Question
A die-casting process is being used to make a cast housing that will be sold to a client who will perform further machining operations on
A die-casting process is being used to make a cast housing that will be sold to a client who will perform further machining operations on the cast part. The weight of the part is a good indicator of process performance. The cast part has a target weight of 775 grams with a tolerance of 20 grams.The results of the 40 subgroups are shown in the table below.An Excel data file is available on eLearning.
Subgroup
X1
X2
X3
X4
X5
1
779
782
771
771
773
2
775
763
775
779
774
3
772
782
770
790
775
4
779
776
773
780
779
5
771
763
779
776
787
6
781
767
772
783
771
7
788
777
770
765
759
8
780
777
778
786
780
9
765
772
775
784
785
10
772
773
775
775
765
11
773
774
772
776
777
12
773
770
783
778
785
13
784
774
778
779
776
14
788
770
779
788
778
15
764
771
765
778
782
16
786
773
771
778
771
17
784
767
771
759
787
18
776
781
766
774
773
19
775
769
783
779
771
20
779
775
773
775
774
21
779
786
785
787
784
22
776
778
788
775
789
23
781
788
784
770
782
24
781
774
772
778
760
25
784
765
765
777
779
26
785
772
776
772
778
27
783
772
772
781
766
28
774
778
774
782
793
29
777
773
774
771
783
30
759
771
785
774
780
31
782
773
776
774
785
32
766
774
779
781
773
33
777
773
777
786
774
34
789
783
771
775
782
35
782
778
766
769
767
36
773
782
767
773
770
37
783
769
777
777
761
38
782
782
780
770
772
39
782
770
770
774
775
40
777
769
780
768
779
Answer the following questions regarding this manufacturing process:
- Construct and interpret X-bar and R controls. If the process is not stable, revised control limits need to be recalculate. Use the single criteria that points are supposed to be within the control limits.
- Process is stable
- Construct a histogram of the 200 individual measurements.Comment on the shape of the histogram to see if approximately a normal distribution assumption is valid.
- The histogram appears to be approximately normal
- What proportion of the observed measurements is above the upper specification limit? Below the lower specification limit?
- The upper specification limit is: 22
- the lower specification limit is: 18
- Give values of the estimated process potential, Cp and process performance, Cpk indices using the standard deviation estimated out of the overall 200 measurements.
a.,
- What is the predicted (expected) proportion of future measurements that will be above the upper specification limit? Below the lower specification limit? Use the standard deviation estimated out of the overall 200 measurements.
- Give values of the estimated process potential, Cp and process performance, Cpk indices using the standard deviation estimated out of the average subgroup range,
- What is the predicted (expected) proportion of future measurements that will be above the upper specification limit? Below the lower specification limit? use the standard deviation estimated out of the average subgroup range
- Is there much difference between your answer in parts (4) and (5) compared to those in (6) and (7).
- There is only a little difference between my answers in part 4 and 5 when comparing to 6 and 7
- Summarize your findings in an executive summary that would be read by a person in management. You may include any graphs that may help management understand what is happening with this process. (must be printed in a Word processor)
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Advanced Calculus
Authors: R Creighton Buck
3rd Edition
147861613X, 9781478616139
