Operation Management

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Mean and Range

Template for Mean and Range Charts
Sample Number Obs 1 Obs 2 Obs 3 Obs 4 Obs 5 X-bar Range x-bar range
1 1010.00 991.00 985.00 986.00 993.00 25.00 993 25
2 995.00 996.00 1009.00 994.00 998.50 15.00 998.5 15
3 990.00 1003.00 1015.00 1008.00 1004.00 25.00 1004 25
4 1015.00 1020.00 1009.00 998.00 1010.50 22.00 1010.5 22
5 1013.00 1019.00 1005.00 993.00 1007.50 26.00 1007.5 26
6 994.00 1001.00 994.00 1005.00 998.50 11.00 998.5 11
7 989.00 992.00 982.00 1020.00 995.75 38.00 995.75 38
8 1001.00 986.00 996.00 996.00 994.75 15.00 994.75 15
9 1006.00 989.00 1005.00 1007.00 1001.75 18.00 1001.75 18
10 992.00 1007.00 1006.00 979.00 996.00 28.00 996 28
11 996.00 1006.00 997.00 989.00 997.00 17.00 997 17
12 1019.00 996.00 991.00 1011.00 1004.25 28.00 1004.25 28
13 981.00 991.00 989.00 1003.00 991.00 22.00 991 22
14 999.00 993.00 988.00 984.00 991.00 15.00 991 15
15 1013.00 1002.00 1005.00 992.00 1003.00 21.00 1003 21
0 0.00 0.00 0 0
0 0.00 0.00 0 0
0 0.00 0.00 0 0
0 0.00 0.00 0 0
0 0.00 0.00 0 0
0 0.00 0.00 0 0
0 0.00 0.00 0 0
0 0.00 0.00 0 0
0 0.00 0.00 0 0
0 0.00 0.00 0 0
999.10 21.73
X-bar Chart Control limit graph coordinates
1014.96 = Upper Control Limit X-bar Chart Range Chart
999.10 = Centerline UCL: 1014.96 0 UCL: 49.54 0
983.24 = Lower Control Limit 1014.96 15 49.54 15
Range Chart C-line: 999.10 0 C-line: 21.73 0
49.54 = Upper Control Limit 999.10 15 21.73 15
21.73 = Centerline
0.00 = Lower Control Limit LCL: 983.24 0 LCL: 0.00 0
983.24 15 0.00 15
Factors
0.73 = A2
0 = D3
2.28 = D4

Mean and Range
X-bar
Upper Control Limit
Lower Control Limit
Centerline
X-bar Chart

Proportion
Range
Upper Control Limit
Lower Control Limit
Centerline
Range Chart

CapabilityIndex

Template: Control Chart for Proportion
Sample Sample Size Number of Defects in Sample Proportion Defective
1 15 3 0.20 0.2
2 15 1 0.07 0.0666666667
3 15 0 0.00 0
4 15 0 0.00 0
5 15 0 0.00 0
6 15 2 0.13 950 0.1333333333
7 15 0 0.00 0
8 15 3 0.20 0.2
9 15 1 0.07 0.0666666667
10 15 0 0.00 0
0 0.00 0
0 0.00 0
0 0.00 0
0 0.00 0
0 0.00 0
150 10
Confidence Level: 95.0%
Control limit graph coordinates
0.0667 = Average proportion defective UCL: 0.192 0
0.064 = Std. Dev of proportion defective 0.192 10
0.192 = Upper Control Limit (UCL) LCL: 0.000 0
0.000 = Lower Control Limit (LCL) 0.000 10
Center Line: 0.0667 0
0.0667 10

CapabilityIndex
Proportion defective
Upper control limit
Lower control limits
CenterLine
Sample Number
Proportion Defective
P-Chart

Factors

Capability Index
Process Mean m 100
Tolerance e 10
Sample Mean x-bar 92
Standard Deviation σ 4
Lower Tolerance Limit LTL 90
Upper Tolerance Limit UTL 110
Cpk 0.1667

Factors

0
X
0

Sheet1

Exhibit TN8.7 Factor for Determining 3-Sigma Limits for R-bar and x-bar Charts
Factor for R Chart
Number of Observations in Subgroup Factor for x-bar Chart Lower Control Limit Upper Control Limit
n A2 D3 D4
2 1.88 0.00 3.27
3 1.02 0.00 2.57
4 0.73 0.00 2.28
5 0.58 0.00 2.11
6 0.48 0.00 2.00
7 0.42 0.08 1.92
8 0.37 0.14 1.86
9 0.34 0.18 1.82
10 0.31 0.22 1.78
11 0.29 0.26 1.74
12 0.27 0.28 1.72
13 0.25 0.31 1.69
14 0.24 0.33 1.67
15 0.22 0.35 1.65
16 0.21 0.36 1.64
17 0.20 0.38 1.62
18 0.19 0.39 1.61
19 0.19 0.40 1.60
20 0.18 0.41 1.59