Excel file with the data for the three questions.
- Piston rings for an automotive engine are produced by a forging process. We wish to establish statistical control of the inside diameter of the rings manufactured. Twenty-five samples, each of size five, have been taken to analyze the process. The inside diameter measurement data from theses samples are shown in the following table:
- Fifteen additional samples from the piston ring manufacturing process were collected after the control charts were established. The data from theses new samples are shown in the following table:
- You are the newly appointed assistant administrator at a local hospital, and your first project is to investigate the quality of the patient meals put out by the food-service department. You conducted a 10-day survey by submitting a simple questionnaire to the 400 patients with each three meals, asking that they simply check-off that the meal was either satisfactory or unsatisfactory. The results are:
|
Observations |
|||||||
|
Nº |
1 |
2 |
3 |
4 |
5 |
Mean (X) |
Range (R) |
|
1 |
74.03 |
74.002 |
74.019 |
73.992 |
74.008 |
74.010 |
0.038 |
|
2 |
73.995 |
73.992 |
74.001 |
74.011 |
74.004 |
74.001 |
0.019 |
|
3 |
73.988 |
74.024 |
74.021 |
74.005 |
74.002 |
74.008 |
0.036 |
|
4 |
74.002 |
73.996 |
73.993 |
74.015 |
74.009 |
74.003 |
0.022 |
|
5 |
73.992 |
74.007 |
74.015 |
73.989 |
74.014 |
74.003 |
0.026 |
|
6 |
74.009 |
73.994 |
73.997 |
73.985 |
73.993 |
73.996 |
0.024 |
|
7 |
73.995 |
74.006 |
73.994 |
74.000 |
74.005 |
74.000 |
0.012 |
|
8 |
73.985 |
74.003 |
73.993 |
74.015 |
73.998 |
73.999 |
0.030 |
|
9 |
74.008 |
73.995 |
74.009 |
74.005 |
74.004 |
74.004 |
0.014 |
|
10 |
73.998 |
74.000 |
73.990 |
74.007 |
73.995 |
73.998 |
0.017 |
|
11 |
73.994 |
73.998 |
73.994 |
73.995 |
73.990 |
73.994 |
0.008 |
|
12 |
74.004 |
74.000 |
74.007 |
74.000 |
73.996 |
74.001 |
0.011 |
|
13 |
73.983 |
74.002 |
73.998 |
73.997 |
74.012 |
73.998 |
0.029 |
|
14 |
74.006 |
73.967 |
73.994 |
74.000 |
73.984 |
73.990 |
0.039 |
|
15 |
74.012 |
74.014 |
73.998 |
73.999 |
74.007 |
74.006 |
0.016 |
|
16 |
74.000 |
73.984 |
74.005 |
73.998 |
73.996 |
73.997 |
0.021 |
|
17 |
73.994 |
74.012 |
73.986 |
74.005 |
74.007 |
74.001 |
0.026 |
|
18 |
74.006 |
74.010 |
74.018 |
74.003 |
74.000 |
74.007 |
0.018 |
|
19 |
73.984 |
74.002 |
74.003 |
74.005 |
73.997 |
73.998 |
0.021 |
|
20 |
74.000 |
74.010 |
74.013 |
74.020 |
74.003 |
74.009 |
0.020 |
|
21 |
73.988 |
74.001 |
74.009 |
74.005 |
73.996 |
74.000 |
0.021 |
|
22 |
74.004 |
73.999 |
73.990 |
74.006 |
74.009 |
74.002 |
0.019 |
|
23 |
74.010 |
73.989 |
73.990 |
74.009 |
74.014 |
74.002 |
0.025 |
|
24 |
74.015 |
74.008 |
73.993 |
74.000 |
74.010 |
74.005 |
0.022 |
|
25 |
73.982 |
73.984 |
73.995 |
74.017 |
74.013 |
73.998 |
0.035 |
- What is the value of and ?
- Construct -charts and R-charts for this problem. Is the process in control?
|
Observations |
|||||||
|
Nº |
1 |
2 |
3 |
4 |
5 |
Mean (X) |
Range (R) |
|
26 |
74.012 |
74.015 |
74.030 |
73.986 |
74.000 |
74.009 |
0.044 |
|
27 |
73.995 |
74.010 |
73.990 |
74.015 |
74.001 |
74.002 |
0.025 |
|
28 |
73.987 |
73.999 |
73.985 |
74.000 |
73.990 |
73.992 |
0.015 |
|
29 |
74.008 |
74.010 |
74.003 |
73.991 |
74.006 |
74.004 |
0.019 |
|
30 |
74.003 |
74.000 |
74.003 |
73.986 |
73.997 |
73.998 |
0.017 |
|
31 |
73.994 |
74.003 |
74.015 |
74.020 |
74.004 |
74.007 |
0.026 |
|
32 |
74.008 |
74.002 |
74.018 |
73.995 |
74.005 |
74.006 |
0.023 |
|
33 |
74.001 |
74.004 |
73.990 |
73.996 |
73.998 |
73.998 |
0.014 |
|
34 |
74.015 |
74.000 |
74.016 |
74.025 |
74.000 |
74.011 |
0.025 |
|
35 |
74.030 |
74.005 |
74.000 |
74.016 |
74.012 |
74.013 |
0.030 |
|
36 |
74.001 |
73.990 |
73.995 |
74.010 |
74.024 |
74.004 |
0.034 |
|
37 |
74.015 |
74.020 |
74.024 |
74.005 |
74.019 |
74.017 |
0.019 |
|
38 |
74.035 |
74.010 |
74.012 |
74.015 |
74.026 |
74.020 |
0.025 |
|
39 |
74.017 |
74.013 |
74.036 |
74.025 |
74.026 |
74.023 |
0.023 |
|
40 |
74.010 |
74.005 |
74.029 |
74.000 |
74.020 |
74.013 |
0.029 |
Is the process now in control? What conclusion can we make?
|
Day |
Unsatisfactory meals |
Sample size |
|
1 |
74 |
1,000 |
|
2 |
39 |
1,100 |
|
3 |
64 |
1,050 |
|
4 |
86 |
1,000 |
|
5 |
35 |
1,078 |
|
6 |
50 |
950 |
|
7 |
65 |
1,141 |
|
8 |
70 |
988 |
|
9 |
67 |
750 |
|
10 |
75 |
1,010 |
|
Total |
625 |
10,067 |
- Construct a p-chart based on the questionnaire results.
- What comments can you make about the results of the survey?
Note: in the attachment you will find an Excel file with the data for the three, please use the attachment for questions
Get 20% discount on your first order with us. Place an order and use coupon: GET20
