1. Statistical Process Control
Douglas M. Stewart, Ph.D.
The Anderson Schools of Management
The University of New Mexico

2. Quality Control (QC)
Control – the activity of ensuring conformance to requirements and taking corrective action when necessary to correct problems
Importance
Daily management of processes
Prerequisite to longer-term improvements

3. Designing the QC System
Quality Policy and Quality Manual
Contract management, design control and purchasing
Process control, inspection and testing
Corrective action and continual improvement
Controlling inspection, measuring and test equipment (metrology, measurement system analysis and calibration)
Records, documentation and audits

4. Example of QC: HACCP System
Hazard analysis
Critical control points
Preventive measures with critical limits for each control point
Procedures to monitor the critical control points
Corrective actions when critical limits are not met
Verification procedures
Effective record keeping and documentation

5. Inspection/Testing Points
Receiving inspection
In-process inspection
Final inspection

6. Receiving Inspection Spot check procedures 100 percent inspection
Acceptance sampling

7. Acceptance Sampling Lot received for inspection
Sample selected and analyzed
Results compared with acceptance criteria
Accept the lot
Send to production
or to customer
Reject the lot
Decide on disposition

8. Pros and Cons of Acceptance Sampling
Arguments for:
Provides an assessment of risk
Inexpensive and suited for destructive testing
Requires less time than other approaches
Requires less handling
Reduces inspector fatigue
Arguments against:
Does not make sense for stable processes
Only detects poor quality; does not help to prevent it
Is non-value-added
Does not help suppliers improve

9. In-Process Inspection
What to inspect?
Key quality characteristics that are related to cost or quality (customer requirements)
Where to inspect?
Key processes, especially high-cost and value-added
How much to inspect?
All, nothing, or a sample

10. If p > C1 / C2 , use 100% inspection
Economic Model
C1 = cost of inspection and removal of
nonconforming item
C2 = cost of repair
p = true fraction nonconforming
Breakeven Analysis: p*C2 = C1
If p > C1 / C2 , use 100% inspection
If p < C1 / C2 , do nothing

11. Human Factors in Inspection
complexity
defect rate
repeated inspections
inspection rate
Inspection should never be a means of assuring quality. The purpose of inspection should be to gather information to understand and improve the processes that produce products and services.

12. Gauges and Measuring Instruments
Variable gauges
Fixed gauges
Coordinate measuring machine
Vision systems

13. Examples of Gauges

14. Metrology - Science of Measurement
Accuracy - closeness of agreement between an observed value and a standard
Precision - closeness of agreement between randomly selected individual measurements

15. Repeatability and Reproducibility
Repeatability (equipment variation) – variation in multiple measurements by an individual using the same instrument.
Reproducibility (operator variation) - variation in the same measuring instrument used by different individuals

16. Repeatability and Reproducibility Studies
Quantify and evaluate the capability of a measurement system
Select m operators and n parts
Calibrate the measuring instrument
Randomly measure each part by each operator for r trials
Compute key statistics to quantify repeatability and reproducibility

17. Reliability and Reproducibility Studies(2)

18. Reliability and Reproducibility Studies(3)

19. R&R Constants Number of Trials 2 3 4 5 K1 4.56 3.05 2.50 2.21
Number of Operators K2
3.65
2.70
2.30
2.08

20. R&R Evaluation Under 10% error - OK 10-30% error - may be OK
over 30% error - unacceptable

21. R&R Example
R&R Study is to be conducted on a gauge being used to measure the thickness of a gasket having specification of 0.50 to 1.00 mm. We have three operators, each taking measurement on 10 parts in 2 separate trials.

23. Calibration
Calibration - comparing a measurement device or system to one having a known relationship to national standards
Traceability to national standards maintained by NIST, National Institute of Standards and Technology

24. Statistical Process Control (SPC)
A methodology for monitoring a process to identify special causes of variation and signal the need to take corrective action when appropriate
SPC relies on control charts

25. Common Causes
Special Causes

26. Histograms do not take into account changes over time.
Control charts can tell us when a process changes

27. Control Chart Applications
Establish state of statistical control
Monitor a process and signal when it goes out of control
Determine process capability

28. Commonly Used Control Charts
Variables data
x-bar and R-charts
x-bar and s-charts
Charts for individuals (x-charts)
Attribute data
For “defectives” (p-chart, np-chart)
For “defects” (c-chart, u-chart)

29. Developing Control Charts
Prepare
Choose measurement
Determine how to collect data, sample size, and frequency of sampling
Set up an initial control chart
Collect Data
Record data
Calculate appropriate statistics
Plot statistics on chart

31. Next Steps Determine trial control limits
Center line (process average)
Compute UCL, LCL
Analyze and interpret results
Determine if in control
Eliminate out-of-control points
Recompute control limits as necessary

36. Typical Out-of-Control Patterns
Point outside control limits
Sudden shift in process average
Cycles
Trends
Hugging the center line
Hugging the control limits
Instability

37. Shift in Process Average

38. Identifying Potential Shifts

39. Cycles

40. Trend

41. Final Steps Use as a problem-solving tool Compute process capability
Continue to collect and plot data
Take corrective action when necessary
Compute process capability

42. Process Capability
Capability Indices

43. Process Capability (2)

44. Capability Versus Control
Capable
Not Capable
In Control Out of Control
IDEAL

45. Process Capability Calculations

46. Excel Template

48. Special Variables Control Charts
x-bar and s charts
x-chart for individuals

53. Charts for Attributes Fraction nonconforming (p-chart)
Fixed sample size
Variable sample size
np-chart for number nonconforming
Charts for defects
c-chart
u-chart

64. Control Chart Selection
Quality Characteristic
variable
attribute
defective
defect no
n>1?
x and MR
constant
sampling
unit?
yes
constant
sample
size?
yes
p or np no
n>=10 or
computer?
x and R
yes no no
yes
p-chart with
variable sample
size
c u
x and s

65. Control Chart Design Issues
Basis for sampling
Sample size
Frequency of sampling
Location of control limits

67. Pre-Control nominal value Green Zone Yellow Zones Red Zone LTL UTL
Good for machining, but only when Cp is 1.14
Initiate mfg run:
5 consecutive must fall in green zone, if not reevaluate setup.
Sample a part. If green continue. If yellow sample another. If second is green continue, and if not look for special cause. If any part is red look for special cause.
Sample rate is time between out of control divided by 6.

68. SPC Implementation Requirements
Top management commitment
Project champion
Initial workable project
Employee education and training
Accurate measurement system