Measurement System Analysis*- Tutorial
Govind Ramu, P. Eng, ASQ FellowASQ CMQOE, CQE, CSSBB, CQA,CSQE, CRE
Quality Manager, Six Sigma MBB
JDSU, Milpitas
ASQ Silicon Valley Two day Quality ConferenceTheme: Road to Innovation QualityTrack: Statistics and Reliability
* Material compiled from external resources, enhanced with additional presenter’s materials for better understanding.
If you see this picture in the slide, Class Room Hands on Exercise involved.Bring your Laptop & MINITAB 16
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Measurement Systems AnalysisHow will you know the measures are
accurate, linear, stable, repeatable andreproducible?
Data Collection PlanWho will
Do it?Type of Operational Measurement Data Tags Needed Data Collection Person(s) What? Where? When? How Many?
Measure Measure Definition or Test Method to Stratify the Data Method Assigned
Name of X or Y Clear definition of Visual Data tags are Manual? State What Location How The numberparameter attribute or the measurement inspection defined for the Spreadsheet? who has measure is for often of data
or condition discrete defined in such a or automated measure. Such Computer based? the being data the points to be data, way as to achieve test? as: time, date, etc. responsibility? collected collection data collected
measured product or repeatable results Test instruments location, tester, is per sampleprocess from multiple are defined. line, customer, collected
data observers buyer, operator,Procedures for etc.data collectionare defined.
Sample PlanDefine What to Measure Define How to Measure
Measurement System Analysis
Control Plan, FMEA, Customer Specification, manufacturing Work instructions CTQ Vs CTP matrix are typical sources of input for “What to measure?”
Responsibility for Measurement System Qualification and release?Responsibility for measurement training?Who will measure?
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Accuracy & Precision
Gage Bias
Linearity
Gage Repeatability
Gage Reproducibility
Gage R&R
% Tolerance Gage R&R
% Process Variation Gage R&R
Gage Resolution
Number of Distinct Categories
Stability
Attribute R & R
Measurement Systems Analysis (MSA)Topics
4
Precise & Not Accurate
Accurate & Not Precise
Accurate & Precise
Target Target Target
Measurement Systems Analysis (MSA)Precision vs. Accuracy
Repeatability portion of GRR studies refers to Precision
Bias refers to Accuracy
5
Width
There Seems To Be A Lot of Variation in Our Widgets!
How Good Is Our Measurement System ?
Freq
uenc
y
Widget Machine
Measurement Systems Analysis (MSA)Context
6
Step 1: A Standard Is Created in Test Lab
Width = 1.032 mmStep 2: Standard Is Measured with Your Equipment
Repeat Measurements Many Times
Always Re-Set Part in Test Fixture Between Measurements
Standard
Measurement Systems Analysis (MSA)Gage Bias
7
Step 3: Plot Data and Compare to Standard
0 1.032
X = 1.046
0.014
Step 4: Calculate Correction (Bias) To Be Applied To Your Measurements
Bias = (1.046 – 1.032) / 1.032 = 1.4%Corrected Measurement = (0.986) x (Your Measurements)
What You Measured
“True” Value
n= =
∑X
Xi
i 1
n
fi
Definition of Mean:
Width
Freq
uenc
y
Measurement Systems Analysis (MSA)Gage Bias - Measurement
Due to linearity errors, you may need to use several standards across your measurement scale to evaluate whether the same correction formula applies everywhere across the scale.
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Linearity
Interpreting the resultsThe %Linearity (absolute value of the slope * 100) is 13.2, which means that the gage linearity accounts for 13% of the overall process variation.The %Bias for the reference average is 0.3, which means that the gage bias accounts for less than 0.3% of the overall process variation.
To address actual process variability, the variation due to the measurement system must first be identified and separated from that of the process
Possible Sources of Variation
ProcessInputs Outputs Inputs MeasurementProcess
Outputs• Observations• Measurements• Data
Long-term Process Variation
Actual Process Variation
Accuracy (Bias)
Measurement Variation
Observed Process Variation
Short-term Process Variation
Variation due to gage
Variation due to operator
Precision (Pure Error)
Stability (time dependent)
Linearity (value dependent)
Repeatability
Reproducibility
within sample variation Operator X Part
Interaction
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How Repeatable Are Measurements Made By One Appraiser?
Measure 1 Production Part Over and Over Again
What We Expected: What We Observed:
Width WidthWhy So Much Variation?
Measurement Systems Analysis (MSA)Gage Repeatability
11
SGage
5.15 SGage
Gage Repeatability
0.5%0.5%
Standard Deviation of Gage (one Appraiser)
Now Gage Repeatability Can Be Calculated
= =
∑i 1
n
Sn -1
fi −( )X X
i
2
Definition of Standard Deviation:
Freq
uenc
y
Width
99% of Measurements Fall in the Gage
Repeatability Range
X
Measurement Systems Analysis (MSA)Gage Repeatability - Measurement
12
How Reproducible Are Measurements Made By Several Appraisers?
Appraiser #1:
Appraiser #2:
Appraiser #3:
All Measurements Pooled Together
Appraiser 1Appraiser 3
Appraiser 2
Measurement Systems Analysis (MSA)Gage Reproducibility
13
T P MS S S= +2 2
Observed Variation (ST)
Measurement Variation (SM)
MSM EV AVS S S= +
2 2
Repeatability Issue
Reproducibility Issue
EV = Equip Variation AV = Appraiser Variation
5.15 SM Gage Repeatability & Reproducibility
Now Let’s Look at the Widget Process Again . . .
Process Variation (SP)Width
Width
ST
Measurement Systems Analysis (MSA)Gage Repeatability and Reproducibility
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USLLSL USLLSL
Resolution Refers To How Many Intervals Are Between USL and LSL
It is highly recommended that Resolution Is ≥ Than 10 divisions of your process variation, 5% of your specification width.
Measurement Systems Analysis (MSA)Resolution
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T P MS S S= +2 2
ST
Width
Observed Variation of Process Output
Number of Distinct Categories = 1.41 x SP
SM
Categories < 2 ---- Gage Has No Value for Controlling Process
Categories = 2 ---- Equivalent To Discrete Measurement
Categories > 4 ---- Acceptable for Measuring / Improving Process
Measurement Systems Analysis (MSA)Number of Distinct Categories
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Guidelines for NDC
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Have Several Appraisers Measure 1 Product Many Times with 1 Gage and Compare Results to the Specification Range :
UPPER SPECLOWER SPEC
Δgood
Δbad
ΔspecΔgood /
ΔspecΔbad /MS
MSSmall Gage Variability
Large Gage Variability
Good Measurement
System:
Bad Measurement
System:
≥ 0 30.
≈ 010.
Recommendation: It Is Best To Repeat This Procedure on Several Parts Across the Full Specification Range
Make Sure You Evaluate Gage Accuracy, Too!
Measurement Systems Analysis (MSA)% Tolerance Gage R&R
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Freq
uenc
y
Cycle Time
USL
0
Sometimes It Is Not Possible To Calculate % Tolerance GR&R - - - The Spec Is One – Sided!
% Process Variation GR&R =SM X 100
Shistorical
Process Standard Dev from Historical Data
6*Historical Std Dev
Measurement Systems Analysis (MSA)% Process Variation Gage R&R
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% Tolerance GR&R =5.15 SM
USL - LSLX 100
UPPER SPECLOWER SPEC
Δ
Diameter
Δ = 5.15*SM
SM
Measurement Systems Analysis (MSA)% Tolerance Gage R&R - Measurement
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Long TermCapability
Short TermCapability
xA
xB
xC
True Value
Repeatability
Reproducibility
Accuracy
Stability
First period of time Second period of time
xA
xB
xC
Measurement Systems Analysis (MSA)The Big Picture
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TYPE 1 Gauge Study
Use the Type 1 Gage Study to evaluate the capability of a measurement process. This study evaluates the combined effects of bias and repeatability based on multiple measurements from a single part.
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What Dangers Exist
LSL USL
True value of the part
Accepting BAD product Rejecting GOOD product
Operator Variation
Instrument Variation
True value of the part
Operator Variation
Instrument Variation
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Chasing Ghosts
Parts
Production Variation
Target
What wasproduced
What wasobserved
Process Adjustment
Operator Variation
Instrument Variation
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Short-Term Vs Long-Term Capability
LSL USLTarget
Time 1
Time 2
Time 3
Time 4
Over long term conditions, a “typical” process will shift and drift by approximately 1.5 standard deviations*.
“Short-term capability” (Cp, Cpk)
“Long-term performance” that includes changes to material, multiple shifts, Operators, environmental changes (Pp, Ppk)
(Back to Basics)
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Capability & GRR Grid
% G
R&
R*
Cpk/Ppk*
Low
High
Low High
>20%
<20%
<1.1 >1.1* GGR 20%, Cp, Cpk 1.1 are an example, decide what is acceptable for your organization.
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Scenario- High GR&R/Low Cp & Cpk
LSL USL
True value of the part
Accepting BAD product Rejecting GOOD product
Instrument VariationRepeatability
Operator VariationReproducibility
Instrument VariationRepeatability
True value of the part
Operator VariationReproducibility
ProcessShift
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Scenario- low GR&R/Low Cp & Cpk
LSL USL
True value of the part
Accepting BAD product Rejecting GOOD product
Instrument VariationRepeatability
Operator VariationReproducibility
True value of the part
Instrument VariationRepeatability
Operator VariationReproducibility
ProcessShift
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Scenario- High GR&R/High Cp/ High Cpk
LSL USL
True value of the part
Accepting BAD product Rejecting GOOD product
Instrument VariationRepeatability
Operator VariationReproducibility
Instrument VariationRepeatability
True value of the part
Operator VariationReproducibility
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Scenario- low GR&R/High Cp/Cpk
LSL USL
True value of the part
Accepting BAD product Rejecting GOOD product
Instrument VariationRepeatability
Operator VariationReproducibility
True value of the part
Instrument VariationRepeatability
Operator VariationReproducibility
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Prioritizing Improvement Efforts
•If new test station/equipment added, operator changed, equipment overhauled, new GRR study is required. If no changes 6 months frequency ofGRR monitoring is a good practice.** If there has been sudden change in process variation (For good or bad), extended period of lack of stability, a new study has to be conducted and control limits to be recalculated. If no changes, 6 months frequency of review of control limits is a good practice.
CTQ: Critical to Quality Characteristics, CTP: Critical to Process Parameters Relationship between CTP to CTQ to be established upfront.
Pro
duct
Pro
cess
CTQ1
CTQ2
CTQ3
CTP1
CTP2
CTP3
LCL UCL Stability** Cp/Pp Cpk/Ppk
DateCL
ESTB.GRR%DateGRR*
Alpha/Beta Risk%
GRR/ CL Next due
Date
Significant Moderate Weak
CTQ 1 2 3
1
2
3
CTP
Relationship
01/07
01/07
01/07
01/07
01/07
01/07
07/07
07/07
07/07
07/07
07/07
07/07
37%
8%
25%
7%
12%
25%
01/07
01/07
01/07
01/07
01/07
01/07
20
1.30
15
200
1.5
1.7
24
1.80
18
208
1.7
2.0
NO
YES
NO
YES
YES
NO
0.8
0.9
1.2
1.3
1.00
0.95
0.6
0.88
1.15
1.25
0.92
0.82
8/20
3/8
1/2
0.03/0.07
4/11
6/17
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Relationship between Gauge R & R, Process Capability
Practical Applications
33
Planning for GR & R
• Verify if the Measurement System is Calibrated. (You might use the GR & R for future Test System comparison). Linearity- Bias study preferably conducted prior to GR & R?
• Verify if the operators are adequately training in measurement ( incl. loading, setting, aligning, etc).
• Verify if the vibration lighting, temperature, humidity and other factors are conducive to measurement.
• Verify the samples selected represent the process variation. Verify the Die positions selected as representative of wafer map.
• Verify the GR & R Design has minimum 15 (n x r)
• Understand the Measurement System Configuration & Human interactions required in measurement process.
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%Contribution
Source VarComp (of VarComp)
Total Gage R&R 1.40E-08 12.27
Repeatability 7.89E-09 6.93
Reproducibility 6.07E-09 5.34
Appraiser No 4.25E-09 3.73
Appraiser No*Part No 1.83E-09 1.61
Part-To-Part 9.99E-08 87.73
Total Variation 1.14E-07 100.00
StdDev Study Var %Study Var %Tolerance
Source (SD) (5.15*SD) (%SV) (SV/Toler)
Total Gage R&R 1.18E-04 6.09E-04 35.02 15.21
Repeatability 8.88E-05 4.57E-04 26.33 11.44
Reproducibility 7.79E-05 4.01E-04 23.10 10.03
Appraiser No 6.52E-05 3.36E-04 19.32 8.39
Appraiser No*Part No 4.27E-05 2.20E-04 12.67 5.50
Part-To-Part 3.16E-04 1.63E-03 93.67 40.69
Total Variation 3.37E-04 1.74E-03 100.00 43.44
% Tolerance GR&R
Total Variation
Process Variation
Measurement Variation
Appraiser Variation
Equipment Variation
Measurement Systems Analysis (MSA)Gage Analysis Using Minitab – Example: Output
35
PartOperatorBy2
Operator2
ityRepeatabil2
Product2
Total2 σσσσσ +++=
Measurement Systems Analysis (MSA)In summary
100.00%
87.73% 12.27%
6.93%
6.93%
5.34%
3.73% 1.61%
Overall Part to Part Repeatability Operator Operator by Part100.00% 87.73% 6.93% 3.73% 1.61%
Reproducibility
12.27%
87.73%
Components of Variation
5.34%
5.34%
Minitab Example Result
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Gage name:Date of study:Reported by:Tolerance:Misc:
0
0.3755
0.3760
0.3765 1 2 3
Xbar Chart by Appraiser No
Sam
ple
Mea
n
Mean=0.3758UCL=0.3760
LCL=0.3757
0
0.0000
0.0001
0.0002
0.0003
0.0004 1 2 3
R Chart by Appraiser No
Sam
ple
Rang
e
R=0.00015
UCL=3.86E-04
LCL=0
1 2 3 4 5 6 7 8 9 10
0.37550.37560.37570.37580.37590.37600.37610.37620.37630.37640.3765
Part No
Appraiser NoAppraiser No*Part No Interaction
Aver
age
1 2 3
1 2 3
0.3755
0.3760
0.3765
Appraiser No
By Appraiser No 1 2 3 4 5 6 7 8 9 10
0.3755
0.3760
0.3765
Part No
By Part No%Contribution %Study Var %Tolerance
Gage R&R Repeat Reprod Part-to-Part0
50
100
Components of Variation
Perc
ent
Target Run Out Diagnostics Chart To Isolate Problems
Measurement Systems Analysis (MSA)Gage Analysis Using Minitab – Example, contd.
37
1 2 3 4 5
Excellent MarginalMarginal Un-AcceptableUn-Acceptable
Solder JointFeed through
Scale:
This Scale Is Discrete ---- There Is No 2.3 or 3.15 !
To Test Our Measurement System, We Need Discrete GRR
Circuit Board
Measurement of Solder Quality:
Measurement Systems Analysis (MSA)Continuous vs. Discrete Gage R&R
38
• Example:
Select 15 parts which span the full range of your “current part capability.” In other words, your sample should include extremes. Use 3 “trained” appraisers to randomly appraise each part 2 times (not consecutively). Also, select an “expert” to appraise each part 1 time (or use a set of known standards). Appraisals by the “expert” are considered to be the “reference values.” The Minitab looks for consistency “within” and “between” appraisers.
• You will need to continue to improve “measurement procedures / definitions” and “training” of appraisers until you can exceed a score of 90% agreement. A score greater than 95% is considered to be excellent.
Measurement Systems Analysis (MSA)Discrete Gage R&R – How to
39
Discrete Gage R&R
Sample Standard AppraiserA-1 AppraiserA-2 AppraiserB-1 AppraiserB-2 AppraiserC-1 AppraiserC-21 Pass Pass Pass Pass Pass Fail Fail2 Pass Pass Pass Pass Pass Fail Fail3 Fail Fail Fail Fail Pass Fail Fail4 Fail Fail Fail Fail Fail Fail Fail5 Fail Fail Fail Pass Fail Fail Fail6 Pass Pass Pass Pass Pass Pass Pass7 Pass Fail Fail Fail Fail Fail Fail8 Pass Pass Pass Pass Pass Pass Pass9 Fail Pass Pass Fail Fail Fail Fail10 Fail Pass Pass Fail Fail Fail Fail11 Pass Pass Pass Pass Pass Pass Pass12 Pass Pass Pass Pass Pass Pass Pass13 Fail Fail Fail Fail Fail Fail Fail14 Fail Fail Fail Fail Pass Fail Fail
Within Each Appraiser(Repeatability for Each Appraiser)
Appraiser # Inspected # Matched Percent (%)
A 14 14 100.0
B 14 11 78.6
C 14 14 100.0
Each Appraiser vs Standard(Accuracy of Each Appraiser)
Appraiser # Inspected # Matched Percent (%)
A 14 11 78.6
B 14 10 71.4
C 14 11 78.6
Between All Appraisers(Repeatability & Reproducibility)
# Inspected # Matched Percent (%)
14 7 50.0
All Appraisers vs StandardAssessment Agreement (Accuracy)
# Inspected # Matched Percent (%)
14 6 42.9
Known Standards Appraisers A, B, C
Measurement Systems Analysis (MSA)Discrete Gage R&R – Example
40
A B C
40
50
60
70
80
90
100
Appraiser
Per
cent
Within Appraiser
A B C
40
50
60
70
80
90
100
Appraiser
Per
cent
Appraiser vs Standard
Assessment Agreement
[ , ] 95.0% CI
Percent
Within Each Appraiser(Repeatability for Each Appraiser)
Appraiser # Inspected # Matched Percent (%)
A 14 14 100.0
B 14 11 78.6
C 14 14 100.0
Each Appraiser vs Standard(Accuracy of Each Appraiser)
Appraiser # Inspected # Matched Percent (%)
A 14 11 78.6
B 14 10 71.4
C 14 11 78.6
To Shrink “Confidence Intervals” Increase Number of Samples and Repetitions
Measurement Systems Analysis (MSA)Discrete Gage R&R – Example: Diagnostics
41
• Discrete GRR > 90%, Recommended
• if < 90%, use graphical output to diagnose
• Observations:
• Appraisers A and C are very consistent “within” themselves but are not consistent with the expert (or standard).
• We can improve Appraisers A and C by re-training them.
• Appraiser B is not consistent in grading the individual “parts.” We need to investigate why there is a lack of consistency. (If “internal consistency” cannot be improved for Appraiser C, it will probably not be useful to re-train them).
• Confidence interval: The GR&R in this example was based on 14 parts observed by 3 appraisers with 2 observations by each appraiser. The large confidence interval (which is an indication of level of uncertainty) is due to the small number of “samples.” To decrease the confidence interval (and improve our certainty), we need to increase the number of “samples” and “repetitions.”
Measurement Systems Analysis (MSA)Discrete Gage R&R – Example: Analysis
42
Measurement Systems Analysis (MSA)Discrete Gage R&R – Example: in Minitab
43
Measurement Systems Analysis (MSA)Gage R&R – Decision on Measurement Capability
Excellent GRR Acceptable GRR Unacceptable GRR
GRR as % of Tolerance < 10% <30% >30%GRR as %
Contribution to Variation
<10% >10%
No. of distinct Categories >4 <4
Discrete Y Appraiser vs. Standard
Lower Confidence level (at 95% Confidence)
> 90%
Variable Y
If GRR acceptability criteria is not met, do not proceedInvestigate the problem areas
Repeatability (Appraiser training)Reproducibility (Measurement system, SOP)Accuracy (Calibration)
Repeat GRR studies until Acceptable
44
Automobile Industry Action Group (AIAG) Guidelines
If the Total Gage R&R contribution in the %Study Var column (% Tolerance, %Process) is:Less than 10% - the measurement system is acceptable.Between 10% and 30% - the measurement system is acceptable depending on the application, the cost of the measuring device, cost of repair, or other factors. Greater than 30% - the measurement system is unacceptable and should be improved.
If you are looking at the %Contribution column, the corresponding standards are: Less than 1% - the measurement system is acceptable.Between 1% and 9% - the measurement system is acceptable depending on the application, the cost of the measuring device, cost of repair, or other factors. Greater than 9% - the measurement system is unacceptable and should be improved.
45
Automobile Industry Action Group (AIAG) GuidelinesNumber of Distinct Categories
Minitab calculates the number in this statement by dividing the standard deviation for Parts by the standard deviation for Gage, then multiplying by 1.41 and truncating this value. This number represents the number of non-overlapping confidence intervals that will span the range of product variation. You can also think of it as the number of groups within your process data that your measurement system can discern.
Imagine you measured 10 different parts, and Minitab reported that your measurement system could discern 4 distinct categories. This means that some of those 10 parts are not different enough to be discerned as being different by your measurement system. If you want to distinguish a higher number of distinct categories, you need a more precise gage.
The Automobile Industry Action Group (AIAG) [1] suggests that when the number of categories is less than 2, the measurement system is of no value for controlling the process, since one part cannot be distinguished from another. When the number of categories is 2, the data can be divided into two groups, say high and low. When the number of categories is 3, the data can be divided into 3 groups, say low, middle and high. A value of 5 or more denotes an acceptable measurement system.
46
© 2010 Minitab, Inc.
MSA – Other Scenarios• Other factors• Comparing two gages
• Joel Smith• MINITAB
© 2010 Minitab, Inc.
MSA – Other Scenarios
Other factors
Comparing two gages
© 2010 Minitab, Inc.
Other factors
© 2010 Minitab, Inc.
Other factors
© 2010 Minitab, Inc.
Other Factors
What are “other factors”• Influence measurement• Exist in production environment• May interact with operator or other factors
© 2010 Minitab, Inc.
Why Reproducability?
Recall from Govind:• Repeatability represents “pure error”• Isolates ability to repeat measurements under equal conditions
Practically:• Reproducability likely similar with different “like” devices• Maintain isolation of effect from device
© 2010 Minitab, Inc.
Effect on Results
Inclusion does not affect rules:• # Distinct Categories (<2, 2-4, >4)• % Contribution (<1%, 1-9%, >9%)• % Tolerance (<10%, 10-30%, >30%)
Inclusion will increase Reproducability• Statistical test important (more later)
© 2010 Minitab, Inc.
Types of Factors
Fixed• Specific levels are important
Random• Specific levels are not important
Nested• Levels of one factor dependent on another
Interactions• Effect of one factor dependent on level of another
© 2010 Minitab, Inc.
Weld Quality Example
We use an electromagnetic test to evaluate weld quality on a bike frame
© 2010 Minitab, Inc.
Weld Quality Example
Our measurement is impedance
We randomly select 10 bicycle frames for testing by 3 operators
We identify the following factors as potentially affecting measurement:
• Temperature• Humidity
© 2010 Minitab, Inc.
Weld Quality Example
Experiment is run with:• 3 Operators (Levi, George, Christian)• 10 Bikes• 2 Temperature Levels (70 and 80)• 2 Humidity Levels (50, 70)
High number of runs (240)
© 2010 Minitab, Inc.
Gage R&R (Expanded)
Stat > Quality Tools > Gage R&R Study > Gage R&R (Expanded)
© 2010 Minitab, Inc.
Weld Quality – ANOVA Table
ANOVA Table with Terms Used for Gage R&R Calculations
Source DF Seq SS Adj SS Adj MS F PBike 9 0.0406778 0.0406778 0.0045198 1623.64 0.000Operator 2 0.0010840 0.0010840 0.0005420 271.63 0.000Temperature 1 0.0002827 0.0002827 0.0002827 101.55 0.000Humidity 1 0.0000814 0.0000814 0.0000814 40.82 0.000Bike*Temperature 9 0.0000251 0.0000251 0.0000028 1.40 0.192Repeatability 217 0.0004330 0.0004330 0.0000020Total 239 0.0425840
© 2010 Minitab, Inc.
Weld Quality - % Contribution
Variance Components
%ContributionSource VarComp (of VarComp)Total Gage R&R 0.0000118 5.90Repeatability 0.0000020 1.00Reproducibility 0.0000098 4.90
Operator 0.0000068 3.37Temperature 0.0000023 1.17Humidity 0.0000007 0.33Bike*Temperature 0.0000001 0.03
Part-To-Part 0.0001882 94.10Bike 0.0001882 94.10
Total Variation 0.0002000 100.00
© 2010 Minitab, Inc.
Weld Quality – Gage EvaluationProcess tolerance = 0.02
Gage Evaluation
Study Var %Study Var %ToleranceSource StdDev (SD) (6 * SD) (%SV) (SV/Toler)Total Gage R&R 0.0034359 0.0206157 24.30 103.08Repeatability 0.0014126 0.0084755 9.99 42.38Reproducibility 0.0031321 0.0187929 22.15 93.96
Operator 0.0025981 0.0155886 18.37 77.94Temperature 0.0015273 0.0091635 10.80 45.82Humidity 0.0008137 0.0048821 5.75 24.41Bike*Temperature 0.0002563 0.0015379 1.81 7.69
Part-To-Part 0.0137189 0.0823132 97.00 411.57Bike 0.0137189 0.0823132 97.00 411.57
Total Variation 0.0141426 0.0848556 100.00 424.28
Number of Distinct Categories = 5
© 2010 Minitab, Inc.
Weld Quality - Misclassification
Probabilities of Misclassification
Joint Probability
Part is bad and is accepted 0.054Part is good and is rejected 0.067
Conditional Probability
False Accept 0.115False Reject 0.126
© 2010 Minitab, Inc.
Weld Quality - Graphical
© 2010 Minitab, Inc.
Effect of Factors
What if the additional factors were not included?• % Contribution and % StudyVar would be lower• Probability of Misclassification lower• % Tolerance lower• Number of Distinct Categories higher
BUT:• This is an illusion• Goal is to assess MS, not minimize MS Variation at this point• Analysis does not change reality
© 2010 Minitab, Inc.
Effect of Factors
Analysis without “other factors” looks better
Which will you experience in production?
Statistic With Factors W/O Factors%Contribution 5.90 5.21%Tolerance 103.08 96.45Distinct Categories 5 6P(Accepting Bad) .054 .051P(Rejecting Good) .067 .063
© 2010 Minitab, Inc.
Comparing Two Gages
© 2010 Minitab, Inc.
Comparing Two Gages
Electromagnetic testing turns out to be very expensive
A cheaper alternative is available
How do we determine if it is equivalent?• Is the new gauge adequate?• Is it biased?• Does it exhibit linearity?
© 2010 Minitab, Inc.
Comparing Two Gages
Alternate gage results in slightly more variation
Still meets acceptability criteria
Statistic Original Alternate%Contribution 5.90 6.69%Tolerance 103.08 110.84Distinct Categories 5 5P(Accepting Bad) .054 .057P(Rejecting Good) .067 .072
© 2010 Minitab, Inc.
Orthogonal Regression
Orthogonal Regression• Assumes measurement error in X and Y direction• Requires prior estimate of these errors• Tests bias and linearity
From our MSA’s:• Original Gage Var: .0000118• Alternate Gage Var: .0000136• Ratio = 1.1525 (Alternate/Original)
Choice of X and Y are arbitrary
© 2010 Minitab, Inc.
Orthogonal Regression
Stat > Regression > Orthogonal Regression
© 2010 Minitab, Inc.
Orthogonal Regression
© 2010 Minitab, Inc.
Orthogonal Regression
What do we want to see here?• Constant ~ 0• Impedance ~ 1
Regression EquationImpedance2 = - 0.114 + 1.009 Impedance
Coefficients
Predictor Coef SE Coef Z P Approx 95% CIConstant -0.11388 0.136040 -0.8371 0.403 (-0.380513, 0.15275)Impedance 1.00948 0.011336 89.0478 0.000 ( 0.987263, 1.03170)
© 2010 Minitab, Inc.
Linearity and Bias
© 2010 Minitab, Inc.
Orthogonal Regression
To evaluate linearity and bias use CI’s:• 0 is contained within Constant CI• 1 is contained within Impedance CI
No evidence of linearity or bias difference between gages
Regression EquationImpedance2 = - 0.114 + 1.009 Impedance
Coefficients
Predictor Coef SE Coef Z P Approx 95% CIConstant -0.11388 0.136040 -0.8371 0.403 (-0.380513, 0.15275)Impedance 1.00948 0.011336 89.0478 0.000 ( 0.987263, 1.03170)
© 2010 Minitab, Inc.
Comparing Two Gages
We have determined:• Alternate gage has slightly more variation• Alternate gage does not consistently measure higher or lower
across all impedances• Alternate gage does not measure higher or lower as
impedance increases
Future measurement plan:• Use alternate gage regularly• Schedule original gage tests to re-establish “equivalence”
© 2010 Minitab, Inc.
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