Problemas inventados.

Problemas.Histogramas, estratificación, Ishikawa, y diagrama de Pareto.

Lizbeth Luévanos Martínez.Universidad Tecnológica de Torreón.

Gerardo Edgar Mata.

La empresa “Perfumes y esencias Fraiche” elabora perfumes con diferentes concentrados 33% y 55% de fragancia. Han recibido una demanda espacial para un concurso de belleza; el cliente pide que se elaboren perfumes con un concentrado de 33% de fragancia con una tolerancia de ±.19, debido a la importancia de este concurso se están trabajando con 3 maquinas para darle mayor rapidez. La persona encargada del departamento de calidad ha decidido tomar una muestra de 300 piezas tomadas de las tres maquinas para verificar que las cosas se estén haciendo bien. ¿Tomando en cuenta los resultados de la investigación crees que las cosas se están haciendo bien? Los datos son los siguientes:

Primero veremos los 1500 datos tomados de las tres maquinas y posteriormente los datos de cada una de las máquinas para poder identificar como se desempeña la empresa:

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

En esta tabla el mayor valore es de: 33.36 y el mínimo es de: 32.7, como es evidente se observa que en estos dos valores están por fuera de la tolerancia pedida por el cliente.

A continuación se realizara la tabla de frecuencias agrupadas en 10 intervalos:

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 0.37449093532.765 32.835 32.8 14 17 0.93% 1.13% 459.2 3.9664 1.12373022832.835 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 2.56733893932.975 33.045 33.01 285 476 19.00% 31.73% 9407.85 20.8943 1.53183078133.045 33.115 33.08 465 941 31.00% 62.73% 15382.2 1.5407 0.00510485333.115 33.185 33.15 355 1296 23.67% 86.40% 11768.25 23.6738 1.57872458633.185 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 1.58061699333.325 33.395 33.36 12 1500 0.80% 100.00% 400.32 3.3202 0.918666138

49624.97 111.6557 14.80603273media= 33.08331333

des. Media= 0.074437129Varianza= 0.009870688

des. Estándar= 0.099351339

"Reales" 'Frecuencias'' Medidas de Tendencia Central

Observaciones:

1.-Los valores más grandes se encuentran un poco cargados hacia el centro mientras que los mínimos en los extremos, esto nos indica que la distribución no es normal.

2.- La media aritmética del proceso varia un poco a el valor deseado esperado por el cliente, 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 los valores deseados, (máximo: 33.6, USL: 33.19 y el valor mínimo: 32.7, LSL: 32.81)

Ahora revisaremos el histograma:

TV USLLSL

media.

0

20

40

60

80

100

120

140

160

180

200

32.7 32.8 32.9 33 33.1 33.2 33.3 33.4

Observaciones:

1.- De forma más clara notamos que algunos valores están fuera del límite de especificación.

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 los limites.

4.- A pesar de que la mayoría de los valores se encuentran centrados hay varios que sobresalen pero, solo el USL, esto indica que los valores sobrepasan la tolerancia mayor.

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 33.133.1 33.1 32.9 33.1 33 33 33.1 33.2 32.9 33.132.9 32.9 33 33.1 33 32.9 33.3 32.9 33.1 3333 33.1 33.1 32.9 32.9 33.1 33.1 32.9 33.1 3333 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 3332.9 33 32.8 33.1 33.1 32.9 33 33.1 33.1 33.132.9 33.1 33 33 32.9 33.1 33 33.1 33.2 3333 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 33.132.8 33 32.9 32.9 33 33 33 33.1 33.2 33.132.8 33 32.8 33.1 33.1 33 33 33 33.2 32.933.1 33.1 32.8 33.1 33.2 33.2 33.1 32.9 33 33.133 33.2 32.9 33.1 32.9 32.7 33 33 33 33.233 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 3333.1 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 33.232.9 33.2 33 33.2 32.8 33.2 32.8 33.2 33 33.132.9 32.9 33 33 32.9 32.8 32.8 33.1 33.1 3333 32.9 33 33.1 33 33.1 32.9 33 33.1 32.833 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 33.133 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 32.932.9 32.9 32.9 33.1 33 33.2 33.1 33.1 32.7 33.133.1 32.9 33.2 32.9 32.9 33.1 33.1 32.9 33 32.933.1 33.1 33.1 33.1 33 33 33 32.8 33 32.932.8 33 33.3 33.1 32.9 33 32.8 33.1 33 32.833.1 32.9 32.9 33 32.9 33 32.9 33.1 33 33.233.2 33.1 33.2 33 33.1 32.8 33 33.2 33 32.932.9 32.9 32.8 32.9 33.2 33.1 33 33.2 33.2 33.233 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 3333.1 32.9 33.2 33 33 33 32.9 33 32.9 32.933 33.1 33 33 33.2 33.1 33 33.1 33 33.233 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 3333 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 33.233 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 32.932.9 33 32.8 33 33.1 33.1 33 33 33 32.933.1 33 33 32.9 33.1 33.3 33 32.9 33 33.133.1 32.8 33 33.1 32.8 33.2 32.9 33.1 32.9 33.132.9 32.9 33 33 33.1 33 33 33 33.1 33.133 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 32.933 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

Los datos se agruparan en 10 intervalos.


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: 16518.97 44.9166 6.1554532

media= 33.03794

des. Media= 0.08983312

Varianza= 0.012310906des. Estándar= 0.110954524

Totales.


Observaciones:

1.- Los valores mayores están centrados mientras que los menores se encuantrane n los extremos.

2.- La desviación estándar es de S=0.110954524 por el momento no la podemos comparar pero cuando obtengamos el valor de las otras dos maquinas lo compararemos.

3.- El LSL=32.81 mientras que el mínimo de estos datos es de 33.31 y el USL= 33.19 mientras el máximo es de 33.31 los cual indica que estos valores no son los que esperábamos y refirma la hipótesis de que algo anda mal.

TV USLLSL

media.

0

20

40

60

80

100

120

140

160

180

200

32.60 32.70 32.80 32.90 33.00 33.10 33.20 33.30 33.40 33.50

Observaciones:

1.- Entre la media y el TV hay una pequeña variación, la mayoría de los valores están un 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 el concentrado del perfume sale con más fragancia que la que se pide.

Maquina 2:

33.05 33.08 33.16 33.15 33 33.03 33.02 32.89 33.02 33.0833.05 33.01 33.02 33.05 33 33.06 32.98 33.07 33.15 33.0832.99 33.06 32.99 33.13 33.02 33.06 33.09 33.02 32.99 33.1133.13 33.09 33.13 33.02 33.02 33.13 33.04 33.11 33.06 33.133.05 33.08 32.94 32.96 32.97 33.1 33.06 33.11 33.06 33.133.11 32.99 33.08 32.92 32.97 32.99 33.02 33.08 33.07 33.1833.02 33.12 33.04 33.06 33.02 33.02 33.04 33.06 33.04 33.0633.11 33.07 33.01 33.08 33.05 33 33.08 33.08 33.15 33.0933.14 33.04 32.98 33.04 33.09 33.05 33.03 33.05 33.05 33.0433.16 33.15 33.02 33 33.11 33.1 32.96 32.99 33.13 33.0933.02 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 33.1133.05 32.99 33.05 33.01 33.1 33.03 33.05 33.05 33 33.0633.06 33.07 33.11 33.1 33.07 33.03 32.98 33.05 33.15 3333.01 33.04 33.08 33.01 32.94 33.15 32.99 33.15 33.07 33.0333.02 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 32.9433.02 33.09 33.08 33.11 32.97 33.09 33.21 33.05 33.09 33.0233.07 33.03 33.11 33.07 33.2 33.1 33.13 33.04 33.19 32.9933.02 33 33.03 33.18 32.98 33.08 33.06 33.07 33.01 33.1132.95 33.1 33.07 33.09 33.04 33.09 33.05 33.08 33 32.9533.08 33.18 33.13 33.12 33.08 33.02 33.04 33.01 33.07 33.0633.06 33.04 33.07 33.04 32.96 32.96 33.08 32.98 33.08 33.0133.05 33.01 33.04 33.05 32.95 33.07 32.98 33.16 33.04 33.0533.14 33.14 33.08 32.98 33.04 33.01 33.03 33.11 33.03 3333.18 33.01 32.95 32.98 33.08 33.02 33.09 33.11 33.11 33.1133.07 33.08 33.09 33.07 33.06 32.93 33.02 33 33.08 33.0232.97 33.04 33.13 33.04 33.01 33.05 33.08 33 32.99 3333.11 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 33.0333.07 33.1 33.1 33.04 33.06 32.96 33.04 32.96 33.06 33.0133.05 33.13 32.99 33.07 33.04 33.07 33.11 33.02 33.08 33.0732.94 33.1 33.11 33.05 33.08 33.04 33.13 33.07 33.05 33.0532.97 32.98 33.13 33.14 33.19 33.08 33.12 33.12 33.07 33.0233.09 33.1 33.21 33.06 33.09 33 33.04 32.96 33.04 33.0733.03 33.24 33.13 33.1 33.02 33.08 32.96 33.18 33.03 33.0932.97 33.1 33.06 33.01 33.06 33.03 33.05 33.04 33.09 33.1233.02 33.05 33.02 33.04 33.03 32.99 33.06 32.99 32.99 33.1133.05 32.95 33.09 33.01 33.13 33 33.04 33 33 33.0133.11 32.96 33.15 33.06 32.99 33.02 33.06 33.01 33.11 33.1233.14 33.03 33.14 32.99 32.94 33.03 33.06 33.07 33.04 33.0533.06 33.1 33.02 33.03 33.16 33.01 33.12 33.06 33.03 33.1232.99 33.04 33 32.98 32.93 33.02 33.06 33.04 33.07 32.9233.11 33.05 33.05 33.13 32.84 32.96 33.12 33.03 33.02 33.0733.06 33.17 33.02 32.98 33.13 33.06 33.22 33.05 33.09 33.0332.99 32.93 32.98 33.1 33.05 33.07 33 33.1 33.01 3333.04 33.08 33.03 33.06 33.05 33.07 33.11 33.09 33.16 32.9833.16 33.11 33.15 33.12 32.96 33.03 33.1 32.97 33.17 33.0333.06 32.98 33.09 33.01 32.97 33.05 33 33.03 32.98 33.1433.01 33.07 33.13 33 33.02 33.1 33.1 33 33.06 33.02

Agruparemos los datos en 10 intervalos:


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




Observaciones.

1.-La mayoría de los valores están centrados y solo los valores mas mínimos están a los extremos esto indica que la distribución no es normal.

2.- La desviación estándar de esta máquina es de S=0.060110814 mientras que la de la otra máquina fue de S= 0.110954524 hasta el momento la maquina 2 tiene más controlado su proceso.

3.- El valor mínimo es de 32.84 y el LSL= 33.19; mientras el máximo es de 33.24 y el USL = 33.19 lo cual es evidente concluir que los valores siguen estando fuera de las tolerancias pedidas por el cliente.

TV USLLSL

media.

0

20

40

60

80

100

120

140

160

180

200

32.7 32.8 32.9 33 33.1 33.2 33.3 33.4

Observaciones.

1.- Es muy claro que la desviación estándar en más pequeña, y si la media hubiera estado centrad, hubieran quedado las tres desviaciones estándar dentro de los límites.

2.- Nuevamente se nota que los valores del USL sobrepasan a esta misma, mientras en el LSL los datos no lo sobrepasan. Se siguen observando muchos errores.

Maquina 3.

33.03 32.95 33.04 32.92 33.15 33.12 33.34 32.92 33.1 33.1432.82 33.09 33.07 32.94 33.05 33.14 33.32 33.05 33.16 33.0633.18 33.09 33.15 33.23 33.09 33.21 33.11 33.05 33.09 33.133.06 33.17 33.06 33.08 33.11 33.14 33.02 33.09 33.11 33.1633.09 33.11 33.13 32.99 33.05 33.08 32.99 33.1 33.17 33.1233.13 33.14 32.91 33.04 33.09 32.94 32.99 33.12 33.11 32.9233.15 33.06 33.16 33.11 33.22 33.03 33.06 33.03 32.94 33.3633.1 32.99 33.15 33.13 33.02 32.97 33.21 33.07 33.13 33.1133.02 33.09 33.06 33.16 33.03 33.32 33.16 33.23 32.99 33.1533.06 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 32.9433.14 33.01 33.23 32.97 33.08 33.02 33.18 32.94 33.11 33.1633.18 33.13 33.01 33.13 32.87 33.18 33.09 33 33.17 33.2232.96 33.25 33.1 33.16 33.22 33.1 33.2 33.21 33.03 33.1633.15 33.15 33.15 33.17 33.12 32.92 33.06 33.12 33.19 33.3533.14 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 33.0333.22 33.14 32.9 32.96 33.04 33.13 33.16 32.95 33.21 32.9933.12 33.04 33.11 33.2 33.13 33.19 33 33.09 33.14 33.233.3 33.18 33.16 33.07 33.11 33.1 33.13 33.07 33.08 33.1333.08 33.15 33.27 33 33.12 33.11 33.17 33.11 33.02 33.1233.03 33.12 33.09 33.1 33.18 33.02 33.02 32.98 33.04 33.1232.9 33.08 33.09 33.03 33.1 33.09 33.13 33.12 33.2 3333.09 32.95 33.13 33 33.01 32.89 33.05 33.22 33.25 33.2233.09 33.04 33.12 33.04 33.25 33.09 33.17 33.27 33.06 33.0533.03 33.14 33 33.06 32.97 33.02 32.93 33.14 33.23 32.9833.06 33.17 32.96 33.17 33.15 33.12 33.01 33 33.29 33.2633.12 33.07 33.22 33.05 33.09 33.13 32.95 33.14 33.17 33.1533.19 33.24 33.19 33.17 33.1 33.14 33.17 32.93 33 32.9633.21 33.18 33.07 33.27 33.03 33.15 33 33.21 33.03 33.0833.15 33.22 33.01 33.12 33.01 33.04 33.13 33.11 33.18 33.0632.97 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 33.1333.02 33.21 33.17 33.06 33.04 33.27 33.08 33.18 33.11 33.0333.24 32.89 33.08 33.14 33.06 33.1 33.14 33.24 32.88 33.1833.13 33 33.03 33.12 33.11 33.14 33.15 32.96 33.1 33.0732.97 32.94 33.11 33.08 33.06 33.12 33.12 33.11 33.14 33.0133.25 33.15 33.2 33.05 33.07 33.21 32.99 33 33.21 33.0332.93 33.09 32.89 33.11 33.16 32.99 33.18 33.1 33.01 33.1733.19 33.2 33.11 33.16 33.13 33.16 33.02 33.12 33.02 33.1432.98 33.11 33.12 33.05 33.29 33.2 33.09 33.17 33.13 33.0133.07 33.03 33.16 33.05 33.12 33.02 33.16 33.01 32.95 33.1233.17 32.94 33.2 33.07 33.06 33.09 33.33 33.16 33.22 33.0533.24 33.02 33.11 33.15 33.14 33.19 33.03 33.11 33.06 33.0733.05 32.93 33.22 33.23 33.18 32.92 33.15 33.06 33.29 33.1433.15 33.27 33.08 33.31 33.14 33.19 33.27 32.83 33.3 33.0733.16 33.02 33.07 32.96 33.01 33.07 33.12 33.14 33.07 33.0633.22 33.02 33.13 33.2 33.19 33.08 33.18 33.05 33.21 3332.98 33.06 33.2 33.15 33.03 33.08 33.04 33.16 33.11 32.9933.15 33.25 33.05 33.19 33.27 33.07 33.05 33.12 33.19 33.11

Datos agrupados en 10 intervalos.


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




Observaciones:

1.- Recopilando las desviaciones estándar de las maquinas concluimos que; la maquina uno tiene una S=0.110954524, maquina 2 S=0.060110814 mientras que la maquina 3 la desviación estándar es igual a S=0.093353626 lo que nos indica que la maquina 2 tiene más controlado su proceso.

2.-Nuevamente los valores sobrepasan los límites; máximo: 33.36, USL= 33,19 mientras el mínimo es de 32,82 y el LSL= 32.81. Como lo mencionamos anteriormente laos valores no sobrepasan el LSL solo el USL, esto no dice que los perfumes están siendo llenados con más concentrado que el que se pide.

TV USLLSL

media.

0

20

40

60

80

100

120

140

160

180

200

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 de los límites de ULS,

3.- Como mencionamos en el inicio los valores de USL fueron sobrepasados por los datos, esto indica que las cosas no se están haciendo bien y que hay factores que están afectando estos resultados recordemos que este evento es muy importante y que se está dejando entre dicho la importancia de la empresa.

Con estos resultados la persona de calidad puede alentar a los de producción sobre este problema y atacarlo a tiempo. Así que se procedió a buscar el problema:

causas Fi Fa Fr Fr aM.O 45 39 0.390 0.390M. ambiente 20 62 0.230 0.620Maquinaria 15 80 0.180 0.800M. prima 10 90 0.100 0.900Mètodo 6 98 0.080 0.980Medidas 4 100 0.020 1.000

0.000

0.200

0.400

0.600

0.800

1.000

1.200

0

5

10

15

20

25

30

35

40

45

50

0 0 0 0 0 0

Según la investigación realizada los operadores debido a que se trabaja a marchas forzadas no estaban dando el 100 en sus actividades, además de que no se les daba

descanso; esto lo resintieron los operadores y el efecto se vio en la calidad del producto que elaboran.

Problemas inventados.

Documents

Transcript of Problemas inventados.