Week Two AssignmentAssignment: Part 1 – Is my manufacturing process in control? (Statistically s
Background on Statistical Controls in Manufacturing: A state of statistical control is defined as a process with a const
changing over time.
Generally speaking, the upper and lower control limits are set at ± three standard deviations from the mean. If a norm
these control limits will include 99.74 percent of the random variation observed.
UCL = Average + 3*Standard-Deviation
CL = Average
LCL = Average – 3*Standard-Deviation
(Upper Control Limit)
(Center Line)
(Lower Control Limit)
Activity: For our hypothetical single-port yogurt filing machine (shown below ). See the filing results of the first 100 cu
filing. Compute the UCL, CL, and LCL to determine if your process is in control.
As a reminder, your process is “in control” if you nearly all of the products produced (99.74% or higher) are within the
Control Limit (LCL) values. Otherwise, your process is not in control and needs to be triaged.
Yogurt Fill in Ounces
9.000
8.000
Weight of Cup (oz)
7.000
6.000
5.000
UCL
4.000
CL
Weight of Cup (oz)
UCL
4.000
CL
3.000
LCL
2.000
1.000
0.000
0
20
40
60
Sample #
Graph Data (automatically pulls entered values)
UCL
CL
LCL
1
0
0.000
0
100
0.000
0.000
0.000
80
100
120
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
l? (Statistically speaking…)
d as a process with a constant mean and variance that is not
s from the mean. If a normal probability distribution is assumed,
(Upper Control Limit)
(Center Line)
(Lower Control Limit)
ng results of the first 100 cups of yogurt and their actual weight after
% or higher) are within the Upper Control Limit (UCL) and Lower
d.
Sample #
Actual Fill (oz)
1
8.028
Within Control
Limits?
FALSE
2
7.986
FALSE
Average =
3
7.985
FALSE
Standard Deviation =
4
8.036
FALSE
5
8.018
FALSE
6
7.937
FALSE
UCL =
7
8.026
FALSE
Center Line =
8
8.050
FALSE
LCL =
9
7.920
FALSE
10
7.974
FALSE
11
12
13
14
15
16
17
7.890
8.032
7.948
8.013
7.943
8.069
7.918
FALSE
FALSE
FALSE
FALSE
FALSE
FALSE
FALSE
18
7.650
FALSE
Statistical Calculations
Is this process in control? (Yes/No) and Why?
Should I keep making yogurt?
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
7.895
7.959
8.030
7.845
7.952
8.036
8.004
7.861
7.899
8.036
8.067
8.037
7.959
7.700
7.844
7.990
7.949
7.991
7.986
7.947
7.890
8.071
8.063
8.048
7.900
8.067
7.834
7.946
7.925
7.977
8.007
8.045
7.875
7.928
7.869
8.041
7.849
7.859
7.888
7.887
7.965
7.895
7.964
7.979
7.952
8.003
FALSE
FALSE
FALSE
FALSE
FALSE
FALSE
FALSE
FALSE
FALSE
FALSE
FALSE
FALSE
FALSE
FALSE
FALSE
FALSE
FALSE
FALSE
FALSE
FALSE
FALSE
FALSE
FALSE
FALSE
FALSE
FALSE
FALSE
FALSE
FALSE
FALSE
FALSE
FALSE
FALSE
FALSE
FALSE
FALSE
FALSE
FALSE
FALSE
FALSE
FALSE
FALSE
FALSE
FALSE
FALSE
FALSE
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
8.028
7.995
7.903
7.839
8.034
7.827
8.010
7.826
7.934
7.936
7.650
7.965
7.963
7.911
8.072
7.923
7.961
7.929
7.847
7.866
7.841
8.065
7.963
7.858
7.954
7.978
8.022
7.834
8.022
7.875
8.006
8.012
7.975
7.916
8.055
7.837
FALSE
FALSE
FALSE
FALSE
FALSE
FALSE
FALSE
FALSE
FALSE
FALSE
FALSE
FALSE
FALSE
FALSE
FALSE
FALSE
FALSE
FALSE
FALSE
FALSE
FALSE
FALSE
FALSE
FALSE
FALSE
FALSE
FALSE
FALSE
FALSE
FALSE
FALSE
FALSE
FALSE
FALSE
FALSE
FALSE
Calculations
oz
oz
oz
oz
oz
/No) and Why?
Tip: Reminder that to calculate the average , you can use Excel’s AVERAGE
function. Just add the function and select all of the actual fill examples.
The same is true with standard deviation , by using Excel’s STDEV formula.
Select the same actual fill examples.
Assignment: Part 2 – How do I control my production?
Background: Once we get the process fixed (i.e., in control), we should still regularly monitor it’s performance. H
Remember that our quality measure is the amount (weight) of yogurt in each cup — not too much or you waste
make a mess, and not too little or customers (and the FDA) will be upset. Weight is a continuous variable measur
accurately in ounces. We need to be concerned not just with the average weight, but also how well our machine
To do that, we’ll need an X-bar chart and an R-chart.
Question: What is “n” (the sub-group size), in the
quality sampling recorded below?
Sample #
Time
1
2
3
4
5
6
8:00am
10:00am
12:00pm
2:00pm
4:00pm
6:00pm
n=
Cup #
1
8.005
7.821
7.989
8.147
8.038
8.142
2
8.200
8.180
7.878
8.164
8.082
8.073
3
7.938
8.069
7.914
8.167
7.892
8.193
4
8.012
7.854
8.151
7.862
7.988
8.017
5
7.941
8.197
8.007
7.952
7.851
8.111
6
7.954
8.152
7.800
7.976
7.839
8.046
Activity: Next, calculate the Sample Averages based on the above samples. This will ultimately help you
calculate X-bar. Then calculate the range within each sample group. To calculate the range in a sample group,
use the following formula:
Range =
Sample
Average
(X-bar)
Range
within
Sample
Maximum values of selected cells – Minimum values of selected cells
MAX(cell range)-MIN(cell range)
Activity: Once you calculate the sample average and range within the
sample, you can calculate the Overall Averages for both. This gives the Xdouble bar and R-bar, which we need for our X-Bar and R-Bar charts.
Overall average =
Activity: In order to create the charts, we need to populate the constants
below. You can find these in our textbook in Table 9.1
UCL =
CL =
LCL =
Weight of yogurt cup (oz)
Activity: Use the formulas below to calculate the Upper Control Limit (UCL), Center Line (CL), and Lower Control L
automatically populate the X-Bar Chart below.
1.00
0.80
0.60
0.40
0.20
0.00
UCL =
CL =
LCL =
Is this process in control? (Yes/No) and Why?
Graph Data (automatically pulls entered values)
X-bar
UCL
CL
LCL
1
0.00
0.00
0.00
8
0.00
0.00
0.00
Range of Weight of yogurt cup
(oz)
Activity: Use the formulas below to calculate the Upper Control Limit (UCL), Center Line (CL), and Lower Control L
automatically populate the R Chart below.
Should I keep making yogurt?
R chart
1
8
UCL
0.00
0.00
CL
0.00
0.00
LCL
0.00
0.00
ularly monitor it’s performance. Here’s how:
cup — not too much or you waste money and
ht is a continuous variable measured very
t, but also how well our machine is performing.
7
7.810
8.089
8.116
7.838
8.056
8.168
8
8.088
8.155
7.803
7.965
8.176
8.060
s will ultimately help you
e the range in a sample group,
elected cells
age and range within the
es for both. This gives the XX-Bar and R-Bar charts.
ed to populate the constants
Table 9.1
nter Line (CL), and Lower Control Limit (LCL) values. This will
Weight of yogurt cup (oz)
X-bar Chart
1.00
0.80
0.60
UCL
0.40
CL
0.20
LCL
0.00
1
2
3
4
5
6
7
8
Sample #
nter Line (CL), and Lower Control Limit (LCL) values. This will
Range of Weight of yogurt cup
(oz)
R Chart
1.00
0.80
0.60
UCL
0.40
CL
0.20
LCL
0.00
1
2
3
Should I keep making yogurt?
4
5
Sample #
6
7
8
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