Statistical Process Controls: Please solve and submit the following questions (50
points).
1. A major record-of-the-month club collected data on the reasons for returned
shipments during a quarter. Results are: wrong selection, 50,000; refused, 195,000;
wrong address, 68,000; order canceled, 5,000; and other, 15,000. Construct a Pareto
diagram and recommend what are the major problems that demand investment.
Pareto Chart of Reason
350000
100
300000
totals
200000
60
150000
40
Percent
80
250000
100000
20
50000
0
reason
Count
Percent
Cum %
Refused
195000
58.6
58.6
Wr. Add
68000
20.4
79.0
Wr. Sel.
50000
15.0
94.0
Other
15000
4.5
98.5
Ord Can
5000
1.5
100.0
0
It does appear that communication is the largest issue in the organization. The
customers are refusing their orders as 60% of our total losses because we are
apparently not getting them proper service. We also have the wrong addresses
for 20% of our customers with issues and 50,000 we have the wrong address for.
Communication with the customer is apparently the largest flaw in need of most
investment.
2.
Calculate the average, median, mode, range, and standard deviation for each
group of numbers.
(a) 50, 45, 55, 55, 45, 50, 55, 45, 55
N N*
C1
Variable
C1
Mean
9
SE Mean StDev Minimum
0 50.56
1.55
4.64
Q1 Median
45.00 45.00
Q3 Maximum
50.00 55.00
55.00
Range
10.00 MODE = 45
(b) 89,87,88,83,86,82,84
Variable
C1
N
7
N*
0
Mean
85.571
Variable
C1
Maximum
89.000
SE Mean
0.997
Range
7.000
StDev
2.637
Minimum
82.000
Q1
83.000
Median
86.000
Q3
88.000
Mode = 83
(c) 11,17,14,12,12,14,14,15,17,17
Variable
C1
N
10
N*
0
Variable
C1
Maximum
17.000
Mean
14.300
SE Mean
0.700
Range
6.000
Mode
13
StDev
2.214
Minimum
11.000
Q1
12.000
Median
14.000
Q3
17.000
(d) 16,25,18,17,16,21,14
Variable
C1
N
7
N*
0
Mean
18.14
Variable
C1
Range
11.00
mode
17
SE Mean
1.40
StDev
3.72
Minimum
14.00
Q1
16.00
Median
17.00
Q3
21.00
Maximum
25.00
(e) 45,39,42,42,43
Variable
C1
N
5
N*
0
Variable
C1
Maximum
45.000
Mean
42.200
Range
6.000
SE Mean
0.970
Mode
42
StDev
2.168
Minimum
39.000
Q1
40.500
Median
42.000
Q3
44.000
3. Control charts for X and R are to be established on a certain dimension part,
measured in millimeters. Data were collected in subgroup sizes of 6 and are given
below. Calculate the trial central line and control limits. Assume assignable causes
and revise the central line and limits.
----------------------------------------------------------------------------------------------------------Subgroup
Subgroup
Number
X
R
Number
X
R
-----------------------------------------------------------------------------------------------------------1
20.35
0.34
14
20.41
0.36
2
20.40
0.36
15
20.45
0.34
3
20.36
0.32
16
20.34
0.36
4
20.65
0.36
17
20.36
0.37
5
20.20
0.36
18
20.42
0.73
6
20.40
0.35
19
20.50
0.38
7
20.43
0.31
20
20.31
0.35
8
20.37
0.34
21
20.39
0.38
9
20.48
0.30
22
20.39
0.33
10
20.42
0.37
23
20.40
0.32
11
20.39
0.29
24
20.41
0.34
12
20.38
0.30
25
20.40
0.30
13
20.40
0.33
-----------------------------------------------------------------------------------------------------------
Xbar-R Chart of X
U C L=20.6556
Sample M ean
20.6
20.5
_
_
X=20.4004
20.4
20.3
20.2
LC L=20.1452
1
2
3
Sample
4
5
1
U C L=0.4320
Sample Range
0.4
0.3
_
R=0.2156
0.2
0.1
0.0
LC L=0
1
2
3
Sample
4
5
4. The following table gives the average and range in kilograms for tensile tests on
an improved plastic cord. The subgroup size is 4. Determine the trial central line
and control limits. If any points are out of control, assume assignable causes, and
determine the revised limits and central line.
Xbar-R Chart of X
Sample Mean
520
U C L=519.75
500
_
_
X=482.52
480
460
LC L=445.29
440
1
2
3
4
Sample
5
6
7
Sample Range
60
U C L=58.29
45
30
_
R=25.55
15
0
LC L=0
1
2
3
4
Sample
5
6
7
5.
The Get-Well Hospital has completed a quality improvement project on the time
to admit a patient using: XC- and R charts. They now wish to monitor the activity
using median and range charts. Determine the central line and control limits with
the latest data in minutes, as given here.
Xbar-R Chart of XBar
Sample M ean
6.8
U C L=6.759
6.4
_
_
X=6.064
6.0
5.6
LC L=5.369
5.2
1
2
3
4
5
6
7
8
Sample
2.0
Sample Range
U C L=1.748
1.5
1.0
_
R=0.679
0.5
0.0
LC L=0
1
2
3
4
5
Sample
6
7
8
6.
The viscosity of a liquid is checked every half hour during one three-shift day.
What does the run chart indicate? Data are 39, 42,38,37,41,40,36,35,37,36,
39,34,38,36,32,37,35,34,33,35,32,38,34,37,35,35, 34, 31, 33, 35, 32,
36,31,29,33,32,31,30,32, and 29.
Run Chart of C1
42
40
C1
38
36
34
32
30
1
5
Number of runs about median:
Expected number of runs:
Longest run about median:
A pprox P-Value for Clustering:
A pprox P-Value for Mixtures:
10
14
20.20000
7
0.01917
0.98083
15
20
25
Observation
Number of runs up or down:
Expected number of runs:
Longest run up or down:
A pprox P-Value for Trends:
A pprox P-Value for Oscillation:
30
35
40
26
26.33333
4
0.44910
0.55090
The viscosity of the liquid appears to be dropping over time from the average. If this
deterioration trend continues, then the liquid will have to be replaced to prevent
damage to equipment.
7.
Determine the trial central line and control limits for a p chart using the following
data, which are for the payment of dental insurance claims. Plot the values on
graph paper and determine if the process is stable. If there are any out -of-control
points, assume an assignable cause and determine the revised central line and
control limits.
P Chart of No. N.C
0.07
1
0.06
Proportion
0.05
0.04
UCL=0.04016
0.03
_
P=0.01747
0.02
0.01
0.00
LCL=0
1
3
5
7
9
11
13 15
Sample
17
19
21
23
25
P Chart of No. N.C
0.04
UCL=0.03676
Proportion
0.03
0.02
_
P=0.01542
0.01
0.00
LCL=0
1
8.
3
5
7
9
11 13 15
Sample
17
19
21
23
Determine the trial limits and revised control limits for a u chart using the data in
the table for the surface finish of rolls of white paper. Assume any out -of-control
points have assignable causes.
U Chart of Total N.C
6
5
Sample Count Per Unit
1
1
UCL=5.043
4
_
U=3.315
3
2
LCL=1.588
1
1
1
0
1
4
7
10
13
16
Sample
19
22
25
28
Tests performed with unequal sample sizes
U Chart of Total N.C
UCL=5.097
Sample Count Per Unit
5
4
_
U=3.358
3
2
LCL=1.620
1
1
3
5
7
9
11
13
Sample
Tests performed with unequal sample sizes
15
17
19
21
23
9.
A quality technician has collected data on the count of rivet nonconformities in
four meters travel trailers. After 30 trailers, the total count of nonconformities is
316. Trial control limits have been determined and a comparison with the data
shows no out-of-control points. What is the recommendation for the central line
and the revised control limits for a count of nonconformities chart?
If the data has been compared to the original data done for testing and all of the
data indicates there are no out of spec process controls, then the revised control
limits will have to be moved to fit the newly gathered data for the next run. If the
nonconformities occurred on the low side of the spectrum, then move the revised
control limits lower. If the phenomenon occurred on the high side, then move the
control limits up.
10.
By means of a scatter diagram, determine if a relationship, exists between
product temperatures and percent foam for a soft drink.
Scatterplot of temp vs foam
50.0
47.5
temp
45.0
42.5
40.0
37.5
35.0
15
20
25
30
foam
35
40
45
From the look of the graph of Product Temperature VS Foam, the data indicates
that there is a correlation between the temperature and the percentage of foam in
the product. My suggestion if foam is a deterrent to a quality end product, is to add
equipment that would eliminate air entrapment to the liquid in the beginning or add
coolers to the process to control the temperature of the product.