1. IENG 486 Statistical Quality & Process Control Gage Capability Studies
4/15/2017
IENG Lecture 15
Gage Capability Studies
4/15/2017
IENG 486 Statistical Quality & Process Control
(c) D.H. Jensen & R. C. Wurl

2. IENG 486 Statistical Quality & Process Control
Bonus Points # 3
In teams of 4 people, go to the Project Office and perform a gage R & R study on the 7 parts.
Half of the teams measured with the micrometer
Half of the teams measured with the dial calipers
Entire team works together to analyze the data – for the 4 Operators, estimate:
σ2 total
σ2 repeatability
σ2 reproducability
σ2 product
P/T for gage, assuming USL – LSL = 0.005”
4/15/2017
IENG 486 Statistical Quality & Process Control

3. IENG 486 Statistical Quality & Process Control
Bonus Points # 4
In teams of 4 people, go to the CIM Lab (CM 203) and set up a control chart strategy for the “pipe-bomb” machine.
Dr. Jensen will demonstrate the system, each team operates afterward.
The team will collect data using the scale, and track the data using the spreadsheet template, each control chart should have 30 samples.
Entire team works together to collect and analyze the data for the system, and to create and interpret x – and R – charts.
For the lab exercise, briefly report:
What your control chart strategy is (what did you measure and why)
Turn in print out of your trial control charts, and describe how the limits were developed
For each control chart, use your Trial Control Limits* on all 30 sample points, and interpret each chart for control using the 4 Western Electric Rules:
Convert your Trial Control Limit data to Standards
Circle Western Electric Rule violations, and describe what they show
4/15/2017
IENG 486 Statistical Quality & Process Control

4. Gage Capability Studies
IENG 486 Statistical Quality & Process Control
4/15/2017
Gage Capability Studies
Ensuring adequate gage and inspection system capability
In any problem involving measurement the observed variability in product is due to two sources:
Product variability - σ2product
Gage variability - σ2gage i.e., measurement error
Total observed variance in product:
σ2total = σ2product + σ2gage (system)
4/15/2017
IENG 486 Statistical Quality & Process Control
(c) D.H. Jensen & R. C. Wurl

5. e.g. Assessing Gage Capability
IENG 486 Statistical Quality & Process Control
4/15/2017
e.g. Assessing Gage Capability
Following data were taken by one operator during gage capability study.
4/15/2017
IENG 486 Statistical Quality & Process Control
(c) D.H. Jensen & R. C. Wurl

6. e.g. Assessing Gage Capability Cont'd
IENG 486 Statistical Quality & Process Control
4/15/2017
e.g. Assessing Gage Capability Cont'd
Estimate standard deviation of measurement error:
Dist. of measurement error is usually well approximated by the Normal, therefore
Estimate gage capability:
That is, individual measurements expected to vary as much as owing to gage error.
4/15/2017
IENG 486 Statistical Quality & Process Control
(c) D.H. Jensen & R. C. Wurl

7. Precision-to-Tolerance (P/T) Ratio
IENG 486 Statistical Quality & Process Control
4/15/2017
Precision-to-Tolerance (P/T) Ratio
Common practice to compare gage capability with the width of the specifications
In gage capability, the spec width is called the tolerance band
(not to be confused with natural tolerance limits, NTLs)
Specs for above example: 32.5 ± 27.5
Rule of Thumb:
P/T  0.1  Adequate gage capability
4/15/2017
IENG 486 Statistical Quality & Process Control
(c) D.H. Jensen & R. C. Wurl

8. Estimating Variance Components of Total Observed Variability
IENG 486 Statistical Quality & Process Control
4/15/2017
Estimating Variance Components of Total Observed Variability
Estimate total variance:
Compute an estimate of product variance
Since :
4/15/2017
IENG 486 Statistical Quality & Process Control
(c) D.H. Jensen & R. C. Wurl

9. Gage Std Dev Can Be Expressed as % of Product Std Dev
IENG 486 Statistical Quality & Process Control
4/15/2017
Gage Std Dev Can Be Expressed as % of Product Std Dev
Gage standard deviation as percentage of product standard deviation :
This is often a more meaningful expression, because it does not depend on the width of the specification limits
4/15/2017
IENG 486 Statistical Quality & Process Control
(c) D.H. Jensen & R. C. Wurl

10. Using x and R-Charts for a Gage Capability Study
IENG 486 Statistical Quality & Process Control
4/15/2017
Using x and R-Charts for a Gage Capability Study
On x chart for measurements:
Expect to see many out-of-control points
x chart has different meaning than for process control
shows the ability of the gage to discriminate between units (discriminating power of instrument)
Why? Because estimate of σx used for control limits based only on measurement error, i.e.:
4/15/2017
IENG 486 Statistical Quality & Process Control
(c) D.H. Jensen & R. C. Wurl

11. Using x and R-Charts for a Gage Capability Study
IENG 486 Statistical Quality & Process Control
4/15/2017
Using x and R-Charts for a Gage Capability Study
On R-chart for measurements:
R-chart directly shows magnitude of measurement error
Values represent differences between measurements made by same operator on same unit using same instrument
Interpretation of chart:
In-control: operator has no difficulty making consistent measurements
Out-of-control: operator has difficulty making consistent measurements
4/15/2017
IENG 486 Statistical Quality & Process Control
(c) D.H. Jensen & R. C. Wurl

12. Repeatability & Reproducibility: Gage R & R Study
IENG 486 Statistical Quality & Process Control
4/15/2017
Repeatability & Reproducibility: Gage R & R Study
If more than one operator used in study then measurement (gage) error has two components of variance:
σ2total = σ2product + σ2gage
σ2reproducibility + σ2repeatability
Repeatability:
σ2repeatability - Variance due to measuring instrument
Reproducibility:
σ2reproducibility - Variance due to different operators
4/15/2017
IENG 486 Statistical Quality & Process Control
(c) D.H. Jensen & R. C. Wurl

13. IENG 486 Statistical Quality & Process Control
4/15/2017
Ex. Gage R & R Study
20 parts, 3 operators, each operator measures each part twice
Estimate repeatability (measurement error):
Use d2 for n = 2 since each range uses 2 repeat measures
Operator i xi Ri 1
22.30
1.00 2
22.28
1.25 3
22.10
1.20
4/15/2017
IENG 486 Statistical Quality & Process Control
(c) D.H. Jensen & R. C. Wurl

14. IENG 486 Statistical Quality & Process Control
4/15/2017
Ex. Gage R & R Study Cont'd
Estimate reproducibility:
Differences in xi  operator bias since all three operators measured the same parts
Use d2 for n = 3 since Rx is from sample of size 3
4/15/2017
IENG 486 Statistical Quality & Process Control
(c) D.H. Jensen & R. C. Wurl

15. IENG 486 Statistical Quality & Process Control
4/15/2017
Ex. Gage R & R Study Cont'd
Total Gage variability:
Gage standard deviation (measurement error):
P/T Ratio:
Specs: USL = 60, LSL = 5
Note:
Would like P/T < 0.1
4/15/2017
IENG 486 Statistical Quality & Process Control
(c) D.H. Jensen & R. C. Wurl

16. Comparison of Gage Capability Examples
IENG 486 Statistical Quality & Process Control
4/15/2017
Comparison of Gage Capability Examples
σ2 repeatability σ2 reproducibility
σ2 product
P/T
Single operator
0.8865
0.0967
Three operators
1.0195
0.1181
1.0263
0.1120
Gage capability is not as good when we account for both reproducibility and repeatability
Train operators to reduce σ2reproducability =
Since σ2repeatability = (largest component), direct effort toward finding another inspection device.
4/15/2017
IENG 486 Statistical Quality & Process Control
(c) D.H. Jensen & R. C. Wurl