1. Statistical Process Control
Gage Capability

2. Gage Capability Studies
TM 720: Statistical Process Control
Gage Capability Studies
Ensuring an adequate gage and inspection system capability is an important consideration!
In any problem involving measurement the observed variability in product due to two sources:
Product variability - σ2product
Gage variability - σ2gage i.e., measurement error
Total observed variance in product:
σ2total = σ2product + σ2gage (system)
(c) D.H. Jensen & R.C. Wurl

3. e.g. Assessing Gage Capability
TM 720: Statistical Process Control
e.g. Assessing Gage Capability
Following data were taken by one operator during gage capability study.
(c) D.H. Jensen & R.C. Wurl

4. e.g. Assessing Gage Capability Cont'd
TM 720: Statistical Process Control
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.
(c) D.H. Jensen & R.C. Wurl

5. Precision-to-Tolerance (P/T) Ratio
TM 720: Statistical Process Control
Precision-to-Tolerance (P/T) Ratio
Common practice to compare gage capability with the width of the specifications
In gage capability, the specification width is called the tolerance band
(not to be confused with natural tolerance limits, NTLs)
Suppose specs are given as : m ± 27.5
Rule of Thumb:
P/T  0.1  Adequate gage capability
(c) D.H. Jensen & R.C. Wurl

6. Estimating Variance Components of Total Observed Variability
TM 720: Statistical Process Control
Estimating Variance Components of Total Observed Variability
Estimate total variance:
Compute an estimate of product variance
Since :
(c) D.H. Jensen & R.C. Wurl

7. Gage Std Dev Can Be Expressed as % of Product Standard Deviation
TM 720: Statistical Process Control
Gage Std Dev Can Be Expressed as % of Product Standard Deviation
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
(c) D.H. Jensen & R.C. Wurl

8. e.g. Assessing Gage Capability
TM 720: Statistical Process Control
e.g. Assessing Gage Capability
Following data were taken by one operator during gage capability study.
(c) D.H. Jensen & R.C. Wurl

9. Using x and R-Charts for a Gage Capability Study
TM 720: Statistical Process Control
Using x and R-Charts for a Gage Capability Study
(c) D.H. Jensen & R.C. Wurl

10. Using x and R-Charts for a Gage Capability Study
TM 720: Statistical Process Control
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 is based only on measurement error, i.e.:
(c) D.H. Jensen & R.C. Wurl

11. Using x and R-Charts for a Gage Capability Study
TM 720: Statistical Process Control
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 the same instrument
Interpretation of chart:
In-control: operator has no difficulty making consistent measurements
Out-of-control: operator has difficulty making consistent measurements
(c) D.H. Jensen & R.C. Wurl

12. Repeatability & Reproducibility: Gage R & R Study
TM 720: Statistical Process Control
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
(c) D.H. Jensen & R.C. Wurl

13. TM 720: Statistical Process Control
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
(c) D.H. Jensen & R.C. Wurl

14. TM 720: Statistical Process Control
Ex. Gage R & R Study Cont'd
Estimate reproducibility:
Differences in xi  operator bias since all operators measured same parts
Use d2 for n = 3 since Rx is from sample of size 3
(c) D.H. Jensen & R.C. Wurl

15. TM 720: Statistical Process Control
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!
(c) D.H. Jensen & R.C. Wurl

16. Comparison of Gage Capability Examples
TM 720: Statistical Process Control
Comparison of Gage Capability Examples
Gage capability is not as good when we account for both reproducibility and repeatability
Train operators to reduce σ2reproducability from
Since σ2repeatability = (largest component), direct effort toward finding another inspection device.
σ2 repeatability σ2 reproducibility
σ2 product
P/T
Single operator
0.8865
0.0967
Three operators
1.0195
0.1181
1.0263
0.1120
(c) D.H. Jensen & R.C. Wurl