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Kelsey Bradley
M0821671
10/01/16
ETM 419/619
Fall 2016
Individual Assignment 3
1. (5 Points) Describe the difference between chance and assignable causes.
Chance causes consist of many different individual causes. Assignable causes consist of a couple
of causes that can be pinpointed to the problem. (page 241)
2. (10 Points) Androx Chemicals manufactures a powdered compound that is used to coat gunite
swimming pools. An important measure is the Dry Brightness (DB) Number, and customers will
not accept product that has a DB number less than 90.3. Because it is difficult to obtain a precise
reading, a technician takes a grab sample of material, divides it into three parts, and then
measures each part. The three measurements are then averaged and plotted on control charts.
The following data represent 20 samples that were obtained from this process. Use control
charts to determine if the process is in control. Show calculations use to find X bar, UCL, LCL,
etc.
Kelsey Bradley
M0821671
10/01/16
Xbar-R Chart of C1, ..., C3
UCL=92.156
Sample Mean
92.00
91.75
__
X=91.578
91.50
91.25
91.00
LCL=91.000
1
1
3
5
7
11
9
13
19
17
15
Sample
1.6
1
UCL=1.454
Sample Range
1.2
2
0.8
2
2
_
R=0.565
0.4
0.0
LCL=0
2
1
3
5
7
11
9
13
15
17
19
Sample
TEST 1. One point more than 3.00 standard deviations from center line.
Test Failed at points: 16
TEST 2. 9 points in a row on same side of center line.
Test Failed at points: 9, 18, 19, 20
This process is not in statistical control, because there are places where the tests failed.
3. (15 points) The following times were recorded for a bagger at a local grocery store.
a. Construct a histogram and comment on shape.
Kelsey Bradley
M0821671
10/01/16
The histogram shows that the bagging times are non normal.
Histogram of C1
10
Frequency
8
6
4
2
0
0
3
6
9
12
C1
b. What is your estimate of the mean and standard deviation for the data? Show calculations.
Descriptive Statistics: C1
Variable
C1
N
30
N*
0
Mean
3.313
SE Mean
0.537
StDev
2.942
Minimum
0.300
Q1
1.020
Median
2.560
Q3
4.675
Maximum
11.740
c. Plot an X and MR pair of control charts and comment on the state of control. Show calculations
used.
Kelsey Bradley
M0821671
10/01/16
I-MR Chart of C1
1
UCL=11.54
Individual Value
10
5
_
X=3.31
0
LCL=-4.91
-5
1
4
7
13
10
16
19
22
25
28
Observation
1
UCL=10.11
Moving Range
10.0
7.5
5.0
__
MR=3.09
2.5
LCL=0
0.0
1
4
7
10
13
16
19
22
25
28
Observation
Test Results for I Chart of C1
TEST 1. One point more than 3.00 standard deviations from center line.
Test Failed at points: 11
Test Results for MR Chart of C1
TEST 1. One point more than 3.00 standard deviations from center line.
Test Failed at points: 11
4. (5 points) A certain mineral is inspected for particle size. Since particles tend to separate out, a
sample is taken from four different locations in the storage silo. The four samples are then
averaged. The results of 30 samples are shown in the table.
Kelsey Bradley
M0821671
10/01/16
Construct an
control.
X and R chart for these data and comment on whether this process is in statistical
Kelsey Bradley
M0821671
10/01/16
Xbar-R Chart of C1, ..., C4
UCL=2.0412
Sample Mean
2.0
1.9
__
X=1.8355
1.8
1.7
1.6
LCL=1.6298
1
4
7
10
16
13
19
22
25
28
Sample
0.8
1
UCL=0.6443
Sample Range
0.6
0.4
_
R=0.2823
0.2
LCL=0
0.0
1
4
7
10
13
16
19
22
25
Sample
Test Results for R Chart of C1, ..., C4
TEST 1. One point more than 3.00 standard deviations from center line.
Test Failed at points: 15
28