Statistical Process Control
(SPC) Tools
ISE 412
Spring 2014
ISE 412 Spring 2014
1
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.
ISE 412 Spring 2014
2
ISE 412 Spring 2014
3
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
ISE 412 Spring 2014
4
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
…
ISE 412 Spring 2014
5
What are SPC tools?
• Histogram
Example 1
ISE 412 Spring 2014
6
What are SPC tools?
• Check Sheet
ISE 412 Spring 2014
7
What are SPC tools?
• Pareto Chart
Example 2
ISE 412 Spring 2014
8
What are SPC tools?
• Cause and Effect Diagram (example3)
ISE 412 Spring 2014
9
What are SPC tools?
• Defect Concentration Diagram
ISE 412 Spring 2014
10
What are SPC tools?
• Scatter Diagram (example4)
ISE 412 Spring 2014
11
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
ISE 412 Spring 2014
12
Why Control Charts?
ISE 412 Spring 2014
13
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)
ISE 412 Spring 2014
14
Application of Control Charts
•
•
•
•
Outlier
Run
Trend
Cyclicity
ISE 412 Spring 2014
15
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.
ISE 412 Spring 2014
16
Process Capability Analysis
ISE 412 Spring 2014
17
Process Capability Analysis
• Specification Limits
• Control Limits
• Natural Tolerance Limits
𝑈𝑁𝑇𝐿 = 𝜇 + 3𝜎
𝐿𝑁𝑇𝐿 = 𝜇 − 3𝜎
𝜇=
𝜎= /c4 or /d2
Example 5
Nominal
value
Lower
Limit
20
ISE 412 Spring 2014
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
ISE 412 Spring 2014
19
Process Capability Ratios
• One-side Process Capability Ratio:
𝑈𝑆𝐿 − 𝜇
𝐶𝑝𝜐 =
3𝜎
𝜇 − 𝐿𝑆𝐿
𝐶𝑝𝑙 =
3𝜎
Example 5
ISE 412 Spring 2014
20
Process Capability Ratios
Nominal
value
Lower
Limit
20
Upper
Limit
25
ISE 412 Spring 2014
30
21
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)
ISE 412 Spring 2014
22
Cp Vs Cpk
ISE 412 Spring 2014
23
Summary
SPC tools:
Capability Ratios:
Histogram, Check Sheet,
Pareto Chart, Cause and Effect
Diagram, Defect Concentration
Diagram, Scatter Diagram,
Control Chart, And so more
𝑈𝑆𝐿 − 𝐿𝑆𝐿
𝐶𝑝 =
6𝜎
𝑈𝑆𝐿 − 𝜇
𝐶𝑝𝑢 =
3𝜎
𝜇 − 𝐿𝑆𝐿
𝐶𝑝𝑙 =
3𝜎
𝐶𝑝𝑘 = 𝑚𝑖𝑛 𝐶𝑝𝑢, 𝐶𝑝𝑙}
ISE 412 Spring 2014
24