3
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)
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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.
Total variability decomposition
Gage R&R
2gage
2product
2total σ+σ=σ
2ilityreproducib
2ityrepeatabil
2gage
2error_tmeasuremen σ+σ=σ=σ
inherent precision of gage different operators or conditions
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6
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.
Gage Capability Criteria
Precision to tolerance ratio or P/T ration
gage error as a percentage of the product variability
1.0LSLUSL
ˆ6
T
P gage <−
σ=
%100ˆ
ˆ
product
gage ×σσ
Example 7-7 P354
2gage
2product
2total σ+σ=σ
• X-bar chart represents variability between different product units• R chart represents the gage measurement variability:
2gage d
Rˆ =σ
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9
Gage R&R : Example 7-7
Sample
Sam
ple
Mean
191715131197531
30
25
20
__X=22.28
UCL=24.06
LCL=20.49
Sample
Sam
ple
Range
191715131197531
3
2
1
0
_R=0.95
UCL=3.104
LCL=0
1
1
11
1
1
111
1
Xbar-R Chart of M1, ..., M2 X-bar: out of control
points, show that measurement system can discriminate between units of products
R-bar: in-control, show that operators are consistent.
Be careful! Don’t interpret this like you would a process control chart.
Example 7-7: continuedSuppose that instead of having only 1 operator measure the parts, you make 3 operators measure each part twice.
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11
)x,x,xmin(x
)x,x,xmax(x
19.0693.1
32.0
|d
Rˆ32.028.2260.22xxR
02.1128.1
15.1
|d
Rˆ15.1)2.125.11(
3
1)RRR(
3
1R
321min
321max
3n2
xilityreproducibminmaxx
2n2ityrepeatabil321
==
===σ=−=−=
===σ=++=++=
=
=
(1) average of all ranges
(2) Difference among operators
(3) Each operator’s average
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Example 7-7: Gage R&R
Gage and Measurement System Capability Variation Decomposition
2ilityreproducib
2ityrepeatabil
2gage
2tmeasuremen
2gage
2product
2total σ+σ=σ=σ⇒σ+σ=σ
Use R chart for estimationr: # of operatorsm: # of samplesn: # of repeated measurementsxkij :i: sample indexj: repeated measurement indexk: operator index
rmn
x
x
rmn
xx
r
k
m
i
n
jkij
r
k
m
i
n
jkij
total
∑∑∑
∑∑∑
= = =
= = =
=
−
−=
1 1 1
1 1 1
2
2
1
)(
σ
2ityrepeatabil d
Rˆ =σ
r
RR
r
1kk∑
==
)x(min)x(maxRm
RR
kijjkijjki
m
1iki
k
−=
=∑
=
)x,x,xmin(x
)x,x,xmax(x
;xxR
r,21min
r,21max
minmaxX
=
=
−=2
Xilityreproducib d
Rˆ =σ
mn
x
m
xx
m
1i
n
1jxij
m
1iki
k
∑∑∑= == ==
Gage capability: precision-to-tolerance ratio (P/T ratio) Generally, an adequate gage capability: P/T≤0.1
gage variability-to-product variability ratio independent of specification limits
Gage and Measurement System Capability (Cont’s)
LSLUSL
ˆ6
T
P gage
−σ
=
%100ˆ
ˆ
product
gage ×σσ
2totalσ
2ilityreproducib
2ityrepeatabil
σ
σ 2gageσ
2productσ2
ilityreproducib2
ityrepeatabil2gage σ+σ=σ
2gage
2total
2product σ−σ=σ
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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
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Gage R&R for Attribute Variables
Then:
inspected parts ofnumber
standard with agree operators all timesof # essEffectiven System Overall
inspected parts ofnumber
standard with matches of # essEffectiven Individual
n
ityRepeatabilOperator ity Repeatabil System Overall
inspected parts ofnumber
ials within trmatchest measuremen of # ityRepeatabilOperator
n
1in
n
=
=
=
=
∑=
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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
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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
Mammogram Standard
1 4 4 4 4 4 4 4 4 4 32 4 4 4 4 4 4 4 4 4 43 2 2 2 2 2 2 2 2 2 24 3 3 3 3 3 3 3 2 3 25 2 2 2 2 2 2 2 1 2 26 1 1 1 1 2 2 1 2 1 27 3 3 3 3 3 3 3 2 2 38 4 4 4 4 4 4 3 4 4 49 4 4 4 4 4 4 4 3 3 4
10 2 2 1 1 2 2 2 2 2 211 2 2 2 2 2 2 2 2 2 112 4 4 4 4 4 4 4 4 4 413 1 2 2 2 1 1 1 1 2 114 1 1 1 1 1 1 1 1 1 215 3 3 3 3 3 3 2 4 4 4
Doctor 3Doctor 2Doctor 1
1234
No cancerBenign cancerPossible malignancyMalignancy
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Gage R&R for Attribute Variables: Example
Results
System Repeatability = 71.1% Overall Effectiveness = 87.7%
RepeatabilityIndividual
EffectivenessDoctor 1 93.3% 93.3%Doctor 2 80.0% 93.3%Doctor 3 40.0% 80.0%
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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
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Current State: Gage R&R results
Appraiser variation takes up 58% of tolerance width Equipment variation takes up 69% of total variation
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Current State: Cause and Effect Diagram
datadiameterboreVariability in
Environment
Measurements
Methods
Material
Machines
Personnel
Dial caliper not precise
Dial caliper not accurate
operatorsVariability between
Lack of training
caliperImproper use of
workLack of standardised
Cause-and-Effect Diagram
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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.
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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