GRR Made Easy

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




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


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

http://www.dmaictools.com

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


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


10PerfectlyMeasuredDeviceSamplesforQualifica:on,1tester0offset,1tester+offset,1tester-offset



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


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%)


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








©VanBrollini2016










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








©VanBrollini2016










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








©VanBrollini2016










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








©VanBrollini2016










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







©VanBrollini2016





Xbar&Rperfectsampleplacement





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








©VanBrollini2016





Xbar&Rperfectsampleplacement





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





9% GRR Target 4.5% GRR Target

30

GRR Made Easy

Engineering

Transcript of GRR Made Easy