### Statistical Process Control (SPC) Tools

```Statistical Process Control
(SPC) Tools
ISE 412
Spring 2014
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Why do we need SPC tools?
• We need Quality!
• With SPC, the process
is monitored through
sampling.
• Considering the results
of the sample, we can
prevent or improve
the our week point in
production lines.
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What do SPC tools monitor?
Process variability
 Random
o common causes
o inherent in a process
o can be eliminated only through improvements in the system
 No-Random
o special causes
o due to identifiable factors
o can be modified through operator or management action
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What are SPC tools?
1.
2.
3.
4.
5.
6.
7.
8.
Histogram
Check Sheet
Pareto Chart
Cause and Effect Diagram
Defect Concentration Diagram
Scatter Diagram
Control Chart
…
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What are SPC tools?
• Histogram
Example 1
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What are SPC tools?
• Check Sheet
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What are SPC tools?
• Pareto Chart
Example 2
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What are SPC tools?
• Cause and Effect Diagram (example3)
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What are SPC tools?
• Defect Concentration Diagram
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What are SPC tools?
• Scatter Diagram (example4)
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What are SPC tools?
• Control Charts!
Control Chart
35
Number
of Errors
30
UCL=28.0
25
20
Avg=16.0
15
10
5
0
LCL=4.0
5
10
15
20
Week
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Why Control Charts?
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What kinds of Control
Charts do we have?
• Attribute
– a product characteristic that can be evaluated with a
discrete response
– good – bad; yes – no 1. Fraction nonconforming (P-chart)
2.
# nonconforming per inspection (C-chart)
• Variable
– a product characteristic that is continuous and can be
measured
1. Range (R-chart)
– weight - length
2. Mean (x bar-chart)
3.
Variability (S-chart)
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Application of Control Charts
•
•
•
•
Outlier
Run
Trend
Cyclicity
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Process Capability Analysis
• Process capability is the ability of the process
to meet the design specifications for a service
or product.
• Nominal value is a target for design
specifications.
• Tolerance is an allowance above or below the
nominal value.
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Process Capability Analysis
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Process Capability Analysis
• Specification Limits
• Control Limits
• Natural Tolerance Limits
=  + 3
=  − 3
=
= /c4 or /d2
Example 5
Nominal
value
Lower
Limit
20
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Upper
Limit
25
30
18
Process Capability Ratios
• Process Capability Ratio, Cp:
the tolerance width divided by 6 standard deviations
(process variability).
Cp =
Upper specification - Lower specification
6
Example 5
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Process Capability Ratios
• One-side Process Capability Ratio:
−
=
3
−
=
3
Example 5
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Process Capability Ratios
Nominal
value
Lower
Limit
20
Upper
Limit
25
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Process Capability Ratios
Cp value could not indicate the proper process
capability if the process is not centered since
Cp does not account for where the process
mean is with respect to the specifications. To
alleviate this issue, another process capability
index, Cpk is used:
Cpk=min(Cpu,Cpl)
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Cp Vs Cpk
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Summary
SPC tools:
Capability Ratios:
Histogram, Check Sheet,
Pareto Chart, Cause and Effect
Diagram, Defect Concentration
Diagram, Scatter Diagram,
Control Chart, And so more
−
=
6
−
=
3
−
=
3
=  , }
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```