13 32.8 33 33.14 32.81 33.15 32.9 33.13 32.91 33.09 33.3 33.18 33.16 33.07 33.11 33.1 33.13 33.07 33.08 33.1332.87 32.93 33 32.97 33.14 33.02 32.98 32.97 33.07 33.06 33.08 33.15 33.27 33 33.12 33.11 33.17 33.11 33.02 33.1233.04 33.15 32.96 32.86 32.98 32.95 33.02 32.91 33.01 32.84 33.03 33.12 33.09 33.1 33.18 33.02 33.02 32.98 33.04 33.1232.81 33.02 33.24 33.08 32.88 32.97 32.9 32.91 33.14 32.85 32.9 33.08 33.09 33.03 33.1 33.09 33.13 33.12 33.2 3333.01 32.95 32.81 33.09 32.8 32.88 33.09 32.95 33.03 32.98 33.09 32.95 33.13 33 33.01 32.89 33.05 33.22 33.25 33.2233.11 32.93 32.92 33.05 32.91 33.01 32.98 32.95 33.01 32.93 33.09 33.04 33.12 33.04 33.25 33.09 33.17 33.27 33.06 33.0533.05 33.08 33.16 33.15 33 33.03 33.02 32.89 33.02 33.08 33.03 33.14 33 33.06 32.97 33.02 32.93 33.14 33.23 32.9833.05 33.01 33.02 33.05 33 33.06 32.98 33.07 33.15 33.08 33.06 33.17 32.96 33.17 33.15 33.12 33.01 33 33.29 33.2632.99 33.06 32.99 33.13 33.02 33.06 33.09 33.02 32.99 33.11 33.12 33.07 33.22 33.05 33.09 33.13 32.95 33.14 33.17 33.1533.13 33.09 33.13 33.02 33.02 33.13 33.04 33.11 33.06 33.1 33.19 33.24 33.19 33.17 33.1 33.14 33.17 32.93 33 32.9633.05 33.08 32.94 32.96 32.97 33.1 33.06 33.11 33.06 33.1 33.21 33.18 33.07 33.27 33.03 33.15 33 33.21 33.03 33.0833.11 32.99 33.08 32.92 32.97 32.99 33.02 33.08 33.07 33.18 33.15 33.22 33.01 33.12 33.01 33.04 33.13 33.11 33.18 33.0633.02 33.12 33.04 33.06 33.02 33.02 33.04 33.06 33.04 33.06 32.97 33.2 33.07 33.15 33.1 33.13 33.08 33.04 33.04 33.0933.11 33.07 33.01 33.08 33.05 33 33.08 33.08 33.15 33.09 33 33.16 33.1 33.18 33.13 33.24 33.32 33.13 33.19 33.1333.14 33.04 32.98 33.04 33.09 33.05 33.03 33.05 33.05 33.04 33.02 33.21 33.17 33.06 33.04 33.27 33.08 33.18 33.11 33.0333.16 33.15 33.02 33 33.11 33.1 32.96 32.99 33.13 33.09 33.24 32.89 33.08 33.14 33.06 33.1 33.14 33.24 32.88 33.1833.02 33.07 33.07 33.01 33.14 33.11 33.08 33.07 33.14 33.01 33.13 33 33.03 33.12 33.11 33.14 33.15 32.96 33.1 33.0733.1 33.18 33.07 33.01 33.02 32.94 33.01 33.05 32.98 33.11 32.97 32.94 33.11 33.08 33.06 33.12 33.12 33.11 33.14 33.0133.05 32.99 33.05 33.01 33.1 33.03 33.05 33.05 33 33.06 33.25 33.15 33.2 33.05 33.07 33.21 32.99 33 33.21 33.0333.06 33.07 33.11 33.1 33.07 33.03 32.98 33.05 33.15 33 32.93 33.09 32.89 33.11 33.16 32.99 33.18 33.1 33.01 33.1733.01 33.04 33.08 33.01 32.94 33.15 32.99 33.15 33.07 33.03 33.19 33.2 33.11 33.16 33.13 33.16 33.02 33.12 33.02 33.1433.02 33.04 33.03 33.08 33.11 32.94 33.02 33.02 33.15 33.01 32.98 33.11 33.12 33.05 33.29 33.2 33.09 33.17 33.13 33.0133.13 33.06 32.96 33.04 33.05 33.1 33.06 33.07 33.08 32.94 33.07 33.03 33.16 33.05 33.12 33.02 33.16 33.01 32.95 33.1233.02 33.09 33.08 33.11 32.97 33.09 33.21 33.05 33.09 33.02 33.17 32.94 33.2 33.07 33.06 33.09 33.33 33.16 33.22 33.0533.07 33.03 33.11 33.07 33.2 33.1 33.13 33.04 33.19 32.99 33.24 33.02 33.11 33.15 33.14 33.19 33.03 33.11 33.06 33.0733.02 33 33.03 33.18 32.98 33.08 33.06 33.07 33.01 33.11 33.05 32.93 33.22 33.23 33.18 32.92 33.15 33.06 33.29 33.1432.95 33.1 33.07 33.09 33.04 33.09 33.05 33.08 33 32.95 33.15 33.27 33.08 33.31 33.14 33.19 33.27 32.83 33.3 33.0733.08 33.18 33.13 33.12 33.08 33.02 33.04 33.01 33.07 33.06 33.16 33.02 33.07 32.96 33.01 33.07 33.12 33.14 33.07 33.0633.06 33.04 33.07 33.04 32.96 32.96 33.08 32.98 33.08 33.01 33.22 33.02 33.13 33.2 33.19 33.08 33.18 33.05 33.21 3333.05 33.01 33.04 33.05 32.95 33.07 32.98 33.16 33.04 33.05 32.98 33.06 33.2 33.15 33.03 33.08 33.04 33.16 33.11 32.9933.14 33.14 33.08 32.98 33.04 33.01 33.03 33.11 33.03 33 33.15 33.25 33.05 33.19 33.27 33.07 33.05 33.12 33.19 33.11
  4. 4. En esta tabla el mayor valore es de: 33.36 y el mínimo es de: 32.7, como es evidentese observa que en estos dos valores están por fuera de la tolerancia pedida por elcliente.A continuación se realizara la tabla de frecuencias agrupadas en 10 intervalos: "Reales" Frecuencias Medidas de Tendencia Central Limite Inferior Limite Superior Marca de Clase Fi Fa Fr Fra fi * xi xl-x*fi xl-x´2*fi 32.695 32.765 32.730 3 3 0.20% 0.20% 98.19 1.0599 0.374490935 32.765 32.835 32.8 14 17 0.93% 1.13% 459.2 3.9664 1.123730228 32.835 32.905 32.870 49 66 3.27% 4.40% 1610.63 10.4524 2.229626331 32.905 32.975 32.94 125 191 8.33% 12.73% 4117.5 17.9142 2.567338939 32.975 33.045 33.01 285 476 19.00% 31.73% 9407.85 20.8943 1.531830781 33.045 33.115 33.08 465 941 31.00% 62.73% 15382.2 1.5407 0.005104853 33.115 33.185 33.15 355 1296 23.67% 86.40% 11768.25 23.6738 1.578724586 33.185 33.255 33.220 155 1451 10.33% 96.73% 5149.1 21.1864 2.895902951 33.255 33.325 33.29 37 1488 2.47% 99.20% 1231.73 7.6474 1.580616993 33.325 33.395 33.36 12 1500 0.80% 100.00% 400.32 3.3202 0.918666138 49624.97 111.6557 14.80603273 media= 33.08331333 des. Media= 0.074437129 Varianza= 0.009870688 des. Estándar= 0.099351339Observaciones:1.-Los valores más grandes se encuentran un poco cargados hacia el centromientras que los mínimos en los extremos, esto nos indica que la distribución no esnormal.2.- La media aritmética del proceso varia un poco a el valor deseado esperado por elcliente, esto nos indica que posiblemente las cosas no anden tan bien.3.- como indicábamos al inicio los valores máximos y mínimos están por fuera de losvalores deseados, (máximo: 33.6, USL: 33.19 y el valor mínimo: 32.7, LSL: 32.81)Ahora revisaremos el histograma:
  5. 5. 200 180 LSL TV USL media. 160 140 120 100 80 60 40 20 0 32.7 32.8 32.9 33 33.1 33.2 33.3 33.4Observaciones:1.- De forma más clara notamos que algunos valores están fuera del límite deespecificación.2. Observamos que hay una pequeña variación entre el TV y la media.3.- La desviación estándar no es tan grande, pero si hay valores que sobresalen loslimites.4.- A pesar de que la mayoría de los valores se encuentran centrados hay varios quesobresalen pero, solo el USL, esto indica que los valores sobrepasan la toleranciamayor.
  6. 6. Ahora hay que identificar en que maquina se presente el problema;Maquina 1: 32.9 33 33 32.9 33 33.1 32.9 32.7 33 33.1 33.1 33.1 32.9 33.1 33 33 33.1 33.2 32.9 33.1 32.9 32.9 33 33.1 33 32.9 33.3 32.9 33.1 33 33 33.1 33.1 32.9 32.9 33.1 33.1 32.9 33.1 33 33 33.1 33.1 33.1 33 33.1 33 33.1 33.1 33 33.2 32.9 33.2 32.8 33 33.1 32.9 33.1 32.7 33 32.9 33 32.8 33.1 33.1 32.9 33 33.1 33.1 33.1 32.9 33.1 33 33 32.9 33.1 33 33.1 33.2 33 33 33.1 33.1 33 33.1 33.2 33 32.9 32.8 33.3 32.9 33 32.9 32.9 33 33 33.1 32.9 33 33.1 32.8 33 32.9 32.9 33 33 33 33.1 33.2 33.1 32.8 33 32.8 33.1 33.1 33 33 33 33.2 32.9 33.1 33.1 32.8 33.1 33.2 33.2 33.1 32.9 33 33.1 33 33.2 32.9 33.1 32.9 32.7 33 33 33 33.2 33 33 32.9 33.1 32.9 33 32.8 33 33.2 32.9 32.8 32.9 32.8 33.2 33.1 33 33 33.1 33 33 33.1 32.9 32.9 33 33.1 33.1 33.1 33 32.9 32.9 32.8 33.1 33 33.1 32.9 33.1 33 32.9 33.1 33.2 32.9 33.2 33 33.2 32.8 33.2 32.8 33.2 33 33.1 32.9 32.9 33 33 32.9 32.8 32.8 33.1 33.1 33 33 32.9 33 33.1 33 33.1 32.9 33 33.1 32.8 33 33.1 33 33 33.1 33 33 33.1 33.2 33.1 33.2 33 33.2 33.1 32.9 33.1 32.9 33.1 33 33.1 33 33.1 33 33 32.9 33.1 33.2 32.9 32.9 33.1 32.9 33.3 33 32.9 33.1 33 33 32.9 32.8 32.9 32.9 32.9 32.9 33.1 33 33.2 33.1 33.1 32.7 33.1 33.1 32.9 33.2 32.9 32.9 33.1 33.1 32.9 33 32.9 33.1 33.1 33.1 33.1 33 33 33 32.8 33 32.9 32.8 33 33.3 33.1 32.9 33 32.8 33.1 33 32.8 33.1 32.9 32.9 33 32.9 33 32.9 33.1 33 33.2 33.2 33.1 33.2 33 33.1 32.8 33 33.2 33 32.9 32.9 32.9 32.8 32.9 33.2 33.1 33 33.2 33.2 33.2 33 33 33.1 33.2 32.9 33 33.1 33.1 33 32.9 32.9 32.8 33.1 32.9 33 33.1 32.8 33 32.9 33 33.1 32.9 33.2 33 33 33 32.9 33 32.9 32.9 33 33.1 33 33 33.2 33.1 33 33.1 33 33.2 33 33 32.9 33.3 33.1 33.1 33 33 33.1 33 32.9 32.8 33.1 33.1 33.2 33.2 33 32.9 32.8 33 33 33.2 33 33.1 33 32.9 33 32.8 32.9 33.1 33.1 33 33.1 33.1 33.2 33.1 33.2 33.1 33.1 33.2 33 33.2 32.8 33 32.9 33 33.1 33.1 33 33 33.1 33 32.9 33.1 32.9 32.9 32.9 33.1 33 32.9 32.9 33 32.8 33 33.1 33.1 33 33 33 32.9 33.1 33 33 32.9 33.1 33.3 33 32.9 33 33.1 33.1 32.8 33 33.1 32.8 33.2 32.9 33.1 32.9 33.1 32.9 32.9 33 33 33.1 33 33 33 33.1 33.1 33 33.2 33 32.9 33 33 33 32.9 33 32.8 32.8 33 33.2 33.1 32.9 33 32.9 32.9 33.1 32.9 33 33 32.8 33.1 32.8 32.9 33.1 33 33 33 33.1 32.9 32.9 33.1 32.9 33 33 33 33 32.9
  7. 7. Los datos se agruparan en 10 intervalos. "Reales" Frecuencias Medidas de Tendencia CentralLimite Inferior Limite Superior Marca de Clase Fi Fa Fr Fra fi * xi xl-x*fi xl-x´2*fi 32.695 32.760 32.728 3 3 0.006 0.0060 98.1825 0.9313 0.289118981 32.760 32.825 32.7925 9 12 0.018 0.0240 295.1325 2.2090 0.542167142 32.825 32.890 32.858 34 46 0.068 0.0920 1117.155 6.1350 1.106992182 32.890 32.955 32.9225 74 120 0.148 0.2400 2436.265 8.5426 0.986153126 32.955 33.020 32.9875 92 212 0.184 0.4240 3034.85 4.6405 0.234065811 33.020 33.085 33.0525 116 328 0.232 0.6560 3834.09 1.6890 0.024591258 33.085 33.150 33.1175 92 420 0.184 0.8400 3046.81 7.3195 0.582341011 33.150 33.215 33.183 57 477 0.114 0.9540 1891.4025 8.2399 1.191162835 33.215 33.280 33.2475 17 494 0.034 0.9880 565.2075 3.5625 0.746561691 33.280 33.345 33.3125 6 500 0.012 1.0000 199.875 1.6474 0.452299162 33.345 33.41 33.3775 0 500 1.0000 Totales. Totales: 16518.97 44.9166 6.1554532 media= 33.03794 des. Media= 0.08983312 Varianza= 0.012310906 des. Estándar= 0.110954524 Observaciones:1.- Los valores mayores están centrados mientras que los menores se encuantrane nlos extremos.2.- La desviación estándar es de S=0.110954524 por el momento no la podemoscomparar pero cuando obtengamos el valor de las otras dos maquinas locompararemos.3.- El LSL=32.81 mientras que el mínimo de estos datos es de 33.31 y el USL= 33.19mientras el máximo es de 33.31 los cual indica que estos valores no son los queesperábamos y refirma la hipótesis de que algo anda mal.
  8. 8. 200 LSL TV USL 180 media. 160 140 120 100 80 60 40 20 0 32.60 32.70 32.80 32.90 33.00 33.10 33.20 33.30 33.40 33.50Observaciones:1.- Entre la media y el TV hay una pequeña variación, la mayoría de los valores estánun poco alejados del TV.2.-Nuevamente se nota que un gran número de valores sobrepasa más el USL,también el LSL pero hay más valores fuera del USL. Lo que nos indica que elconcentrado del perfume sale con más fragancia que la que se pide.
  9. 9. Maquina 2: 33.05 33.08 33.16 33.15 33 33.03 33.02 32.89 33.02 33.08 33.05 33.01 33.02 33.05 33 33.06 32.98 33.07 33.15 33.08 32.99 33.06 32.99 33.13 33.02 33.06 33.09 33.02 32.99 33.11 33.13 33.09 33.13 33.02 33.02 33.13 33.04 33.11 33.06 33.1 33.05 33.08 32.94 32.96 32.97 33.1 33.06 33.11 33.06 33.1 33.11 32.99 33.08 32.92 32.97 32.99 33.02 33.08 33.07 33.18 33.02 33.12 33.04 33.06 33.02 33.02 33.04 33.06 33.04 33.06 33.11 33.07 33.01 33.08 33.05 33 33.08 33.08 33.15 33.09 33.14 33.04 32.98 33.04 33.09 33.05 33.03 33.05 33.05 33.04 33.16 33.15 33.02 33 33.11 33.1 32.96 32.99 33.13 33.09 33.02 33.07 33.07 33.01 33.14 33.11 33.08 33.07 33.14 33.01 33.1 33.18 33.07 33.01 33.02 32.94 33.01 33.05 32.98 33.11 33.05 32.99 33.05 33.01 33.1 33.03 33.05 33.05 33 33.06 33.06 33.07 33.11 33.1 33.07 33.03 32.98 33.05 33.15 33 33.01 33.04 33.08 33.01 32.94 33.15 32.99 33.15 33.07 33.03 33.02 33.04 33.03 33.08 33.11 32.94 33.02 33.02 33.15 33.01 33.13 33.06 32.96 33.04 33.05 33.1 33.06 33.07 33.08 32.94 33.02 33.09 33.08 33.11 32.97 33.09 33.21 33.05 33.09 33.02 33.07 33.03 33.11 33.07 33.2 33.1 33.13 33.04 33.19 32.99 33.02 33 33.03 33.18 32.98 33.08 33.06 33.07 33.01 33.11 32.95 33.1 33.07 33.09 33.04 33.09 33.05 33.08 33 32.95 33.08 33.18 33.13 33.12 33.08 33.02 33.04 33.01 33.07 33.06 33.06 33.04 33.07 33.04 32.96 32.96 33.08 32.98 33.08 33.01 33.05 33.01 33.04 33.05 32.95 33.07 32.98 33.16 33.04 33.05 33.14 33.14 33.08 32.98 33.04 33.01 33.03 33.11 33.03 33 33.18 33.01 32.95 32.98 33.08 33.02 33.09 33.11 33.11 33.11 33.07 33.08 33.09 33.07 33.06 32.93 33.02 33 33.08 33.02 32.97 33.04 33.13 33.04 33.01 33.05 33.08 33 32.99 33 33.11 32.97 32.95 32.97 33.06 32.98 33.03 33.01 33.05 33.02 33.1 33.04 33.09 33.05 33.11 33.03 33.15 33.01 33.12 33.03 33.07 33.1 33.1 33.04 33.06 32.96 33.04 32.96 33.06 33.01 33.05 33.13 32.99 33.07 33.04 33.07 33.11 33.02 33.08 33.07 32.94 33.1 33.11 33.05 33.08 33.04 33.13 33.07 33.05 33.05 32.97 32.98 33.13 33.14 33.19 33.08 33.12 33.12 33.07 33.02 33.09 33.1 33.21 33.06 33.09 33 33.04 32.96 33.04 33.07 33.03 33.24 33.13 33.1 33.02 33.08 32.96 33.18 33.03 33.09 32.97 33.1 33.06 33.01 33.06 33.03 33.05 33.04 33.09 33.12 33.02 33.05 33.02 33.04 33.03 32.99 33.06 32.99 32.99 33.11 33.05 32.95 33.09 33.01 33.13 33 33.04 33 33 33.01 33.11 32.96 33.15 33.06 32.99 33.02 33.06 33.01 33.11 33.12 33.14 33.03 33.14 32.99 32.94 33.03 33.06 33.07 33.04 33.05 33.06 33.1 33.02 33.03 33.16 33.01 33.12 33.06 33.03 33.12 32.99 33.04 33 32.98 32.93 33.02 33.06 33.04 33.07 32.92 33.11 33.05 33.05 33.13 32.84 32.96 33.12 33.03 33.02 33.07 33.06 33.17 33.02 32.98 33.13 33.06 33.22 33.05 33.09 33.03 32.99 32.93 32.98 33.1 33.05 33.07 33 33.1 33.01 33 33.04 33.08 33.03 33.06 33.05 33.07 33.11 33.09 33.16 32.98 33.16 33.11 33.15 33.12 32.96 33.03 33.1 32.97 33.17 33.03 33.06 32.98 33.09 33.01 32.97 33.05 33 33.03 32.98 33.14 33.01 33.07 33.13 33 33.02 33.1 33.1 33 33.06 33.02
  10. 10. Agruparemos los datos en 10 intervalos: "Reales" Frecuencias Medidas de Tendencia CentralLimite Inferior Limite Superior Marca de Clase Fi Fa Fr Fra fi * xi xl-x*fi xl-x´2*fi 32.835 32.885 32.860 1 1 0.002 0.0020 32.86 0.2237 0.05004169 32.885 32.935 32.91 1 2 0.002 0.0040 32.91 0.1737 0.03017169 32.935 32.985 32.960 18 20 0.036 0.0400 593.28 2.2266 0.27543042 32.985 33.035 33.01 79 99 0.158 0.1980 2607.79 5.8223 0.42910351 33.035 33.085 33.06 163 262 0.326 0.5240 5388.78 3.8631 0.09155547 33.085 33.135 33.11 142 404 0.284 0.8080 4701.62 3.7346 0.09821998 33.135 33.185 33.16 75 479 0.15 0.9580 2487 5.7225 0.43662675 33.185 33.235 33.210 17 496 0.034 0.9920 564.57 2.1471 0.27117873 33.235 33.285 33.26 4 500 0.008 1.0000 133.04 0.7052 0.12432676 33.285 33.335 33.31 0 500 0 1.0000 0 0.0000 0 16541.85 24.6188 1.806655 media= 33.0837 des. Media= 0.0492376 Varianza= 0.00361331 des. Estándar= 0.060110814Observaciones.1.-La mayoría de los valores están centrados y solo los valores mas mínimos están alos extremos esto indica que la distribución no es normal.2.- La desviación estándar de esta máquina es de S=0.060110814 mientras que lade la otra máquina fue de S= 0.110954524 hasta el momento la maquina 2 tiene máscontrolado su proceso.3.- El valor mínimo es de 32.84 y el LSL= 33.19; mientras el máximo es de 33.24 y elUSL = 33.19 lo cual es evidente concluir que los valores siguen estando fuera de lastolerancias pedidas por el cliente.
  11. 11. 200 LSL TV USL 180 media . 160 140 120 100 80 60 40 20 0 32.7 32.8 32.9 33 33.1 33.2 33.3 33.4Observaciones.1.- Es muy claro que la desviación estándar en más pequeña, y si la media hubieraestado centrad, hubieran quedado las tres desviaciones estándar dentro de loslímites.2.- Nuevamente se nota que los valores del USL sobrepasan a esta misma, mientrasen el LSL los datos no lo sobrepasan. Se siguen observando muchos errores.
  12. 12. Maquina 3. 33.03 32.95 33.04 32.92 33.15 33.12 33.34 32.92 33.1 33.14 32.82 33.09 33.07 32.94 33.05 33.14 33.32 33.05 33.16 33.06 33.18 33.09 33.15 33.23 33.09 33.21 33.11 33.05 33.09 33.1 33.06 33.17 33.06 33.08 33.11 33.14 33.02 33.09 33.11 33.16 33.09 33.11 33.13 32.99 33.05 33.08 32.99 33.1 33.17 33.12 33.13 33.14 32.91 33.04 33.09 32.94 32.99 33.12 33.11 32.92 33.15 33.06 33.16 33.11 33.22 33.03 33.06 33.03 32.94 33.36 33.1 32.99 33.15 33.13 33.02 32.97 33.21 33.07 33.13 33.11 33.02 33.09 33.06 33.16 33.03 33.32 33.16 33.23 32.99 33.15 33.06 33.05 33.08 33.03 33.21 32.97 33.13 33.26 33.11 33.09 33 33.05 33.12 33.14 33.03 33.21 33.18 33.13 33.26 32.94 33.14 33.01 33.23 32.97 33.08 33.02 33.18 32.94 33.11 33.16 33.18 33.13 33.01 33.13 32.87 33.18 33.09 33 33.17 33.22 32.96 33.25 33.1 33.16 33.22 33.1 33.2 33.21 33.03 33.16 33.15 33.15 33.15 33.17 33.12 32.92 33.06 33.12 33.19 33.35 33.14 32.97 33.04 33.15 33.16 33.07 33.09 33.09 33.16 33.33 33.22 33.21 33.13 33.04 33.05 33.06 32.99 33.23 33.07 33.03 33.22 33.14 32.9 32.96 33.04 33.13 33.16 32.95 33.21 32.99 33.12 33.04 33.11 33.2 33.13 33.19 33 33.09 33.14 33.2 33.3 33.18 33.16 33.07 33.11 33.1 33.13 33.07 33.08 33.13 33.08 33.15 33.27 33 33.12 33.11 33.17 33.11 33.02 33.12 33.03 33.12 33.09 33.1 33.18 33.02 33.02 32.98 33.04 33.12 32.9 33.08 33.09 33.03 33.1 33.09 33.13 33.12 33.2 33 33.09 32.95 33.13 33 33.01 32.89 33.05 33.22 33.25 33.22 33.09 33.04 33.12 33.04 33.25 33.09 33.17 33.27 33.06 33.05 33.03 33.14 33 33.06 32.97 33.02 32.93 33.14 33.23 32.98 33.06 33.17 32.96 33.17 33.15 33.12 33.01 33 33.29 33.26 33.12 33.07 33.22 33.05 33.09 33.13 32.95 33.14 33.17 33.15 33.19 33.24 33.19 33.17 33.1 33.14 33.17 32.93 33 32.96 33.21 33.18 33.07 33.27 33.03 33.15 33 33.21 33.03 33.08 33.15 33.22 33.01 33.12 33.01 33.04 33.13 33.11 33.18 33.06 32.97 33.2 33.07 33.15 33.1 33.13 33.08 33.04 33.04 33.09 33 33.16 33.1 33.18 33.13 33.24 33.32 33.13 33.19 33.13 33.02 33.21 33.17 33.06 33.04 33.27 33.08 33.18 33.11 33.03 33.24 32.89 33.08 33.14 33.06 33.1 33.14 33.24 32.88 33.18 33.13 33 33.03 33.12 33.11 33.14 33.15 32.96 33.1 33.07 32.97 32.94 33.11 33.08 33.06 33.12 33.12 33.11 33.14 33.01 33.25 33.15 33.2 33.05 33.07 33.21 32.99 33 33.21 33.03 32.93 33.09 32.89 33.11 33.16 32.99 33.18 33.1 33.01 33.17 33.19 33.2 33.11 33.16 33.13 33.16 33.02 33.12 33.02 33.14 32.98 33.11 33.12 33.05 33.29 33.2 33.09 33.17 33.13 33.01 33.07 33.03 33.16 33.05 33.12 33.02 33.16 33.01 32.95 33.12 33.17 32.94 33.2 33.07 33.06 33.09 33.33 33.16 33.22 33.05 33.24 33.02 33.11 33.15 33.14 33.19 33.03 33.11 33.06 33.07 33.05 32.93 33.22 33.23 33.18 32.92 33.15 33.06 33.29 33.14 33.15 33.27 33.08 33.31 33.14 33.19 33.27 32.83 33.3 33.07 33.16 33.02 33.07 32.96 33.01 33.07 33.12 33.14 33.07 33.06 33.22 33.02 33.13 33.2 33.19 33.08 33.18 33.05 33.21 33 32.98 33.06 33.2 33.15 33.03 33.08 33.04 33.16 33.11 32.99 33.15 33.25 33.05 33.19 33.27 33.07 33.05 33.12 33.19 33.11
  13. 13. Datos agrupados en 10 intervalos. "Reales" Frecuencias Medidas de Tendencia CentralLimite Inferior Limite Superior Marca de Clase Fi Fa Fr Fra fi * xi xl-x*fi xl-x´2*fi 32.815 32.873 32.844 2 2 0.004 0.0040 65.688 0.5733 0.164320393 32.873 32.931 32.902 7 9 0.014 0.0180 230.314 1.6005 0.365920943 32.931 32.989 32.960 28 37 0.056 0.0740 922.88 4.7778 0.815266046 32.989 33.047 33.018 46 83 0.092 0.1660 1518.828 5.1813 0.583595951 33.047 33.105 33.076 106 189 0.212 0.3780 3506.056 5.7914 0.316419805 33.105 33.163 33.134 129 318 0.258 0.6360 4274.286 0.4340 0.001459828 33.163 33.221 33.192 106 424 0.212 0.8480 3518.352 6.5046 0.399147293 33.221 33.279 33.250 52 476 0.104 0.9520 1729 6.2069 0.740883754 33.279 33.337 33.308 15 491 0.03 0.9820 499.62 2.6605 0.471869827 33.337 33.395 33.366 9 500 0.018 1.0000 300.294 2.1183 0.498565912 16565.318 35.8484 4.357449752 media= 33.130636 des. Media= 0.071696816 Varianza= 0.0087149 des. Estándar= 0.093353626Observaciones:1.- Recopilando las desviaciones estándar de las maquinas concluimos que; lamaquina uno tiene una S=0.110954524, maquina 2 S=0.060110814 mientras que lamaquina 3 la desviación estándar es igual a S=0.093353626 lo que nos indica que lamaquina 2 tiene más controlado su proceso.2.-Nuevamente los valores sobrepasan los límites; máximo: 33.36, USL= 33,19mientras el mínimo es de 32,82 y el LSL= 32.81. Como lo mencionamosanteriormente laos valores no sobrepasan el LSL solo el USL, esto no dice que losperfumes están siendo llenados con más concentrado que el que se pide.
  14. 14. 200 LSL TV USL 180 160 media. 140 120 100 80 60 40 20 0 32.7 32.8 32.9 33 33.1 33.2 33.3 33.4 Observaciones:1.- La media y el TV están muy separados, la distribución no es normal.2.- A pesar de que los errores en los extremos no son tantos siguen sobresaliendo delos límites de ULS,3.- Como mencionamos en el inicio los valores de USL fueron sobrepasados por losdatos, esto indica que las cosas no se están haciendo bien y que hay factores queestán afectando estos resultados recordemos que este evento es muy importante yque se está dejando entre dicho la importancia de la empresa.Con estos resultados la persona de calidad puede alentar a los de producción sobreeste problema y atacarlo a tiempo. Así que se procedió a buscar el problema:
  15. 15. 50 1.200 causas Fi Fa Fr Fr a 45M.O 45 39 0.390 0.390 1.000 40M. ambiente 20 62 0.230 0.620 35Maquinaria 15 80 0.180 0.800 0.800 30M. prima 10 90 0.100 0.900 25 0.600Mètodo 6 98 0.080 0.980 20Medidas 4 100 0.020 1.000 0.400 15 10 0.200 5 0 0.000 0 0 0 0 0 0 Según la investigación realizada los operadores debido a que se trabaja a marchasforzadas no estaban dando el 100 en sus actividades, además de que no se les daba
  16. 16. descanso; esto lo resintieron los operadores y el efecto se vio en la calidad delproducto que elaboran.

×