1. Statistical Process Control (SPC)
By WEI ZHENGTAI
School of Electrical and Electronics Engineering(Power), Nanyang Technological University
Diploma in Mechatronics Engineering with MERIT(Wafer Fabrication), Nanyang Polytechnic

2. Contents
 Why SPC
 SPC-4M+1E
 Terminology
 Control Charts
 Process Improvement Tool: 6σ
 How to Derive Control Limits
 Reference

3. Why SPC
 Maintain good product quality
 Control the production costs(rejection costs included)
 Provide clear objectives and reduce workloads
 Easier to detect machine fault and helps in condition-based maintenance
 Production personnel will gain awareness
 Gain good business reputation among the customers
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4. SPC-4M + 1E
 Man
 Machine
 Method
 Material
 Environment
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5. Terminology
 Max, Min, Mean
 Range=𝑋 𝑚𝑎𝑥-𝑋 𝑚𝑖𝑛
 MR=𝑋n+i-𝑋 𝑛
 Standard Deviation
 Variance=
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6. Terminology (Cont’d)
 CL(Control Limit),UCL(Upper Control Limit) and LCL(Lower Control Limit)
 𝑋 chart:
UCL= 𝑋+3σ= 𝑋+𝐴2 𝑅
LCL= 𝑋-3σ= 𝑋-𝐴2 𝑅 (𝐴2=defined factors used in calculating the control limits)
CL= 𝑋
 R chart:
UCL= 𝑅+3σ=𝐷4 𝑅
LCL= 𝑅–3σ=𝐷3 𝑅 (𝐷4 and 𝐷3 is defined factors used in calculating the control
limits)
CL= 𝑅
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7. Terminology (Cont’d)
 SL(Specification Limit), USL(Upper Specification Limit) and LSL(Lower Specification Limit)
 PC(Process Capability)=6σ
 Cp(Capability of Potential Process),Cpk,Cpl(Z(L)),Cpu(Z(U)),Cmk(Machine) and Cr
- Cp=
𝑈𝑆𝐿−𝐿𝑆𝐿
6𝜎
If 6σ<specification tolerances => Cp > 1
If 6σ=specification tolerances => Cp = 1
If 6σ>specification tolerances => Cp < 1
- Cmk=
𝑈𝑆𝐿−𝐿𝑆𝐿
8𝜎
- Cr=𝐶𝑝−1
- Cpl=
𝑥−𝐿𝑆𝐿
3𝜎
- Cpu=
𝑈𝑆𝐿− 𝑥
3𝜎
- Cpk=Min(Cpl,Cpu)=Cp(1-K), whereK =
|𝑀− 𝑥|
(𝑈𝑆𝐿−𝐿𝑆𝐿)/2
, 𝑀 = (𝑈𝑆𝐿 + 𝐿𝑆𝐿)/2
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8. Control Charts
 Variable Control Charts
- Measurement is critical
- Precision required
- Accurate test devices
- 1 characteristics
- Example:Xbar-R, Xbar-S, CuSum charts
 Attribute Control Charts
- Measurement is not possible
- Measurement is time consuming
- > 1 characteristics
-Example: np, c and u charts
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9. Control Charts (Cont’d)
 Xbar-R charts (average-range)
- Average : variability between samples
– Range: variability within samples
 np Control Chart
- Determine the defective items produced by a process
- Constant sample size
- Steps
1.Gather data :
Determine sample size (n)
Determine sampling frequency or subgroup, (k)
Determine total no. of samples (n x k)
Record the no. of non-conforming units for each sample group.
2.Calculate process average number of non-conforming p
3.Calculate the Control limits
4.Plot the np chart.
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10. Control Charts (Cont’d)
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 np Control Chart Calculation

11. Control Charts (Cont’d)
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 p Control Chart
- Determines the fraction or percentage of
defective, whereas the np control chart
determines the number of defective
- When the number of samples per
subgroup is constant or when the number of
samples per subgroup varies
- Preferred where more people seemed to
be able to conceptualized as the data are in
terms of percentage defective.

12. Control Charts (Cont’d)
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 p Control Chart Calculation

13. Process Improvement Tool: 6σ
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 Introduced by Engineer Bill Smith in 1986, accepted by most of the large
companies
 Keep improving the product and make its behaviour stable
 Provide important data as a reference of important strategy
 Methods(DMAIC for business process and DMADV/RDMADV/DFSS for
manufacturing and design)
- R:Recognition
- D:Define
- M:Measure
- A:analyse
- D:Design - I:Improve
- V:Verify - C:Control
DFSS: Design for six Sigma

14. Process Improvement Tool: 6σ(Cont’d)
σ Level Defects Per Million
Opportunities(DPMO)
Yield(%)
1 690,000 30.85
2 308,000 69.15
3 66,810 93.32
4 6,210 99.38
5 230 99.977
6 3.4 99.99966
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15. How to Derive Control Limits
 Steps
① Identify the characteristics we need to control
② Select the sample size
③ Data collection
④ Select chart type
⑤ Calculation
⑥ Generate the chart
⑦ Cooperate with operators and seek improvement
⑧ If the situation is not improved, analyse the problem and repeat the previous
steps
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16. Reference
 Course Notes:
Topic 6, EGB205 Quality Assurance, Diploma in Mechatronics Engineering, School
of Engineering, Nanyang Polytechnic
 Internship (Globalfoundries)
 Google Open Search: Six Sigma
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