1. ENGM 621: SPC
Process Capability

2. Outline Process Capability Process Capability Indices
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

3. 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

4. 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:

5. 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

6. 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:

7. Process Capability Ratio Note
There are many ways we can estimate the capability of our process
If σ is unknown, we can replace it with one of the following estimates:
The sample standard deviation S
R-bar / d2

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

9. 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

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

11. PCR and an Off-Center Process
CPK = min (CPU, CPL)
Generally, if CP = CPK, then the process is centered at the midpoint of the specifications
If CP ≠ CPK, then the process is off-center
PCR=potential capability
PCR(k) = actual capability

12. Quality Design & Process Variation
Lower Spec
Limit
Upper Spec
Limit
Acceptance
Sampling 60 80
100
120
140
Statistical
Process
Control 60
140
Experimental
Design
140 60