IOE 466 W08
Gage and Measurement System Analysis
1

Topics
Measurement Systems Analysis

 Gage R&R for Variable data
 Attribute Gage R&R
 Case Study
2

Measurements Systems Analysis
Purpose:

 Determine how much variability is due to the gage
or instrument
 Isolate the components of variability of the
measurement system
 Assess whether the instrument or gage is capable
(suitable for intended application)
3

Components of a Measurement System
Equipment or Gage

Type of Gage:

Attribute: go-no go, vision systems (part present or not present)

Variable: calipers, probe, tape measure, coordinate measurement machines, checking

fixture with inspection device
Discrimination of Measurement – General Rules:

At least 1/10 of tolerance (tol = 1 mm, measure to at least 0.1)

Or, at least 1/10 of 6*process standard deviation (6σ)

Operator & Operating Instructions

Part locating or orientation scheme

gage must be able to consistently locate the part being measured.

4

Gage R&R
Total variability decomposition

σ2 = σ2 + σ gage
2
7
total product
σ2 = σ gage = σ 2 + σ2
2
measurement _ error repeatability reproducibility
different operators or conditions
inherent precision of gage

Gage R&R
In conducting a Gage R&R study, we need to identify # parts, # trials

per part, and # operators.
We also need tolerance width for each feature.

Tolerance Width = USL – LSL

USL ~ Upper Spec Limit and LSL ~ Lower Spec Limit.

Common Applications (parts x trials x operators):

5 or 10 parts

2 or 3 trials

2 or 3 operators

Example: 5x3x2  Two operators will measure each of 5 parts three

times.
6

Gage Capability Criteria
Precision to tolerance ratio or P/T ration

6σ gage
ˆ
P
= < 0.1
T USL − LSL
gage error as a percentage of the product variability

σ gage
ˆ
×100%
σ product
ˆ

Example 7-7 P354 7
σ2 = σ2 + σ gage
2
total product
R
σ gage =
ˆ
d2
• X-bar chart represents variability between different product units
• R chart represents the gage measurement variability:

Gage R&R : Example 7-7
Be careful! Don’t interpret this like you would a process control

chart.
X-bar: out of control

Xbar-R Chart of M1, ..., M2
points, show that
30 1
measurement system
1
Sample Mean
1
1
25
can discriminate
UCL=24.06
_
_
X=22.28
between units of
LCL=20.49
20
1 1
1
1
products
1 1
1 3 5 7 9 11 13 15 17 19
Sample
UCL=3.104
3
Sample Range
R-bar: in-control, show

2
that operators are
_
1 R=0.95
consistent.
0 LCL=0
1 3 5 7 9 11 13 15 17 19
Sample
9

7
Example 7-7: continued
Suppose that instead of having only 1 operator measure the parts, you
make 3 operators measure each part twice.

7
Example 7-7: Gage R&R
(1) average of all ranges
1 1 R 1.15
R = (R 1 + R 2 + R 3 ) = (1 + 1.25 + 1.2) = 1.15 σ repeatability = = = 1.02
ˆ
3 3 d 2 |n = 2 1.128
Rx 0.32
R x = x max − x min = 22.60 − 22.28 = 0.32 σ reproducibility = = = 0.19
ˆ
d 2 |n =3 1.693
x max = max(x1 , x 2 , x 3 )
(2) Difference among operators
x min = min( x1 , x 2 , x 3 )
(3) Each operator’s average
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Gage and Measurement System Capability
Variation Decomposition

σ2 = σ2 + σ gage ⇒ σ 2 = σ gage = σ 2 + σ2
2 2
total product measurement repeatability reproducibility
r m n
∑∑∑ ( x − x )2
kij
k =1 i =1 j =1
σ total =
2
rmn − 1
r m n
∑∑∑ x RX
kij
σreproducibility =
ˆ
k =1 i =1 j =1
x= R d2
rmn σrepeatability =
ˆ
d2
R X = x max − x min ;
r
Use R chart for estimation
∑R x max = max(x1 , x 2,  , x r )
k
r: # of operators
R= k =1
m: # of samples x min = min( x1 , x 2,  , x r )
r
n: # of repeated measurements m
∑R m n
m
ki
xkij :
∑∑ x
∑x
Rk = i =1
xij
ki
m
i: sample index i =1 j=1
xk = =
i =1
R ki = max j ( x kij ) − min j ( x kij ) m mn
j: repeated measurement index
k: operator index

Gage and Measurement System Capability (Cont’s)
Gage capability: precision-to-tolerance ratio (P/T ratio)

Generally, an adequate gage capability: P/T≤0.1

6σ gage
ˆ
P
=
T USL − LSL
gage variability-to-product variability ratio

independent of specification limits

σ gage
ˆ
× 100%
σ
ˆ product
σ2
σ2
product = σ total − σ gage
2 2
total
σ2 σ2
σ gage = σ 2
repeatability + σ reproducibility
2 2
product
repeatability
σ gage
2
σ2
reproducibility

Gage R&R for Attribute Variables
Some quality inspection systems rely on human

judgment – “good/bad” or “best/good/poor”
Examples

 Fabric color matching
 Contact Lens appraisal
 Delamination (printing)
How can we test whether the measurement system is

working accurately?
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Gage R&R for Attribute Variables
Gage R&R Study set up steps

 Select 20-30 product samples (include mix of
“good” and “bad” parts)
 Identify # of parts, # of inspectors and # of trials
 Have a master appraiser (expert) rate each part
 Inspectors rate each part an ‘x’ number of trials, at
random, without knowing the master results
15

Gage R&R for Attribute Variables
Then:
# of measurement matches within trials
Operator Repeatability n =
number of parts inspected
n
∑ Operator Repeatability n
Overall System Repeatability = i =1
n
# of matches with standard
Individual Effectiveness =
number of parts inspected
# of times all operators agree with standard
Overall System Effectiveness =
number of parts inspected
16

Gage R&R for Attribute Variables
General Guideline: 90% effectiveness is acceptable

Next steps:

 Identify best measurement system procedure
 Document standardized work
 Train all operators in new system
 Periodically check gage R&R of system
17

Gage R&R for Attribute Variables: Example
A hospital is trying to evaluate the consistency of their doctors in rating
mammograms. Each mammogram is rated according to the following
scale:
1 – No cancer (best)
2 – Benign cancer
3 – Possible malignancy
4 – Malignancy (worst)
A sample of 15 mammograms is collected, and three randomly selected
doctors within that specialty are selected. Each doctor rates each
mammogram three times at random. In the study, these ratings will also
be compared to a standard (ratings provided by a panel of senior
doctors).
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Gage R&R for Attribute Variables: Example
1 No cancer
2 Benign cancer
3 Possible malignancy
4 Malignancy
Mammogram Standard Doctor 1 Doctor 2 Doctor 3
1 4 4 4 4 4 4 4 4 4 3
2 4 4 4 4 4 4 4 4 4 4
3 2 2 2 2 2 2 2 2 2 2
4 3 3 3 3 3 3 3 2 3 2
5 2 2 2 2 2 2 2 1 2 2
6 1 1 1 1 2 2 1 2 1 2
7 3 3 3 3 3 3 3 2 2 3
8 4 4 4 4 4 4 3 4 4 4
9 4 4 4 4 4 4 4 3 3 4
10 2 2 1 1 2 2 2 2 2 2
11 2 2 2 2 2 2 2 2 2 1
12 4 4 4 4 4 4 4 4 4 4
13 1 2 2 2 1 1 1 1 2 1
14 1 1 1 1 1 1 1 1 1 2
15 3 3 3 3 3 3 2 4 4 4
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Gage R&R for Attribute Variables: Example
Results

Individual
Repeatability
Effectiveness
Doctor 1 93.3% 93.3%
Doctor 2 80.0% 93.3%
Doctor 3 40.0% 80.0%
System Repeatability = 71.1%

Overall Effectiveness = 87.7%

20

Case Study:
Improving Data Reliability for Valve Bodies
Need to adequately measure bore diameter data.

Excessive variation is causing rejects from process.
Suspected that data for water valve bodies not reliable

Critical measurement is the bore diameter, with a

specification of 1.334 +/- .002”
Bore diameter
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Problem Definition
Need to adequately measure bore diameter data.

Excessive variation is causing rejects from process –

need to ensure diameter is measured properly
because of small tolerance for error.
Currently utilizing a dial caliper method

To find the current state of the process:

 10 x 3 x 3 Gage R&R experiment
22

Current State: Gage R&R results
23

Current State: Gage R&R results
Appraiser variation takes up 58% of tolerance width

Equipment variation takes up 69% of total variation

24

Current State: Cause and Effect Diagram
Cause-and-Effect Diagram
Measurements Material Personnel
Lack of training
Variability between
operators
Variability in
bore
diameter
data
I mproper use of Dial caliper not precise
caliper
Lack of standardised Dial caliper not accurate
work
Environment Methods Machines
25

Improvement alternatives
Use different type of gage

 Plug-gages
 Internal calipers
 Self centering electronic bore gauge
Gage R&R done for top two alternatives, internal

calipers and electronic bore gauge.
26

Self centering bore gauge: Gage R&R results
27

Self centering bore gauge: Gage R&R results
Appraiser variation takes up 2.7% of tolerance width

Equipment variation takes up 5.2% of total variation

28

Results
Switch from Dial Caliper to Self Centering Bore Gage

Reduced % of R&R compared to total variance

from 90.2% to 6.2%.
Expected reduction in errors reported is 75%

29