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.
The diagram shows that most of the problems came from the refused and the
wrong address. I would put forth most of the effort in fixing these two areas.
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
(b) 89,87,88,83,86,82,84
(c) 11,17,14,12,12,14,14,15,17,17
(d) 16,25,18,17,16,21,14
(e) 45,39,42,42,43
Descriptive Statistics: C1, C2, C3, C4, C5
Variable
C1
C2
C3
C4
C5
N
9
7
10
7
5
N*
0
0
0
0
0
Mean
50.56
85.571
14.300
18.14
42.200
SE Mean
1.55
0.997
0.700
1.40
0.970
StDev
4.64
2.637
2.214
3.72
2.168
Minimum
45.00
82.000
11.000
14.00
39.000
Q1
45.00
83.000
12.000
16.00
40.500
Median
50.00
86.000
14.000
17.00
42.000
Q3
55.00
88.000
17.000
21.00
44.000
Variable
C1
C2
C3
C4
C5
Maximum
55.00
89.000
17.000
25.00
45.000
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
-----------------------------------------------------------------------------------------------------------
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.
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.
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.
The viscosity of the liquid breaks down over time from shift to shift it keeps
degrading
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 C1
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
17
19
21
23
25
Sample
As you can see the subgroup number 5 is out of the control limits.
P Chart of C1
0.04
UCL=0.03676
Proportion
0.03
0.02
_
P=0.01542
0.01
0.00
LCL=0
1
3
5
7
9
11
13
15
17
19
Sample
Here is the new chart with out of control point taken out.
21
23
8.
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 C1
1
UCL=5.028
Sample Count Per Unit
5
4
_
U=3.304
3
2
LCL=1.579
1
1
1
0
1
4
7
10
13
16
19
Sample
As you can see there are 3 points out of control
22
25
28
U Chart of C1
5.5
UCL=5.169
Sample Count Per Unit
5.0
4.5
4.0
_
U=3.416
3.5
3.0
2.5
2.0
LCL=1.663
1.5
1
3
5
7
9
11
13
15
17
19
21
23
25
Sample
Here is the chart with the points taken out
9.
A quality technician has collected data on the count of rivet nonconfonnities in
four meters travel trailers. After 30 trailers, the total count of nonconfonnities 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?
Since there are no out of control points the process seems to be in control and the
process should continue.
10.
By means of a scatter diagram, determine if a relationship, exists between
product temperatures and percent foam for a soft drink.
From the look of the graph the data indicates that there is a correlation
between the temperature and the percentage of foam in the product.
For some reason I could not get the graph to upload to the doc.