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GRR Made Simple
1
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
YES!!
4
There are 2 boundary conditions that a test engineer can
understand that are only “Sometimes” shown
5
This is the first!!6
This is the second!!7
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
conditions1. 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
XInstrumentError
0
2XInstrumentError
LSL
USL
ΔCV
ΔCV-Boundary Condition # 2
LCV - Boundary Condition # 1
Test Engineering Boundary Conditions
LCV
WhereUSL=UpperSpecifica>onLimitLSL=LowerSpecifica>onLimitLCV=LowestCapableValue ΔCV=USL-LSL=Differen>alCapability
The variable, the RED “X”, needs to be understood9
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 selectionPlus 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
4. 10 select samples to cause worst case within center ±100% of perfect samples placement
5. 10 select samples to cause worst case within center ±150% of perfect samples placement
6. 10 select samples to cause worst case within center ±200% of perfect samples placement
6 ways to look at:
# Instrument errors range from 10X to shown on graphs
13
Necessary Equations
The diagram on Slide 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
1−10GEUSL − LSL = ΔCVΔCV = 10 GE i (USL + LSL)+ 2 iOE( )ΔCV = 20 iOE +10 GE i (USL + LSL)( )
LSL = +LCV = OE0.1−GE
+LCV = OE0.1−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 11X0
LSL
USL
12X0
LSL
USL
13X0
LSL
USL
14X0
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
Per
centa
ge(
%)
ove
r 10%
GRR%Xbar&
R
Xbar&RMonteCarloSimula3oninExcel.5200simula3onsof10devices.Randomdeviceswithinlimits
UsingGageR&R(XBar&RMotorolaVersion)fromSta;s;calSolu;ons
Pleasenotethat11Xandgreaterisacceptable.HoweverneithertheXbar&RMethodnorANOVAcorrectlycalculateGRRatthecornersofinstrumentlimits
GRR%AN
OVA
ANOVAMonteCarloSimula3oninExcel.1010simula3onsof10devices.Randomdeviceswithinlimits
± 4mV offset ErrorLSL starts at +40mV (10X)USL starts at +120mVUSL-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
GR
R
ANOVA±50%ofperfectsampleplacement
ANOVA±100%ofperfectsampleplacement
10PerfectlyMeasuredDeviceSamplesforQualifica:on,1tester0offset,1tester+offset,1tester-offset
ANOVA±150%ofperfectsampleplacement
ANOVA±200%ofperfectsampleplacement
AnovaPerfect16.5(6.06%)Anova±50 17.8(5.62%)Anova±10019.3(5.18%)Anova±15021.0(4.76%)Anova±20022.9(4.37%)
XbarPerfect37.1(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%)
©VanBrollini2016
© Van Brollini 2016 © Van Brollini 2016 © Van Brollini 2016 © Van Brollini 2016 © Van Brollini 2016
© Van Brollini 2016 © Van Brollini 2016
© Van Brollini 2016
© Van Brollini 2016
ANOVAperfectsampleplacement
AnovaPerfect33.1(3.02%)Anova±50 35.7(2.80%)Anova±100 38.8(2.58%)Anova±150 42.2(2.37%)Anova±200 46.1(2.17%)
XbarPerfect18.4(5.43%)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:%numbersshownarerangepercenterror
EffectofOnlyDeviceSpecifica:onandSamplePlacementonGRRAllDeviceMeasurementsPerfect
±50% perfect sample placement
20
Next slide contains ANOVA 1. 10 perfect samples
2. 10 perfect samples ±50% 3. 10 perfect samples ±100% 4. 10 perfect samples ±150% 5. 10 perfect samples ±200%
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
GR
R
ANOVA±50%ofperfectsampleplacement
ANOVA±100%ofperfectsampleplacement
10PerfectlyMeasuredDeviceSamplesforQualifica:on,1tester0offset,1tester+offset,1tester-offset
ANOVA±150%ofperfectsampleplacement
ANOVA±200%ofperfectsampleplacement
AnovaPerfect16.5(6.06%)Anova±50 17.8(5.62%)Anova±10019.3(5.18%)Anova±15021.0(4.76%)Anova±20022.9(4.37%)
XbarPerfect37.1(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%)
©VanBrollini2016
© Van Brollini 2016 © Van Brollini 2016 © Van Brollini 2016 © Van Brollini 2016 © Van Brollini 2016
© Van Brollini 2016 © Van Brollini 2016
© Van Brollini 2016
© Van Brollini 2016
ANOVAperfectsampleplacement
AnovaPerfect33.1(3.02%)Anova±50 35.7(2.80%)Anova±100 38.8(2.58%)Anova±150 42.2(2.37%)Anova±200 46.1(2.17%)
XbarPerfect18.4(5.43%)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:%numbersshownarerangepercenterror
EffectofOnlyDeviceSpecifica:onandSamplePlacementonGRRAllDeviceMeasurementsPerfect
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
GR
R
ANOVA±50%ofperfectsampleplacement
ANOVA±100%ofperfectsampleplacement
10PerfectlyMeasuredDeviceSamplesforQualifica:on,1tester0offset,1tester+offset,1tester-offset
ANOVA±150%ofperfectsampleplacement
ANOVA±200%ofperfectsampleplacement
AnovaPerfect16.5(6.06%)Anova±50 17.8(5.62%)Anova±10019.3(5.18%)Anova±15021.0(4.76%)Anova±20022.9(4.37%)
XbarPerfect37.1(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%)
©VanBrollini2016
© Van Brollini 2016 © Van Brollini 2016 © Van Brollini 2016 © Van Brollini 2016 © Van Brollini 2016
© Van Brollini 2016 © Van Brollini 2016
© Van Brollini 2016
© Van Brollini 2016
ANOVAperfectsampleplacement
AnovaPerfect33.1(3.02%)Anova±50 35.7(2.80%)Anova±100 38.8(2.58%)Anova±150 42.2(2.37%)Anova±200 46.1(2.17%)
XbarPerfect18.4(5.43%)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:%numbersshownarerangepercenterror
EffectofOnlyDeviceSpecifica:onandSamplePlacementonGRRAllDeviceMeasurementsPerfect
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
GR
R
ANOVA±50%ofperfectsampleplacement
ANOVA±100%ofperfectsampleplacement
10PerfectlyMeasuredDeviceSamplesforQualifica:on,1tester0offset,1tester+offset,1tester-offset
ANOVA±150%ofperfectsampleplacement
ANOVA±200%ofperfectsampleplacement
AnovaPerfect16.5(6.06%)Anova±50 17.8(5.62%)Anova±10019.3(5.18%)Anova±15021.0(4.76%)Anova±20022.9(4.37%)
XbarPerfect37.1(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%)
©VanBrollini2016
© Van Brollini 2016 © Van Brollini 2016 © Van Brollini 2016 © Van Brollini 2016 © Van Brollini 2016
© Van Brollini 2016 © Van Brollini 2016
© Van Brollini 2016
© Van Brollini 2016
ANOVAperfectsampleplacement
AnovaPerfect33.1(3.02%)Anova±50 35.7(2.80%)Anova±100 38.8(2.58%)Anova±150 42.2(2.37%)Anova±200 46.1(2.17%)
XbarPerfect18.4(5.43%)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:%numbersshownarerangepercenterror
EffectofOnlyDeviceSpecifica:onandSamplePlacementonGRRAllDeviceMeasurementsPerfect
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
GR
R
ANOVA±50%ofperfectsampleplacement
ANOVA±100%ofperfectsampleplacement
10PerfectlyMeasuredDeviceSamplesforQualifica:on,1tester0offset,1tester+offset,1tester-offset
ANOVA±150%ofperfectsampleplacement
ANOVA±200%ofperfectsampleplacement
AnovaPerfect16.5(6.06%)Anova±50 17.8(5.62%)Anova±10019.3(5.18%)Anova±15021.0(4.76%)Anova±20022.9(4.37%)
XbarPerfect37.1(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%)
©VanBrollini2016
© Van Brollini 2016 © Van Brollini 2016 © Van Brollini 2016 © Van Brollini 2016 © Van Brollini 2016
© Van Brollini 2016 © Van Brollini 2016
© Van Brollini 2016
© Van Brollini 2016
ANOVAperfectsampleplacement
AnovaPerfect33.1(3.02%)Anova±50 35.7(2.80%)Anova±100 38.8(2.58%)Anova±150 42.2(2.37%)Anova±200 46.1(2.17%)
XbarPerfect18.4(5.43%)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:%numbersshownarerangepercenterror
EffectofOnlyDeviceSpecifica:onandSamplePlacementonGRRAllDeviceMeasurementsPerfect
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 2. 10 perfect samples ±50%
3. 10 perfect samples ±100% 4. 10 perfect samples ±150% 5. 10 perfect samples ±200%
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
GR
R
Xbar&R±50%ofperfectsampleplacement
Xbar&R±100%ofperfectsampleplacement
10PerfectlyMeasuredDeviceSamplesforQualifica:on,1tester0offset,1tester+offset,1tester-offset
Xbar&R±150%ofperfectsampleplacement
Xbar&R±200%ofperfectsampleplacement
XbarPerfect18.4(5.43%)Xbar±50 19.5(5.13%)Xbar±100 20.7(4.83%)Xbar±150 22.0(4.55%)Xbar±200 23.7(4.22%)
XbarPerfect37.1(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%)
©VanBrollini2016
© Van Brollini 2016 © Van Brollini 2016 © Van Brollini 2016 © Van Brollini 2016 © Van Brollini 2016
© Van Brollini 2016 © Van Brollini 2016
© Van Brollini 2016
© Van Brollini 2016
Xbar&Rperfectsampleplacement
AnovaPerfect16.5(6.06%)Anova±50 17.8(5.62%)Anova±10019.3(5.18%)Anova±15021.0(4.76%)Anova±20022.9(4.37%)
AnovaPerfect33.1(3.02%)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:%numbersshownarerangepercenterror
EffectofOnlyDeviceSpecifica:onandSamplePlacementonGRRAllDeviceMeasurementsPerfect
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
GR
R
Xbar&R±50%ofperfectsampleplacement
Xbar&R±100%ofperfectsampleplacement
10PerfectlyMeasuredDeviceSamplesforQualifica:on,1tester0offset,1tester+offset,1tester-offset
Xbar&R±150%ofperfectsampleplacement
Xbar&R±200%ofperfectsampleplacement
XbarPerfect18.4(5.43%)Xbar±50 19.5(5.13%)Xbar±100 20.7(4.83%)Xbar±150 22.0(4.55%)Xbar±200 23.7(4.22%)
XbarPerfect37.1(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%)
©VanBrollini2016
© Van Brollini 2016 © Van Brollini 2016 © Van Brollini 2016 © Van Brollini 2016 © Van Brollini 2016
© Van Brollini 2016 © Van Brollini 2016
© Van Brollini 2016
© Van Brollini 2016
Xbar&Rperfectsampleplacement
AnovaPerfect16.5(6.06%)Anova±50 17.8(5.62%)Anova±10019.3(5.18%)Anova±15021.0(4.76%)Anova±20022.9(4.37%)
AnovaPerfect33.1(3.02%)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:%numbersshownarerangepercenterror
EffectofOnlyDeviceSpecifica:onandSamplePlacementonGRRAllDeviceMeasurementsPerfect
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
AnovaPerfect16.5(6.06%)Anova±50 17.8(5.62%)Anova±10019.3(5.18%)Anova±15021.0(4.76%)Anova±20022.9(4.37%)
XbarPerfect18.4(5.43%)Xbar±50 19.5(5.13%)Xbar±100 20.7(4.83%)Xbar±150 22.0(4.55%)Xbar±200 23.7(4.22%)
XbarPerfect37.1(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%)
AnovaPerfect33.1(3.02%)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