1. Basic Training for Statistical Process Control
12/5/2018
Basic Training for Statistical Process Control
Process Capability & Measurement System Capability Analysis
Process Capability Analysis

2. Process Capability Analysis
Outline
Process Capability
Natural Tolerance Limits
Histogram and Normal Probability Plot
Process Capability Indices Cp
Cpk
Cpm & Cpkm
Measurement System Capability
Using Control Charts
Using Factorial Experiment Design (ANOVA)
Hands On Measurement System Capability Study
12/5/2018
Process Capability Analysis

3. Process Capability Analysis
Process Capability Analysis (PCA)
Is only done when the process is in a state of Statistical Control
Meaning: NO SPECIAL CAUSES are present
Process does not have to be centered to do PCA
Yield will improve if process is centered, but the value is in knowing what / where to improve the process
PCA is done periodically when the process has been operating in a state of statistical control
Allows for measuring improvement over time
Allows for marketing your competitive edge
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Process Capability Analysis

4. Process Capability - Timing
Reduce Variability
Identify Special Causes - Good (Incorporate)
Improving Process Capability and Performance
Characterize Stable Process Capability
Head Off Shifts in Location, Spread
Identify Special Causes - Bad (Remove)
Continually Improve the System
Process Capability Analysis is performed when there are NO special causes of variability present – ie. when the process is in a state of statistical control, as illustrated at this point.
Time
Center the Process
LSL  USL
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Process Capability Analysis

5. Process Capability Analysis
Process Capability is INDEPENDENT of product specifications
Most specifications are set without regard for process capability
However, understanding process capability helps the engineer to set more reasonable specifications
PCA reflects only the Natural Tolerance Limits of the process
PCA is done by examining the process
Histogram
Normal Probability Plot
12/5/2018
Process Capability Analysis

6. Natural Tolerance Limits
The natural tolerance limits assume:
The process is well-modeled by the Normal Distribution
Three sigma is an acceptable proportion of the process to yield
The Upper and Lower Natural Tolerance Limits are derived from:
The process mean () and
The process standard deviation ()
Equations:
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Process Capability Analysis

7. Natural Tolerance Limits
+2
-2
+3 or UNTL
-3 or
LNTL + -
The Natural Tolerance Limits cover 99.73% of the process output
  1 :68.26% of the total area
  2 :95.46% of the total area
  3 :99.73% of the total area
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Process Capability Analysis

8. PCA: Histogram Construction
Verify rough shape and location of histogram
Symmetric (roughly bell-shaped)
Mean = median = mode
Quickly confirm applicability prior to statistical analysis
Can be very hard to distinguish a Normal Distribution from a t-Distribution
Sometimes even a Normal distribution doesn’t look normal
More data and columns (bins) can make a difference
Verify location of process with respect to Specifications
Quick inspection will show what to do to improve the process
12/5/2018
Process Capability Analysis

9. PCA: Normal Probability Plot
A Normal Plot better clarifies whether the distribution is Normal by a visual inspection for:
Non-random patterns (non-Normal)
Fat Pencil Test (Normal if passes) C u m F r e q X
12/5/2018
Process Capability Analysis

10. PCA: Parameter Estimation
The Normal Plot mid-point estimates the process mean
The slope of the “best fit” line for the Normal Plot estimates the standard deviation
Choose the 25th and 75th percentile points to calculate the slope
The Histogram mode should be close to the mean
The range/d2 (from Histogram) should be close to the standard deviation
Can also estimate standard deviation by subtracting 50th percentile from the 84th percentile of the Histogram
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Process Capability Analysis

11. Process Capability Indices
Cp:
Measures the potential capability of the current process - if the process were centered within the product specifications
Two-sided Limits:
One-sided Limit:
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Process Capability Analysis

12. Cp Relation to Process Fallout
Recommended Minimum Ratios: (D. C. Montgomery, 2001)
Existing Process (1-sided) 1.33 (2-sided)
Existing, Safety / Critical Parameter
New Process
New, Safety / Critical Parameter
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Process Capability Analysis

13. Process Capability Indices
Cpk:
Measures actual capability of current process - at its’ current location with respect to product specifications
Formula:
Where:
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Process Capability Analysis

14. Process Capability Indices
Regarding Cp and Cpk:
Both assume that the process is Normally distributed
Both assume that the process is in Statistical Control
When they are equal to each other, the process is perfectly centered
Both are pretty common reporting ratios among vendors and purchasers
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Process Capability Analysis

15. Process Capability Indices
Two very different processes can have identical Cpk values, though:
because spread and location interact!
USL
LSL
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Process Capability Analysis

16. Process Capability Indices
Cpm:
Measures the current capability of the process - using the process target center point within the product specifications in the calculation
Formula:
Where target T is:
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Process Capability Analysis

17. Process Capability Indices
Cpkm:
Similar to Cpm - just more sensitive to departures from the process target center point
Not really in very common use
Formula:
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Process Capability Analysis

18. Measurement System Capability
Examines the relative variability in the product and measurement systems, together
Total variation is the result of
Product variation
Gage variation
Operator variation gaging system variation
Random variation
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Process Capability Analysis

19. Measurement System Analysis
Measurement system can be assessed by
X-bar and R-Charts
Using a single part as the rational subgroup
Is easy to visualize
Requires alternate interpretation of the control charts
Designed Experiments
Using Analysis of Variance
Allows assessment of part x operator interactions
Is statistically complex to compute & analyze
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Process Capability Analysis

20. Process Capability Analysis
X-Bar & R-Chart Method
Have each operator measure the same part twice - so the part becomes the rational sample unit
Parts should be representative of those to be measured
Use a sample of parts
Use a representative set of operators
Either collect data from every operator, or
Randomly select from the set of operators
Collect data under representative conditions
Carefully specify and control the conditions for measurement
Randomly sequence the combination of parts and operators
Preserve the time-order of the collected data & note observations
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Process Capability Analysis

21. Process Capability Analysis
X-Bar & R-Chart Method
If each operator measures the same part twice:
Variation between samples is plotted on the X-Chart
Out of control points indicate success in identifying differences between parts
Variation within samples is plotted on the R-Chart
Centerline of R-Chart is the magnitude of the gage variation
Out of control points indicate excessive operator to operator variation (fix with training?)
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Process Capability Analysis

22. Process Capability Analysis
X-Bar & R-Chart Method
R - Control Chart
LCL
UCL
Sample Number R
X-Bar Control Chart x
Out of control points indicate ability to distinguish between product samples (Good)
Out of control points indicate inability of operators to use gaging system (Bad)
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Process Capability Analysis

23. Process Capability Analysis
X-Bar & R-Chart Method
Precision to Tolerance Ratio (P/T):
“Rule of Ten”:
The measurement device should be at least ten times more accurate than the smallest measurement
Calculations: and
Interpretation:
Resulting ratio should be 0.10 or smaller if the gage is truly capable
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Process Capability Analysis

24. X-Bar & R-Chart Method: R & R
Repeatability:
Inherent precision of the gage
Reproducibility:
Variability of the gage under differing conditions
Environment
Operator
Time …
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Process Capability Analysis

25. X-Bar & R-Chart Method: R & R
Process is the same as before ( parts, …):
But we estimate the Repeatability from the Range Mean computed across all the operators and all parts:
And we estimate the Reproducibility from the Range of variability across all operators for each individual part:
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Process Capability Analysis

26. X-Bar & R-Chart Method: R & R
What to do with the information?
More variation is bad, so…
If the reproducibility variation is larger, improve the operators
If the repeatability variation is larger, improve the gaging instrument
Hands-On Experiment
Micrometer Study
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Process Capability Analysis

27. Gage Capability Analysis: ANOVA
A form of Designed Experiment:
Two-Treatment Full Factorial with Replications
Analysis is done using ANOVA software
Comparisons of variance components is through a series of F-tests (either exceed critical region or look for small p-value)
Can distinguish part X operator interaction
Want to find non-significant operator, interaction terms, and a significant part term - capable system!
12/5/2018
Process Capability Analysis