�ݺ�ߣ

When looking at GRR and
MSA all the information is
“EXACTLY CORRECT”
There is however a LOT of detailed information to
understand
2

Is there a way to make it
simpler to understand
and implement?
Especially for Test
Engineers?
3

There are 2 boundary conditions
that a test engineer can
understand that are only
“Sometimes” shown
5

Using freely available
spreadsheet off of the Internet
for Excel analysis of GRR a
model was developed for
analysis using these 2
boundary conditions
8

Test Engineers
have been told to
follow 2 boundary
conditions
1. The error in the
measurement has to be 10
times less than the
measured value.
2. The error between the
USL and LSL has to be 10%
of the difference between
USL and LSL
X Instrument Error
0
2X Instrument Error
LSL
USL
ΔCV
ΔCV - Boundary Condition # 2
LCV - Boundary Condition # 1
Test Engineering Boundary Conditions
LCV
Where
USL = Upper Specifica>on Limit LSL = Lower Specifica>on Limit
LCV = Lowest Capable Value ΔCV = USL - LSL = Differen>al Capability
The variable, the RED “X”, needs to be understood
9

GRR Tools
Critical Evaluation with underlying Test
Engineering Boundary Conditions
The model created is using an OE (offset error of
±4mV with GE (gain error = 0%). The initial
evaluation used 10 samples, 3 tests, 3 Testers. One
tester had 0 offset, another -4mV, and the third
+4mV. Repeatability was 0.0001 to insure that just
equipment reproducibility is what is being examined.
Manage Instrument Error to achieve a passing
qualification on devices for GRR: ANOVA or XBAR&R
The experiment objective is to understand instrument
specification and how it affects GRR ALONE
10

GRR Tools
Manage Instrument Error to achieve a passing
qualification on devices for GRR: ANOVA or XBAR&R
GRR Calculation
# Samples
# Testers
Methods
# of Measurements
USL & LSL
Objective: Understand GRR from Instrument
Error Perspective
2-10 samples
Sample location: determines GRR
Random Selection
Intelligent selection
Plus Offset - one tester
Zero Offset - one tester
Minus Offset - one tester
ANOVA
Xbar&R
One value - Ideal
Second value: + 0.0001
Third value: - 0.0001
Note: sample location is
NOT usually looked at;
and it turns out to be
very important
11

How do these affect GRR
Results
• There are essentially 2 methods for doing GRR
• ANOVA
• Xbar&R
• Spreadsheets for each can be found on the internet free of
charge. Some with just one of the methods or the other, and
at least one with both methods in the spreadsheet.
• Each method was confirmed to give the same results with
identical data when comparing ANOVA to ANOVA and
Xbar&R to Xbar&R
12

The question is:
Are the 2 boundary conditions listed on slides 6 and 7 necesary
and sufficient to insure that the goal of GRR 10% passes?
1. Random samples within USL and LSL
2. 10 perfect evenly distributed samples within USL and LSL
3. 10 select samples to cause worst case within center ±50% of perfect samples placement
6 ways to look at:
# Instrument errors range from 10X to shown on graphs
13

Necessary Equations
The diagram on �ݺ�ߣ 2 shows 11X for instrument errors
to take into account the need for repeatability. This
works out to a GRR of approximately 9% for just
instrument errors, which is the objective of the exercise
USL =
LSL 1+10GE( )+ 20OE
1−10GE
USL − LSL = ΔCV
ΔCV = 10 GE i(USL + LSL)+ 2 iOE( )
ΔCV = 20 iOE +10 GE i(USL + LSL)( )
LSL = +LCV =
OE
0.1− GE
+LCV =
OE
0.1− GE
The model created us using an OE (offset error of ±4mV with GE
(gain error = 0%). The initial evaluation used 10 samples, 3 tests, 3
Testers. One tester had 0 offset, another -4mV, and the third +4mV.
Repeatability was 0.0001 to insure that just equipment reproducibility
is what is being examined.
14

0
LSL
USL
±100% of perfect
samples
placement
±50% of perfect
samples
placement
0
LSL
USL
Random perfect
samples
placement
0
LSL
USL
Perfect Placement
±100 % Placement - Worst Case
0
LSL
USL
0
LSL
USL
Perfect Placement
±50 % Placement - Worst Case
15

# Instrument errors range from 10X to what is shown on graph, 10 measurement points perfectly evenly distributed
0
LSL
USL
10X 11X
0
LSL
USL
12X
0
LSL
USL
13X
0
LSL
USL
14X
0
LSL
USL
15X
0
LSL
USL
16X
0
LSL
USL
24X
0
LSL
USL
23X
0
LSL
USL
22X
0
LSL
USL
21X
0
LSL
USL
20X
0
LSL
USL
19X
0
LSL
USL
18X
0
LSL
USL
17X
0
LSL
USL
Red lines represent perfect evenly spaced samples
16

Random selection of measurement for 10 DUTs with zero offset, +
offset and - offset.
1.5200 10 device randomly selected measurement values
using Monte Carlo simulations for Xbar&R from Statistical
Solutions, Tolerance and GRR results.
2.1010 10 device randomly selected measurement values
using Monte Carlo simulations using the ANOVA method
from www.dmaictools.com, Tolerance and GRR results.
Lower Specification limits started at 40mV (10X), Upper Specification limit start at 120mV (10X), ranging to
40X instrument errors. This means that the difference between USL-LSL, ranged from 10X to 40X.
Simulations were done for a process distribution width of 5.15 (encloses the central 99% of the process
distribution).
0
LSL
USL
Please note that the number of instrument
errors is the inverse of the instrument error
17

409 12 14 16 18 20 22 24 26 28 30 32 34 36 38
1
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
(# X) Number of Instrument Errors
Percentage(%)over10%
GRR% Xbar&R
Xbar&R Monte Carlo Simula3on
in Excel. 5200 simula3ons of 10
devices.
Random devices within limits
Using Gage R&R
(XBar&R Motorola Version)
from Sta;s;cal Solu;ons
Please note that 11X and
greater is acceptable. However
neither the Xbar&R Method
nor ANOVA correctly calculate
GRR at the corners of
instrument limits
GRR% ANOVA
ANOVA Monte Carlo Simula3on
in Excel. 1010 simula3ons of 10
devices.
Random devices within limits
± 4mV offset Error
LSL starts at +40mV (10X)
USL starts at +120mV
USL-LSL starts at 80mV (10X)
Anova - www.dmaictools.com/measure/grr
30.0
Percentage of simulations (Monte Carlo) that showed the instances greater than GRR
10% for each Instrument X.
To read the graph, 20 on the X axis is the number of instrument errors. For GRR ANOVA,
approximately 0.5% of the simulation results showed greater than a GRR of 10%. For
GRR Xbar&R 1% of the simulation results showed greater than a GRR of 10%.
0
LSL
USL
Random
samples
placement
18

4. 10 select perfect samples to cause worst case
within center ±50% of perfect samples placement
NOTE: solid line on graph of next slide
1. ANOVA 5.15 Standard deviations
2.Xbar&R 5.15 Standard deviations
Lower Specification limits started at 40mV (10X), Upper Specification limit
start at 120mV (10X), ranging to 40X instrument errors. This means that
the difference between USL-LSL, ranged from 10X and following.
Calculations were done for a process distribution width of 5.15 (encloses
the central 99% of the process distribution) at worst case values..
0
LSL
USL
±50% of perfect
samples
placement
Please note that the number of instrument
errors is the inverse of the instrument error
19

4816 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47
0.1
0.035
0.04
0.045
0.05
0.055
0.06
0.065
0.07
0.075
0.08
0.085
0.09
0.095
# Instrument Errors
GRR
ANOVA ±50% of perfect sample placement
10 Perfectly Measured Device Samples for Qualifica:on, 1 tester 0 offset, 1 tester +offset, 1 tester - offset
Anova Perfect 16.5 (6.06%)
Anova ±50 17.8 (5.62%)
Anova ±100 19.3 (5.18%)
Anova ±150 21.0 (4.76%)
Anova ±200 22.9 (4.37%)
Xbar Perfect 37.1 (2.70%)
Xbar ±50 39.3 (2.54%)
Xbar ±100 41.7 (2.40%)
Xbar ±150 44.4 (2.25%)
Xbar ±200 47.8 (2.09%)
© Van Brollini 2016
© Van Brollini 2016© Van Brollini 2016© Van Brollini 2016 © Van Brollini 2016 © Van Brollini 2016
© Van Brollini 2016© Van Brollini 2016
ANOVA perfect sample placement
Anova ±50 35.7 (2.80%)
Anova ±100 38.8 (2.58%)
Anova ±150 42.2 (2.37%)
Anova ±200 46.1 (2.17%)
Xbar ±50 19.5 (5.13%)
Xbar ±100 20.7 (4.83%)
Xbar ±150 22.0 (4.55%)
Xbar ±200 23.7 (4.22%)
Note: % numbers shown are range percent error
Effect of Only Device Specifica:on
and Sample Placement on GRR
All Device Measurements Perfect
±50% perfect sample placement
20

Next slide contains ANOVA
1. 10 perfect samples
2. 10 perfect samples ±50%
21

4816 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47
0.1
0.035
0.04
0.045
0.05
0.055
0.06
0.065
0.07
0.075
0.08
0.085
0.09
0.095
# Instrument Errors
GRR
Anova ±50 17.8 (5.62%)
Anova ±100 19.3 (5.18%)
Anova ±150 21.0 (4.76%)
Anova ±200 22.9 (4.37%)
Xbar ±50 39.3 (2.54%)
Xbar ±100 41.7 (2.40%)
Xbar ±150 44.4 (2.25%)
Xbar ±200 47.8 (2.09%)
Anova ±50 35.7 (2.80%)
Anova ±100 38.8 (2.58%)
Anova ±150 42.2 (2.37%)
Anova ±200 46.1 (2.17%)
Xbar ±50 19.5 (5.13%)
Xbar ±100 20.7 (4.83%)
Xbar ±150 22.0 (4.55%)
Xbar ±200 23.7 (4.22%)
22

Next 4 slides using
ANOVA show how to use
23

4816 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47
0.1
0.035
0.04
0.045
0.05
0.055
0.06
0.065
0.07
0.075
0.08
0.085
0.09
0.095
# Instrument Errors
GRR
Anova ±50 17.8 (5.62%)
Anova ±100 19.3 (5.18%)
Anova ±150 21.0 (4.76%)
Anova ±200 22.9 (4.37%)
Xbar ±50 39.3 (2.54%)
Xbar ±100 41.7 (2.40%)
Xbar ±150 44.4 (2.25%)
Xbar ±200 47.8 (2.09%)
Anova ±50 35.7 (2.80%)
Anova ±100 38.8 (2.58%)
Anova ±150 42.2 (2.37%)
Anova ±200 46.1 (2.17%)
Xbar ±50 19.5 (5.13%)
Xbar ±100 20.7 (4.83%)
Xbar ±150 22.0 (4.55%)
Xbar ±200 23.7 (4.22%)
Have to choose something LESS than
10%. Need room for repeatability
24

4816 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47
0.1
0.035
0.04
0.045
0.05
0.055
0.06
0.065
0.07
0.075
0.08
0.085
0.09
0.095
# Instrument Errors
GRR
Anova ±50 17.8 (5.62%)
Anova ±100 19.3 (5.18%)
Anova ±150 21.0 (4.76%)
Anova ±200 22.9 (4.37%)
Xbar ±50 39.3 (2.54%)
Xbar ±100 41.7 (2.40%)
Xbar ±150 44.4 (2.25%)
Xbar ±200 47.8 (2.09%)
Anova ±50 35.7 (2.80%)
Anova ±100 38.8 (2.58%)
Anova ±150 42.2 (2.37%)
Anova ±200 46.1 (2.17%)
Xbar ±50 19.5 (5.13%)
Xbar ±100 20.7 (4.83%)
Xbar ±150 22.0 (4.55%)
Xbar ±200 23.7 (4.22%)
Choose 24 Instrument Errors (4.17%)
25

4816 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47
0.1
0.035
0.04
0.045
0.05
0.055
0.06
0.065
0.07
0.075
0.08
0.085
0.09
0.095
# Instrument Errors
GRR
Anova ±50 17.8 (5.62%)
Anova ±100 19.3 (5.18%)
Anova ±150 21.0 (4.76%)
Anova ±200 22.9 (4.37%)
Xbar ±50 39.3 (2.54%)
Xbar ±100 41.7 (2.40%)
Xbar ±150 44.4 (2.25%)
Xbar ±200 47.8 (2.09%)
Anova ±50 35.7 (2.80%)
Anova ±100 38.8 (2.58%)
Anova ±150 42.2 (2.37%)
Anova ±200 46.1 (2.17%)
Xbar ±50 19.5 (5.13%)
Xbar ±100 20.7 (4.83%)
Xbar ±150 22.0 (4.55%)
Xbar ±200 23.7 (4.22%)
If sample selection process is more or
less evenly distributed then error caused
by instrument specification will result in
≈ 6.6 - 7.9% GRR leaving plenty of room
for repeatability to achieve final goal of
10% GRR
26

Next slide contains Xbar&R
Xbar&R is more stringent than ANOVA
1. 10 perfect samples
27

4816 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47
0.1
0.035
0.04
0.045
0.05
0.055
0.06
0.065
0.07
0.075
0.08
0.085
0.09
0.095
# Instrument Errors
GRR
Xbar&R ±50% of perfect sample placement
Xbar ±50 19.5 (5.13%)
Xbar ±100 20.7 (4.83%)
Xbar ±150 22.0 (4.55%)
Xbar ±200 23.7 (4.22%)
Xbar ±50 39.3 (2.54%)
Xbar ±100 41.7 (2.40%)
Xbar ±150 44.4 (2.25%)
Xbar ±200 47.8 (2.09%)
Xbar&R perfect sample placement
Anova ±50 17.8 (5.62%)
Anova ±100 19.3 (5.18%)
Anova ±150 21.0 (4.76%)
Anova ±200 22.9 (4.37%)
Anova ±50 35.7 (2.80%)
Anova ±100 38.8 (2.58%)
Anova ±150 42.2 (2.37%)
Anova ±200 46.1 (2.17%)
Note: Xbar&R is more stringent to pass.
Choose 25 instrument errors
28

4816 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47
0.1
0.035
0.04
0.045
0.05
0.055
0.06
0.065
0.07
0.075
0.08
0.085
0.09
0.095
# Instrument Errors
GRR
Xbar ±50 19.5 (5.13%)
Xbar ±100 20.7 (4.83%)
Xbar ±150 22.0 (4.55%)
Xbar ±200 23.7 (4.22%)
Xbar ±50 39.3 (2.54%)
Xbar ±100 41.7 (2.40%)
Xbar ±150 44.4 (2.25%)
Xbar ±200 47.8 (2.09%)
Xbar&R perfect sample placement
Anova ±50 17.8 (5.62%)
Anova ±100 19.3 (5.18%)
Anova ±150 21.0 (4.76%)
Anova ±200 22.9 (4.37%)
Anova ±50 35.7 (2.80%)
Anova ±100 38.8 (2.58%)
Anova ±150 42.2 (2.37%)
Anova ±200 46.1 (2.17%)
29

For 9% GRR the correct choices for allowable
instrument error to achieve the desired 10%
GRR with the 1% selection for repeatability are:
• Primary conclusion: Initial boundary condition is NOT SUFFICIENT to pass GRR at all!!
• Perfect parts and ONLY instrument error use 5.43% to 6.06% of the GRR 10% Goal
• Perfect parts and ONLY instrument error use 2.7% to 3.02% of the GRR 5% Goal
• Perfect parts, ONLY instrument and Sample Placement variation error use 4.22% to 5.62% of the GRR 10% Goal
• Perfect parts, ONLY instrument and Sample Placement variation error use 2.09% to 2.80% of the GRR 5% Goal
• Sample placement accounts for up to 1.3% of GRR 10% Goal for ANOVA
• Sample placement accounts for up to 0.63% of GRR 10% Goal for XBAR&R
Anova ±50 17.8 (5.62%)
Anova ±100 19.3 (5.18%)
Anova ±150 21.0 (4.76%)
Anova ±200 22.9 (4.37%)
Xbar ±50 19.5 (5.13%)
Xbar ±100 20.7 (4.83%)
Xbar ±150 22.0 (4.55%)
Xbar ±200 23.7 (4.22%)
Xbar ±50 39.3 (2.54%)
Xbar ±100 41.7 (2.40%)
Xbar ±150 44.4 (2.25%)
Xbar ±200 47.8 (2.09%)
Anova ±50 35.7 (2.80%)
Anova ±100 38.8 (2.58%)
Anova ±150 42.2 (2.37%)
Anova ±200 46.1 (2.17%)
9% GRR Target 4.5% GRR Target
30

�ݺ�ߣ

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