Solved Problem 3
Normal Distribution
<Back
Mean = 0
Std Dev = 1 -3.5 0.000873
-1.4 0.149727
z = 1.9 -0.7 0.312254
P(>x) = 0.02871656 0.7 0.312254
1.4 0.149727
P(two tail) = 0.05743312 2.1 0.043984
2.8 0.007915
3.5 0.000873
Normal Inverse 1.9 0
1.9 0.398942
Mean = 0
Std Dev = 1
P(two tail) = 0.02
z = 2.326347874
x = -2.326347874 2.326347874
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c-Chart
<Back
UCL = 7.8497 AVE = 3.9000 LCL = 0.0000
Average defects/unit 3.9 111.79937 7.8497 3.9000 0.0000 0
Calculations:
c
Average
Sample c
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19 Note: To display more data on the above graph, right click on the x-axis,
20 select Format Axis, and set Maximum to higher value.
21 The size of the graph may also be increased.
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2.00
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c-Chart
AVE = 3.9000
LCL = 0.0000
Clear
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0.14 p-Chart
LCL = 0.0008
Sample p’s
Clear
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Runs Tests
<Back
Number of observations 11
Median 21 Median = 21.0000
121.0000
Median U/D 20 21.0000
Expected runs E(r) = 6.5 7
Standard Deviatio
s = 1.58113883 1.278019301
Median 21
Sample Mean A/B U/D
122 A
217 B D
319 B U
425 A U
518 B D
620 B U
721 B U
817 B D
923 A U
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Runs Tests
Median = 21.0000 Sample Means
Clear
Actual Runs 5 6
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Solved Problem 6
Process Capability
<Back
Standard Process Specification
Process Deviation Capability Width Cp
A0.1 0.6 11.666666667
Non centered
Process Standard Lower Upper
Process Mean Deviation Specification Index Specification Index
Cpk
A7.5 0.1 71.666666667 81.666666667 1.666666667
Clear
Page 72
Chapter 10 – Problems 1-7 Note: This worksheet displays results only, you must copy the shaded
<Back area into the corresponding template to make additional calculations.
1a. Normal Distribution
Mean = 24.5
Std Dev = 0.2
x = 24
1b. Normal Inverse Mean Control Chart (s known)
Mean = 24.5 Average of sample means 24.5
Std Dev = 0.2 Process standard deviation s = 0.2
2. Mean Control Chart (s known)
Average of sample means 1
Process standard deviation s = 0.01
UCL = 1.004340181
LCL = 0.995659819
3. Mean Control Chart (s unknown) Range Control Chart
Average of sample means 3.1
Calculations: Calculations:
Mean Range Range
Average 3.1 0.45 Average 0.45
Sample Mean Range Sample Range
13.06 0.42 10.42
23.15 0.5 20.5
33.11 0.41 30.41
43.13 0.46 40.46
53.06 0.46 50.46
63.09 0.45 60.45
4. Mean Control Chart (s unknown) Range Control Chart
Average of sample means 79.96
Sample size n = 5 Sample size n = 5
UCL = 81.04266667 UCL = 3.93867
LCL = 78.87733333 LCL = 0
Calculations: Calculations:
Sample size n = 20 Sample size n = 25
UCL = 3.181 UCL = 0.7155
LCL = 3.019 LCL = 0.1845
Mean Range Range
Average 79.96 1.866666667 Average 1.866666667
Sample Mean Range Sample Range
179.48 2.6 12.6
280.14 2.3 22.3
479.6 1.7 41.7
580.02 2 5 2
680.38 1.4 61.4
5. p-Chart
Average proportion 0.025 0.025 0.02
Sample size n = 200 n = 200 n = 200
Calculations: Note: decrement z to achieve desires control limits.
p
Average 0.025
Sample p
10.02
20.01
30.025
40.045
6. p-Chart p-Chart
380.14 1.2 31.2
Average proportion 0.009615385 Average proportion 0.0075
UCL = 0.023416058 UCL = 0.0197
LCL = 0 LCL = 0
Calculations: Calculations:
p p
Average 0.009615385 Average 0.0075
Sample p Sample p
10.005 10.005
20.01 20.01
30.01 30.01
4 0 4 0
50.01 50.01
60.005 60.005
70.01 70.01
8 0 8 0
90.01 90.01
10 0.035 10 0.015
11 0.015 11 0.01
12 0.01 12 0.005
13 0.005
7. c-Chart
Average defects/unit 7.857142857
Sample size n = 200 Sample size n = 200