Question
In: Statistics and Probability
The following data represent samples that were taken on 10 separate days. Each day has a...
The following data represent samples that were taken on 10 separate days. Each day has a varying sample size and the number of defects for the items sampled is listed. We want to see if this process is consistent and in control.
|
Day |
Sample Size |
Defects |
|
1 |
110 |
6 |
|
2 |
112 |
3 |
|
3 |
195 |
8 |
|
4 |
185 |
6 |
|
5 |
245 |
10 |
|
6 |
250 |
7 |
|
7 |
100 |
5 |
|
8 |
170 |
7 |
|
9 |
250 |
20 |
|
10 |
270 |
25 |
a. Find the UCL.
b. Find the LCL.
c. Is the process in control? Why/why not?
Solutions
Expert Solution
From the given data
| Size (ni) | Number of defects (ui) | ||||
| Day | ui = ci/ni | LCL | UCL | ||
| 1 | 110 | 6 | 0.0545 | -0.01345 | 0.116257 |
| 2 | 112 | 3 | 0.0268 | -0.01287 | 0.115675 |
| 3 | 195 | 8 | 0.041 | 0.002696 | 0.100113 |
| 4 | 185 | 6 | 0.0324 | 0.001397 | 0.101412 |
| 5 | 245 | 10 | 0.0408 | 0.00795 | 0.094859 |
| 6 | 250 | 7 | 0.028 | 0.008386 | 0.094422 |
| 7 | 100 | 5 | 0.05 | -0.01661 | 0.119422 |
| 8 | 170 | 7 | 0.0412 | -0.00076 | 0.103571 |
| 9 | 250 | 20 | 0.08 | 0.008386 | 0.094422 |
| 10 | 270 | 25 | 0.0926 | 0.01001 | 0.092799 |
| Total : | 1887 | 97 |
c) NControl Chart:
Interpretation: The process is under control since all points lies between LCL and UCL.
The number of defects per unit is stable. No subgroups are out of control
orchestra answered 2 years agoRelated Solutions
The following data represent samples that were taken on 10 separate days. Each day has a...
The following data represent samples that were taken on 10
separate days. Each day has a varying sample size and the number of
defects for the items sampled is listed. We want to see if this
process is consistent and in control.
Day
Sample Size
Defects
1
100
6
2
110
4
3
190
10
4
190
7
5
240
15
6
255
8
7
105
3
8
175
6
9
245
22
10
265
27
a. Find the UCL....
2. The following data represent samples that were taken on 10 separate days. Each day has...
2. The following data represent samples that were taken on 10
separate days. Each day has a varying sample size and the number of
defects for the items sampled is listed. We want to see if this
process is consistent and in control.
Day
Sample Size
Defects
1
100
6
2
110
4
3
190
10
4
190
7
5
240
15
6
255
8
7
105
3
8
175
6
9
245
22
10
265
27
a. Find...
Twenty samples with 100 units each were taken; with the following number of defectives in each...
Twenty samples with 100 units each were taken; with the
following number of defectives in each respective sample: 11, 2, 7,
5, 6, 7, 8, 5, 3, 6, 4, 3, 5, 6, 2, 5, 0, 9, 10, and 8.
Calculate the center line, upper control limit, and lower
control limit for a 3s p-chart. (RE: As your starting
point, recall that p-charts represent percentages
of defects for samples.)
Plot the points on the chart.
Comment on whether the process is...
The following data were obtained in a study using three separate samples to compare three different...
The following data were obtained in a study using three separate
samples to compare three different treatments. Conduct an analysis
of variance with α=0.05α=0.05 to determine whether these data are
sufficient to conclude that there are significant differences
between the treatments.
Treatment A
Treatment B
Treatment C
6
4
11
8
6
9
7
6
9
7
4
7
F-ratio =
p-value =
Conclusion:
These data do not provide evidence of a difference between the
treatments
There is a significant...
The following data were obtained in a study using three separate samples to compare three different...
The following data were obtained in a study using three separate
samples to compare three different treatments. Conduct an analysis
of variance with α=0.05α=0.05 to determine whether these data are
sufficient to conclude that there are significant differences
between the treatments.
Treatment A
Treatment B
Treatment C
22
21
22
23
19
24
21
19
24
22
21
26
F-ratio =
p-value =
Conclusion:
There is a significant difference between treatments
These data do not provide evidence of a difference...
The following data were obtained in a study using three separate samples to compare three different...
The following data were obtained in a study using three separate
samples to compare three different treatments. Conduct an analysis
of variance with α=0.05α=0.05 to determine whether these data are
sufficient to conclude that there are significant differences
between the treatments.
Treatment A
Treatment B
Treatment C
14
10
13
13
12
15
12
12
17
13
10
15
F-ratio =
p-value =
Conclusion:
These data do not provide evidence of a difference between the
treatments
There is a significant...
The following data were obtained in a study using three separate samples to compare three different...
The following data were obtained in a study using three separate
samples to compare three different treatments. Conduct an analysis
of variance with α=0.05 to determine whether these data are
sufficient to conclude that there are significant differences
between the treatments.
Treatment A
Treatment B
Treatment C
9
5
12
8
7
10
7
7
10
8
5
8
F-ratio =____________________
p-value =__________________
Conclusion:
__These data do not provide evidence of a difference between
the treatments
__There is a significant...
The following data were obtained in a study using three separate samples to compare three different...
The following data were obtained in a study using three separate
samples to compare three different treatments.
Treatment 1
Treatment 2
Treatment 3
4
3
8
3
1
4
5
4
3
1
6
6
M = 4
M = 2
M = 6
SS = 2
SS = 4
SS = 8
a. State the null and alternative hypotheses.
b. Fill in the ANOVA table below.
Source
SS
df
MS
F
Between treatments
Within treatments
Total
c. If α...
Problem 10-23 Ten samples of 15 parts each were taken from an ongoing process to establish...
Problem 10-23
Ten samples of 15 parts each were taken from an ongoing process
to establish a p-chart for control. The samples and the
number of defectives in each are shown in the following table:
SAMPLE
n
NUMBER OF DEFECTIVE ITEMS IN THE SAMPLE
1
15
2
2
15
1
3
15
1
4
15
1
5
15
3
6
15
1
7
15
0
8
15
2
9
15
1
10
15
0
a. Determine the p−p−, Sp,
UCL...
The following data represent the filling weights based on samples of 350-gram containers. Ten samples of...
The following data represent the filling weights based on
samples of 350-gram containers. Ten samples of size 5 were
taken.
Sample
Observ. 1
Observ. 2
Observ. 3
Observ. 4
Observ. 5
1
333.6226
339.3906
361.9761
339.1192
346.4578
2
365.5820
347.4967
349.5748
352.6524
363.7096
3
363.8708
367.4003
335.0422
328.8487
355.8509
4
338.4916
338.6541
346.3491
366.9538
343.1767
5
355.2305
345.7635
356.5218
347.2718
334.5434
6
345.6990
326.0756
328.9903
362.4881
352.8718
7
334.7083
359.4960
333.1609
352.2697
360.8256
8
341.2400
356.8819
369.7263
336.0729
361.5562
9...
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