1. Chapter 10
Quality Control

2. Phases of Quality Assurance
Figure 10-1
Acceptance
sampling
Process
control
Continuous
improvement
Inspection
before/after
production
Corrective
action during
Quality built
into the
process
The least
progressive
The most
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Chapter 10 Quality Control

3. Chapter 10 Quality Control
The Process (1 of 2)
Over time, the output of any process shows a certain amount of natural or inherent variability
This is also referred to as random variability
It is due to countless minor factors and is assumed to be out of management’s control in the short run, i.e., you have to live with it
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4. Chapter 10 Quality Control
The Process (2 of 2)
The distribution of a process’ output has a mean, , and a standard deviation, ; it can have a wide variety of shapes
Process distribution
Mean
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5. Process Capability (1 of 3)
When selecting a process to perform an operation, the inherent variability of process output should be compared to the range or tolerances allowed by the designer’s specifications
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6. Process Capability (2 of 3)
process distribution
Lower Specification
Upper Specification
Much of the process output fits within specification width
In other words, is the process capable of producing the item
within specifications?
Almost all of the process output fits within the specification width
A significant portion of the process output falls outside of the specification width
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7. Process Capability (3 of 3)
The process capability index (cp) compares the design specifications with a measure of process variability
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8. Chapter 10 Quality Control
Three-Sigma Quality
Lower
design specification
Upper
1350 ppm
1350 ppm
+3 Sigma
-3 Sigma
mean
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9. Three-Sigma Quality vs. Six-Sigma Quality
Lower
design specification
Upper
1350 ppm
1350 ppm
+3 Sigma
-3 Sigma
mean
1.7 ppm
1.7 ppm
+6 Sigma
-6 Sigma
mean
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Chapter 10 Quality Control

10. Chapter 10 Quality Control
Normal Distribution
Figure 10-5




Mean
95.5%
99.7%
Standard deviation
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Chapter 10 Quality Control

11. Chapter 10 Quality Control
Process Control (1 of 6)
Once a process is in operation, a goal is to maintain the status quo, i.e., keep the process “in control”
What can make the process no longer be in control, i.e., go “out of control”?
The presence of an assignable cause
The presence of an assignable cause may cause the process distribution to
shift to the left or right, and/or
increase the variability (flatten out)
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12. Chapter 10 Quality Control
Process Control (2 of 6)
If the process mean shifts, more of output falls outside the specifications
upper design
specification
Time
lower design
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13. Chapter 10 Quality Control
Process Control (3 of 6)
If the process mean shifts, more of output falls outside the specifications
If process variance increases, more of the output falls outside of the specifications
Time
upper design
specification
lower design
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14. Chapter 10 Quality Control
Process Control (4 of 6)
In either case, the process is considered to be out of control
It should be stopped, investigated (the assignable cause found if present) and corrected (the process brought back to the status quo)
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15. Chapter 10 Quality Control
Process Control (5 of 6)
Examples of assignable causes include
operator
raw material
equipment
environment
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16. Chapter 10 Quality Control
Process Control (6 of 6)
How does management detect the presence of an assignable cause?
Process output is monitored to detect any changes by inspecting the output of the process
Inspection means assessing some characteristic of a unit of output
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17. Chapter 10 Quality Control
Inspection Issues
Figure 10-2
How Much/How Often
Where/When
Centralized vs. On-site
Inputs
Transformation
Outputs
Acceptance
sampling
Process
control
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Chapter 10 Quality Control

18. Optimal Amount of Inspection
Figure 10-3
Cost of passing
defectives
Total Cost
Cost
Cost of inspection
Inspection Effort
Optimal Amount of Inspection
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Chapter 10 Quality Control

19. Where to Inspect in the Operations System
Raw materials and purchased parts
Finished products
Before a costly operation
Before an irreversible process
Before a covering process
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Chapter 10 Quality Control

20. Examples of Inspection Points
Table 10-1
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Chapter 10 Quality Control

21. Chapter 10 Quality Control
Inspection Options
100% inspection of the process output
can be costly and/or time consuming
inspection may alter or destroy unit
Sample from the process output
referred to as statistical process control (SPC)
based on the Central Limit Theorem
error possible when deciding if the process is in control
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22. Overview of the Statistical Quality Control (QC) Process
Sample
of size n
Process
Output
Inspect Each Item in the Sample
IN CONTROL
Sample
Information
Compare
OUT OF CONTROL
Decision
Criteria
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Chapter 10 Quality Control

23. Chapter 10 Quality Control
Central Limit Theorem
The distribution of sample means tend to be normally distributed even though the process distribution is not normal
The mean of the distribution sample means (x) is equal to the mean of the process distribution( )
The standard deviation of the distribution of sample means ( ) is equal to the standard deviation of the process distribution( ) divided by
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24. Chapter 10 Quality Control
Process Distribution
Process distribution
Measure
lower
design
specification
upper
design
specification
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Chapter 10 Quality Control

25. Sampling Distribution
Process distribution
Sample Statistic
lower
design
specification
upper
design
specification
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Chapter 10 Quality Control

26. Statistical Process Control (1 of 3)
Primary purpose is to decide when the process output may be affected by an assignable cause
The decision is based on
an indicator of the status of the output of a process (sample statistic)
the criteria placed on the distribution of the sample statistic (control limits)
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27. Sampling Distribution
Figure 10-4
Sampling distribution
Process distribution
Lower control limit
Upper control limit
lower
design
specification
upper
design
specification
sample statistic
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28. Chapter 10 Quality Control
Control Chart (1 of 5)
This information is typically displayed as a control chart
upper control limit
Time
Sample
Statistic
Sampling
distribution
central
line
lower
control limit
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29. Chapter 10 Quality Control
Control Chart (2 of 5)
After a sample is taken and inspected, the resulting sample statistic is computed and plotted
upper control limit
Sample
Statistic
central
line
lower
control limit
Time
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30. Chapter 10 Quality Control
Control Chart (3 of 5)
If the sample statistic falls between the control limits, the process is considered to be in control
upper control limit
Sample
Statistic
central
line
lower
control limit
Time
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31. Chapter 10 Quality Control
Control Chart (4 of 5)
If the sample statistic falls outside the control limits, the process is considered to be out of control
upper control limit
Sample
Statistic
central
line
lower
control limit
Time
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32. Chapter 10 Quality Control
Control Chart (5 of 5)
Under this arrangement, there is the possibility of making an error in determining the process’s status
upper control limit
Time
Sample
Statistic
Probability of deciding the
process is out of control
when it is still in control
Sampling
distribution
central
line
lower
control limit
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33. Possible Errors When Sampling (A Summary)
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34. Statistical Process Control (3 of 3)
Control charts for the two inspection methods will be examined
Two control charts for variables inspection
sample means chart (x-bar chart)
sample range chart (R chart)
One control chart for attributes inspection
sample proportion defective chart (p chart)
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35. Control Charts for Variables (1 of 3)
A sample of size n is taken from the process output
Each unit in the sample is inspected a variables basis
Measurement of the specified value is taken on a continuous scale
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36. Chapter 10 Quality Control
Variables (2 of 3)
These data are used to calculate two sample statistics
sample mean, x (the sum of measurement of each unit in the sample divided by n)
sample range, R, (the highest measurement in the sample minus the lowest measurement in the sample)
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37. Chapter 10 Quality Control
Variables (3 of 3)
In this case two separate control charts are used to monitor two different aspects of the process output
central tendency
variability
The central tendency of the output is monitored using the x-chart
The variability of the output is monitored using the R-chart
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38. Chapter 10 Quality Control
x-Chart
The central line is x, the sum of a number of sample means collected while the process was considered to be “in control” divided by the number of samples
The lower control limit is x - A2R
The upper control limit is x + A2R
Factor A2 is based on sample size
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39. Chapter 10 Quality Control
x-Chart
If the process distribution standard deviation, , or variance, is given, the upper and lower control limits can be calculated using
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40. Chapter 10 Quality Control
R (range)-Chart
The 3 lower control limit is D3R
The 3 upper control limit is D4R
Factors D3 and D4 are based on sample size
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41. Chapter 10 Quality Control
Mean and Range Charts
process mean is shifting upward
Shift Detected
No shift detected
Figure 10-10A
Process
Distribution
UCL
LCL
x-Chart
UCL
LCL
R-chart
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42. Chapter 10 Quality Control
Mean and Range Charts
process variability is increasing
Figure 10-10B
No shift detected
Increase detected
Process
Distribution
UCL
LCL
x-Chart
UCL
LCL
R-chart
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43. Control Chart for Attributes (1of 3)
A sample of size n is taken from the process output
Each unit in the sample is inspected a attributes basis
A unit is classified in one of two categories
good or bad
pass or fail
operates or doesn’t operate
does or does not meet design specifications
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44. Chapter 10 Quality Control
Attributes (2 of 3)
These data are used to calculate the sample statistic
sample percentage defective, p (the number of units found to be defective in that sample divided by n)
Although the distribution of sample statistic follows a binomial distribution, that distribution can be approximated by a normal distribution with a mean of and a standard deviation of
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45. Chapter 10 Quality Control
Attributes (3 of 3)
The lower control limit is
The upper control limit is
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46. Chapter 10 Quality Control
Use of c-Charts
Use only when the number of occurrences per unit of measure can be counted; nonoccurrences cannot be counted.
Scratches, chips, dents, or errors per item
Cracks or faults per unit of distance
Breaks or Tears per unit of area
Bacteria or pollutants per unit of volume
Calls, complaints, failures per unit of time
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