just problem 4 only

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Mean Charts

Mean Charts
Mean Charts: Mean charts are used to monitor changes in a process. They are good for detecting anomalies and then isolating the causes of those irregularities in order to resolve issues.
Sample Number Observations Average Range
1 2 3 4 R
1 15.85 16.02 15.83 15.93 15.91
Kathleen Irwin: Tips: Use the AVERAGE function here to find the mean of the data. 		0.19
Kathleen Irwin: Tips: To get the range, subtract the MIN from the MAX for the range of cells
2 16.12 16.00 15.85 16.01 16.00 0.27
3 16.00 15.91 15.94 15.83 15.92 0.17
4 16.20 15.85 15.74 15.93 15.93 0.46
5 15.74 15.86 16.21 16.10 15.98 0.47
6 15.94 16.01 16.14 16.03 16.03 0.20
7 15.75 16.21 16.01 15.86 15.96 0.46
8 15.82 15.94 16.02 15.94 15.93 0.20
9 16.04 15.98 15.83 15.98 15.96 0.21
10 15.64 15.86 15.94 15.89 15.83 0.30
11 16.11 16.00 16.01 15.82 15.99 0.29
12 15.72 15.85 16.12 16.15 15.96 0.43
13 15.85 15.76 15.74 15.98 15.83 0.24
14 15.73 15.84 15.96 16.10 15.91 0.37
15 16.20 16.01 16.10 15.89 16.05 0.31
16 16.12 16.08 15.83 15.94 15.99 0.29
17 16.01 15.93 15.81 15.68 15.86 0.33
18 15.78 16.04 16.11 16.12 16.01 0.34
19 15.84 15.92 16.05 16.12 15.98 0.28
20 15.92 16.09 16.12 15.93 16.02 0.20
21 16.11 16.02 16.00 15.88 16.00 0.23
22 15.98 15.82 15.89 15.89 15.90 0.16
23 16.05 15.73 15.73 15.93 15.86 0.32
24 16.01 16.01 15.89 15.86 15.94 0.15
25 16.08 15.78 15.92 15.98 15.94 0.30
Total 398.67 7.17
0.29
15.95 Center line of the control data is the average of all the averages
0.14 This information was given in the problem data
0.07
z-value 3 This information was given in the problem data
A2 0.73 From Table 6-1 on page 194 in text
UCL 16.156264
LCL 15.737536

 =

𝑅 ̅ =

Range Charts

Range Charts
Range Charts: Range change measure the variability in the data.
Sample Number Observations Average Range
1 2 3 4 R
1 15.85 16.02 15.83 15.93 15.91
Kathleen Irwin: Tips: Use the AVERAGE function here to find the mean of the data. 		0.19
Kathleen Irwin: Tips: To get the range, subtract the MIN from the MAX for the range of cells
2 16.12 16.00 15.85 16.01 16.00 0.27
3 16.00 15.91 15.94 15.83 15.92 0.17
4 16.20 15.85 15.74 15.93 15.93 0.46
5 15.74 15.86 16.21 16.10 15.98 0.47
6 15.94 16.01 16.14 16.03 16.03 0.20
7 15.75 16.21 16.01 15.86 15.96 0.46
8 15.82 15.94 16.02 15.94 15.93 0.20
9 16.04 15.98 15.83 15.98 15.96 0.21
10 15.64 15.86 15.94 15.89 15.83 0.30
11 16.11 16.00 16.01 15.82 15.99 0.29
12 15.72 15.85 16.12 16.15 15.96 0.43
13 15.85 15.76 15.74 15.98 15.83 0.24
14 15.73 15.84 15.96 16.10 15.91 0.37
15 16.20 16.01 16.10 15.89 16.05 0.31
16 16.12 16.08 15.83 15.94 15.99 0.29
17 16.01 15.93 15.81 15.68 15.86 0.33
18 15.78 16.04 16.11 16.12 16.01 0.34
19 15.84 15.92 16.05 16.12 15.98 0.28
20 15.92 16.09 16.12 15.93 16.02 0.20
21 16.11 16.02 16.00 15.88 16.00 0.23
22 15.98 15.82 15.89 15.89 15.90 0.16
23 16.05 15.73 15.73 15.93 15.86 0.32
24 16.01 16.01 15.89 15.86 15.94 0.15
25 16.08 15.78 15.92 15.98 15.94 0.30
Total 398.67 7.17
0.29
D3 0.00 From Table 6-1 on page 194 in text
D4 2.28
UCL 0.6612
LCL 0.0000

𝑋 ̅

P-Charts

P-Charts Use P-charts to measure the proportion of sample that is defective--use this type when you know both the total sample size and the number of defects.
Sample Number Number of Defective Tires Number of Observations Fraction Defective
1 3 20 0.15 To create the chart, select the first column of data, then hold the ctrl key and select the
2 2 20 0.10 fraction defective data. Choose Insert/Chart/Line and choose a type.
3 1 20 0.05
4 2 20 0.10
5 1 20 0.05
6 3 20 0.15
7 3 20 0.15
8 2 20 0.10
9 1 20 0.05
10 2 20 0.10
11 3 20 0.15
12 2 20 0.10
13 2 20 0.10
14 1 20 0.05
15 1 20 0.05
16 2 20 0.10
17 4 20 0.20
18 3 20 0.15
19 1 20 0.05
20 1 20 0.05
Total 40 400
z = 3.00
= 0.100
σP = 0.067
UCL= 0.301
LCL= 0.00 Round any negative number up to -0-
Fraction Defective 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 0.15 0.1 0.05 0.1 0.05 0.15 0.15 0.1 0.05 0.1 0.15 0.1 0.1 0.05 0.05 0.1 0.2 0.15 0.05 0.05

C-Charts

C-Charts Use C-charts to measure the number of defects per unit
Sample Number Number of Complaints
1 3
2 2
3 3
4 1
5 3
6 3
7 2
8 1
9 3
10 1
11 3
12 4
13 2
14 1
15 1
16 1
17 3
18 2
19 2
20 3
Total 44
z = 3.00
= 2.200
UCL= 6.650
LCL= 0.000 Round any negative number up to -0-

Process capab

Computing CP
Bottling Machine σ USL-LSL 6σ CP
A 0.050 0.40 0.30 1.33 ü CP =1 Process variability just meets standards
B 0.100 0.40 0.60 0.67 CP ≤1 Process variability is outside the range of specifications
C 0.200 0.40 1.20 0.33 CP ≥1 Process variability is tighter than the range of specifications and exceeds minimal capability

Example

Problem 1
Sample Number Observations Standard Deviation
1 5.80 0.0285
2 5.90 0.0047
3 6.00 0.0010
4 6.10 0.0172
5 6.20 0.0535
6 6.00 0.0010
7 5.90 0.0047
8 5.90 0.0047
9 6.10 0.0172
10 5.90 0.0047
11 6.00 0.0010
12 5.80 0.0285
13 6.00 0.0010
14 5.90 0.0047
15 5.90 0.0047
16 6.10 0.0172
5.97 0.1944
5.97
0.1138
0.0569
z-value 3
UCL 6.14
LCL 5.80

 =

6-4

Problem 4
Sample Data
1 2 3 4 Mean Range CL UCL LCL
1 16.40 16.11 15.90 15.78
2 15.97 16.10 16.20 15.81
3 15.91 16.00 16.04 15.92
4 16.20 16.21 15.93 15.95
5 15.87 16.21 16.34 16.43
6 15.43 15.49 15.55 15.92
7 16.43 16.21 15.99 16.00
8 15.50 15.92 16.12 16.02
9 16.13 16.21 16.05 16.01
10 15.68 16.43 16.20 15.97
A 0.73 From table 6-1
UCL 16.3
LCL 15.7

 =

Mean CL UCL LCL

 =

6-6

Problem 6
X bar chart
Sample X R
1 12.10 0.7
2 11.80 0.4
3 12.30 0.6
4 11.50 0.4
5 11.60 0.9
CL 12.00
A2

Author: Professor: Your sample size is now many items are in the sample, not how many samples you take. In this case, there were 6 containers in the sample.		 UCL
LCL
r-chart
CL
D3
D4
UCL
LCL

6-10

Problem 10
Number of Errors UCL CL LCL
1 4 0.00 0.00 0
2 5 0.00 0.00 0
3 6 0.00 0.00 0
4 6 0.00 0.00 0
5 3 0.00 0.00 0
6 2 0.00 0.00 0
7 6 0.00 0.00 0
8 7 0.00 0.00 0
9 3 0.00 0.00 0
10 4 0.00 0.00 0
11 3 0.00 0.00 0
12 4 0.00 0.00 0
Cbar
Zvalue
Sigma
LCL
UCL
Number of Errors 4 5 6 6 3 2 6 7 3 4 3 4 UCL 0 0 0 0 0 0 0 0 0 0 0 0 CL 0 0 0 0 0 0 0 0 0 0 0 0 LCL 0 0 0 0 0 0 0 0 0 0 0 0

Delta Case

Extra Credit
Since you do not know how many total units were processed to result in these errors (batches), you only
know the amount of errors per day each week, you will choose to use a c-chart for this set of data.
Standard Material
Week 1 Week 2 Week 3 Week 4 =SUM(B5:U5) =V5/4
Defect Type M T W TH F M T W TH F M T W TH F M T W TH F Total Avg/WK
Uneven edges
Cracks
Scratches
Air bubbles
Thickness variation
c-bar =AVERAGE(W5:W9)
z value 3
These limits will set the standard--then you are looking to see if the other material can meet this standard UCL
LCL
Super Plastic
Week 1 Week 2 Week 3 Week 4
Defect Type M T W TH F M T W TH F M T W TH F M T W TH F Total Avg/WK
Uneven edges
Cracks Compare these values
Scratches
Air bubbles
Thickness variation

Fill in data

PARETP

Since you do not know how many total units were processed to result in these errors (batches), you only
know the amount of errors per day each week, you will choose to use a c-chart for this set of data.
Standard Material Standard Material % Defective Super Plastic % Defective
Week 1 Week 2 Week 3 Week 4
Defect Type M T W TH F M T W TH F M T W TH F M T W TH F Total
Air bubbles 0 ERROR:#DIV/0! ERROR:#DIV/0!
Cracks 0 ERROR:#DIV/0! ERROR:#DIV/0!
Scratches 0 ERROR:#DIV/0! ERROR:#DIV/0!
Thickness variation 0 ERROR:#DIV/0! ERROR:#DIV/0!
Uneven edges 0 ERROR:#DIV/0! ERROR:#DIV/0!
0
Super Plastic
Week 1 Week 2 Week 3 Week 4
Defect Type M T W TH F M T W TH F M T W TH F M T W TH F Total Super Plastic % Defective
Cracks 0 ERROR:#DIV/0!
Air bubbles 0 ERROR:#DIV/0!
Uneven edges 0 ERROR:#DIV/0!
Thickness variation 0 ERROR:#DIV/0!
Scratches 0 ERROR:#DIV/0!
0
Standard Material % Defective Air bubbles Cracks Scratches Thickness variation Uneven edges 0 0 0 0 0 Super Plastic % Defective Air bubbles Cracks Scratches Thi ckness variation Uneven edges 0 0 0 0 0

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