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8/14/2019 3RD Edition February 2003 OMNEX, Inc 3025 Boardwalk Suite 120
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MSA(Measurement System Analysis)
1
3RD EditionFebruary 2003
OMNEX, Inc3025 Boardwalk Suite 120
Ann Arbor, MI 48108USA
Tel: 734.761.4940Fax: 734.761.4966
e-mail: [email protected]
www.omnex.com
Omnex provides training and software to the international market with offices inthe USA, Brazil, Canada, India and T hailand. Omnex offers over 25 training
courses in business a nd quality management systems worldwide.
1998-2003
2
Intent of MSA Training
To provide participants with:
An understanding of the importance of MSA incontrolling and improving the process
An understanding that Measurement systems areprocesses for decision making
A practical knowledge of the use of statisticalmethods in analyzing measurement systems
Information needed to establish quantifiers,measurables and limits for measurement uncertaintyto make professional, informed estimates.
3
Chapter 1 Introduction to MSA
Chapter 2 MSA: ISO/9001:2000 & Sector-specific Requirements
Chapter 3 Statistical Properties of Measurement Systems3b Discrimination, Ca libration, Reference Standards3c Bias, Linearity, Stability3d GRR Studies
Chapter 4 Other Topics4a Advanced analysis (ANOVA)4b Attribute Systems,4c Automatic Systems4d Non-Replicable Systems
Chapter 5 Measurement Planning
Chapter 6 Application of MSA to Continual Improvement
Chapter 7 Analysis of Results
Chapter 8 Summary and definitions
Chapter 9 Appendix
MSA Course Map
Chapter 1
Introduction to MSAIntroduction to MSA
5
Measurement system is the collection of instrumentsor gages, standards, operations, methods, fixtures,software, personnel, environment and assumptionsused to quantify a unit of measure or fix assessmentto the feature characteristic being measured; the
complete process used to obtain measurement.
What is a Measurement System?
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6
A measurement system is a process
What is a Measurement System?
OperationInput Output
Key Process Output VariableKPOV (deliverable) = a decision on a product,
process, or service
via a number assigned to a characteristic of aproduct, process, or service
The first step in assessing a system is to understandthis process and determine if it will satisfy ourrequirements
7
From this definition, it follows that a measurement process maybe viewed as a manufacturing process that produces decisions
via numbers (data) for its output.
Viewing a measurement system this way is useful because itallows us to bring to bear all the concepts, philosophy and toolsthat have already demonstrated their usefulness in the area ofstatistical process control.
What is a Measurement System?(contd)
8
Foundation of Analysis
Data is derived from objects, situations, or
phenomenon in the form of measurements.
Data is used to classify, describe, improve
or control objects, situations or phenomenon.
9
Measurement System Example
As a result of theactivity, we make adecision based on avalue that representsthe diameter
To measure the insidediameter of a tube, weuse a system thatincludes:
item of interest
personnel
method to use theequipment
environment wherethe measurement isperformed
10
1. Use experience, not data.
2. Collect data, but just look at the numbers.
3. Group the data so as to form charts and graphs.
4. Use census data with descriptive statistics.
5. Use sample data with descriptive statistics.
6. Use sample data with inferential statistics.
Levels of Analysis
11
Measurement Issues
Does the measurement system have adequatediscrimination?
Is the measurement system statistically stable overtime?
Is the measurement error (variation) small?
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12
Measurement knowledge to be obtained
How big is the measurement error?
What are the sources of measurement error?
Is the measurement system stable over time?
Is the measurement system capable for this study?
How do we improve the measurement system?
13
What is MSA?
Measurement System Analysis (MSA)
MSA primarily deals with analyzing the effect of
the measurement system on the measured value
The objective of MSA is to assess the quality ofthe measurement system.
We test the system to determine its statisticalproperties, and use them in comparison with acceptedstandards, our needs and customer requirements.
14
Overall Objective of MSA
Understanding the Measurement System as a process
Uncertainty of Measurement
The range within which the true value of acharacteristic is estimated to lie.
System properties can be expressed as
statistical distribution of a series of measurements,
standard deviations,
probability,
percentages,
error as the difference between actual value and thereference value,
as points on a control chart or diagram,
etc.
15
Best-in-Class Approach
Determinations on these fundamental issues aremost meaningful if made relative toprocessvariation
Reporting measurement error as only a per cent oftolerance is generally inadequate for the worldwidemarket where emphasis is on continual processimprovement
Chapter 2
MSA & ISO 9001:2000& Sector-Specific Requirements
MSA & ISO 9001:2000
& Sector-Specific Requirements
17
QS 9000
Control of Inspection, Measuring and Test Equipment - 4.11
General - 4.11.1
all inspection, measuring and test equipment
including software or hardware shall have themeasurement uncertainty known and be withinacceptable guidelines
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Control Procedure - 4.11.2
determine accuracy and precision (required)
product accepted previously by inspection,measurements, and test devices discovered tobe out of calibration must be re-inspected
environmental conditions during calibrationand testing must be evaluated to assess theireffect on the measurement system
ensure handling, preservation and storage
safeguard inspection of test hardware andsoftware from adjustments
QS 9000
19
Inspection, Measuring and Test Equipment - 4.11.3
Records shall extend to employee gages
gage conditions and actual readings must be recordedwhen gages are checked
notify customer if suspect material is shipped
conform to measurement system analysis manual ofcustomer approval methods
Caution:Most people interpret MSA as nothing more than GR&R.
This is a misconception far from the truth
QS 9000
20
Measurement System Analysis - 4.11.4
conduct statistical studies on each type ofinspection, measurement and test system as definein the customer approved control plan
suppliers should extend it from studying gage typeto at least each family of products
QS 9000
21
ISO/TS 16949:2002
7.6 Control of Monitoring and Measuring Devices
The organization shall establish processes to ensurethat monitoring and measurement can be carried outand are carried out in a manner that is consistent withthe monitoring and measurement requirements.
22
ISO/TS 16949:2002
7.6.1. MEASUREMENT SYSTEMS ANALYSIS
Statistical studies shall be conducted to analyze thevariation present in the results of each type of measuringand test equipment system. This requirements shallapply to measurement systems referenced in thecontrol plan. The analytical methods and acceptancecriteria used shall conform to those in customerreference manuals on measurement systems analysis.Other analytical methods and acceptance criteria maybe used if approved by the customer.
23
PPAP MSA Requirements
I.2.2.10 MEASUREMENT SYSTEM ANALYSIS
shall include bias, linearity, stability and GageR&R studies forALL new or modified gages, testand measuring equipment.
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Customer/Industry MSA RequirementsTypically satisfied with GRR
Proposed Semi-conductor supplement to TS7.6.1S Measurement system analysis
In order to provide adequate measurement system discrimination, formeasurement equipment used to measure special characteristics,the apparent resolution of the equipment shall be at most one-tenthof the total process six sigma standard deviation. (ReferenceMeasurement System Analysis, Section 2.)
NOTE: Suppliers are expected to obtain value a dded state of the artmeasurement equipment. There are rare instances when a s pecialcharacteristic distribution is very narrow and the state of the artequipment cannot discriminate at the stated level The supplier shouldrepeat gage R&R studies when warranted by measurement systemchange (including operator) and have a systematic method toimprove gaging.
The supplier gage R&R studies shall be per Measurement SystemAnalysis reference manual, consistent with process Cp.
25
Common Sense MSA Requirements
What is in the Control Plan?
Does it cover Process and Product Parameters?Does it cover IMT from incoming to shipping?
Does it cover end of line and requirements fordownstream activities?
Does it cover lab equipment used for testing andanalysis?
Does it cover IMT for characterization and validationtesting?
26
Best-in-class: Control Of IMT Equipment
Minimize types and number of IMTs at each site
Buy IMT for part and process families
Conduct statistical studies per MSA guideline by part family
Only accept IMT per the 10-to-1 Rule and MSA guidelines
Do not allow personal IMT
Use six sigma process spread vs.specification/tolerancelimits to determine acceptance for product control
27
ImplementingGood Measurement Systems
Identify all inspection, measuring and test equipment (IMT)
Ascertain bias, linearity, and stability of IMT
show calibration status
records of calibration shall include employee gages
Conduct variation studies of IMT
Provide validity of previous results when IMT is found outof calibration
Ensure handling, preservation, cleaning, maintenance andstorage of all IMT
Use all criteria of MSA
Chapter 3
Statistical Properties ofMeasurement Systems
Statistical Properties of
Measurement Systems
29
APPLICATION OF MSA
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Measurement is Not Always Exact
Measurement system variation affects individualmeasurements and decisions based on data
Measurement system errors are classified into fivecategories:
Bias
Stability
Linearity
Repeatability
Reproducibility
31
Measurement is Not Always Exact
Bias
Difference between the observed average ofmeasurements and the reference value
A systematic error component of themeasurement system
32
Measurement is Not Always Exact
Stability
The change in bias over time
A stable measurement
process is in statistical control
with respect to location
Alias: Drift
33
Measurement is Not Always Exact
Linearity
The change in bias over the normal operating range
The correlation of multiple and independent bias errorsover the operating range
A systematic error component of the measurementsystem
34
Measurement is Not Always Exact
Repeatability
Variation in measurements obtained with one measuringinstrument when used several times by an appraiser whilemeasuring the identical characteristic on the same part
The variation in successive (short term) trials under fixedand defined conditions of measurement
Commonly referred to asE.V. Equipment Variation
Instrument (gage) capabilityor potential
Within-system variation
35
Measurement is Not Always Exact
ReproducibilityVariation in the average of the measurements made bydifferent appraisers using the same gage when measuringa characteristic on one part
For product and process qualification, error may beappraiser, environment (time), or method
Commonly referred to as A.V. Appraiser Variation
Between-system (conditions) variation
ASTM E456-96 includes repeatability, laboratory, andenvironmental effects as well as appraiser effects
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Ideal Measurement Systems
Produce correct measurements each time used andeach measurement agrees with a master standard
Have statistical properties of:
zero variance
zero bias
And consequently
zero probability of mis-classifying any productmeasured
37
Measurement Systems Variation
Measurement process components and their interactionscontribute variation in outcome of data
MeasuredValues
Variation
EnvironmentEnvironment MethodMethod Equipment(Machine)
Equipment
(Machine)
MaterialMaterial PeoplePeopleStandardsStandards
38
How Materials & People Affect Data
Material:
Composition
Variation
People:
Training
Alertness
39
Measurement System
Temp Fluxctuation
Line Voltage Variati
Vibration
Cleanliness
Humidity
Algorithm Instabilit
Electrical Instabili
Wear
Mechanical Integrety
Operator Technique
Standard Procedure
Sufficient Work time
Maintenance Standard
Calibration Frequenc
Operator Training
Ease of use
Density
Conductivity
Hardness
Corrosion
Weight
Dimension
Temperature
Cleanliness
Wear
Stability
Resolution
Calibration
Precision
Design
Temperature
Cleanliness
Vision
DexterityKnowledge
Coordination
Speed
Interpretation
Calibration Error
AttentionFatigue
Procedure
Men
Machines
Materials
Methods
Measurements
Environment
Measurement System C&E Matrix
Sources of Measurement Variation
40
How Environment Affects Data
Temperature variation could cause expansion and/orcontraction, giving different reading for the samecharacteristic on the same unit
Poor lighting could hinder correct reading
Glare could cause false reading of dataTime affects material - ie. aluminum, plastic, glass
Humidity
Contamination - ie. electricity, dust
Vibration
41
How Measurement Equipment
Affects Data
The type of measurement equipment must beappropriate
The incremental division of the equipment must besmaller than that of the specification
The accuracy and precision of the equipment
The Bias and Linearity
The Repeatability and Reproducibility
Stability
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How Measurement Equipment
Affects Data
Methods, procedures or work instructions must be
precisely followed by everyone performingmeasurements, testing or calibration or any part ofit, such as sample preparation or set up of thedevices.
If National, International, industry or professionally(e.g. SAE, ASTM, JEDEC) accepted methods arenot used, the organization must validate anydocumentation created or revised.
(continued)
43
Equipment Examples
Industry-specific types of inspection, measuring and testequipment
ball shear testwire pull test
profilometer
dial indicators
high power microscope
x ray thickness gage
What types of IMTequipment do you have?
44
Mathematical Perspective
Data collected for controlling a processcontains variations from two different andindependent sources:
Manufacturing Process Variation (MPV)
Measurement System Variation (MSV)
Total Variation (TV) = MPV + MSV
45
Sources of Variation
Product Variability
(Actual variability)
Product Variability
(Actual variability)
Measurement
Variability
Measurement
Variability
Total Variability
(Observed variability)
Total Variability
(Observed variability)
46
Measurement system variation must be smaller than themanufacturing process variation
MSV < MPV
Total Variation of
Manufacturing Process
+MSV MPV
Total Variation (TV)
Specification Tolerance
Note: Measurement system variation must be as small as possible
47
Effects of Measurement Error
AveragesAverages
VariabilityVariability
m m mtotal product measurement = +
s s stotal product measurement 2 2 2= +
Measurement
System Bias Determined through
Bias Study
Measurement System
Variability
Determined through
R&R Study
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Measurement ErrorEffect on Capability Index
CUSL LSL
p
Act
Act =-
6s
s s s Act Obs MS = -2 2
CU SL L SL
pAct
Obs MS
=-
-6 2 2s s
We know that
Therefore:
where
pC
49
R&R Effect on Capability
0.0
1.0
2.0
3.0
4.0
5.0
6.0
0.5 0.6 0.7 0.8 0.9 1.0 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2.0
Observed Cp
ActualC
p 0%
10%
20%
30%
40%
50%
60%
70%
%R&R
70% 60% 50%
40%
30%
10%
* As % of tolerance
Chapter 3b
Discrimination and UncertaintyDiscrimination and Uncertainty
51
APPLICATION OF MSA
52
Measurement Uncertainty
Measurement Uncertainty is the sum of all thevariations assigned to the variables that make upthe measurement system.
The total of those probabilities should be weighed
and carry importance in proportion to theseriousness and criticality of the measurementsbeing made.
53
Measurement Uncertainty
Decisions resulting from measurement system analysisinclude:
Use the system as is, taking into account its
uncertainty.Improve the system to control the variation in thecontributing factors.
Consider other measurement systems of higher levelsof discrimination and capability. (These will usually costmore but your MSA data will help to identify and justify adequateresources.)
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Measurement Uncertainty and Calibration
Uncertainty-traceability chain
The first measurement uncertainty associatedwith a measurement system is generated by theprocess of calibration.
Calibration permits the estimate of errors ofindication of the measurement instrument,measuring system, or the assignment of values tomarks on arbitrary scales
55
Measurement Uncertainty and Calibration
The reference material itself, the calibrationprocess and the environment and personnel
performing the activity actually contribute to themeasurement uncertainty.
Thus the reason for accredited and/or qualifiedlabs and the usefulness of the data you shouldreceive regarding calibrations you do or pay tohave done for your measurement, inspection andtest equipment.
56
Discrimination
Understand measurement system capability toprovide information on process variability
Measurement system is unacceptable for analysis ifit cannot detect process variation
Measurement system is unacceptable for controllingprocess if it cannot detect special cause variation
57
Understanding Discrimination
Measuring a Coins Thickness
Which measurement systemprovides better information onthe variation of the three coins?
Discrimination: The ability of
the system to detect andindicate even small changes of
the measured characteristic;
also known as resolution.
58
Discrimination & the Control Chart
Example
Measurement of same samples by two system
Create X-bar and R charts (shown on following
page)
Observe contrast between measurement systemwith resolution of 0.001 and one with 0.01
59
Process Control Charts
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Inadequate Discrimination
Inadequate discrimination of a measurement systemis shown on Range Charts when:
only one, two or three values for ranges canbe read
more than 1/4 of ranges are zero
To correct inadequate discrimination choose gages ofresolution proportionally smaller than the specificationor process variation
61
Measurement system variation must be smallcompared to the specification and process tolerance
(+ 3s)Measurement system s incremental markings(discrimination) must be smaller than those of thespecification
Specifications or Standard Deviations
Specification: 2.530 +/- 0.005
Measurement system increment: 0.0001
This is our rule of 10-to-1
62
Discrimination Decision Rules
Resolution of 1/10th of tolerance or process spread
Study gage discrimination during APQP and test foradequacy before PPAP
Evaluate range chart of manufacturing process orsimilar process, per previous page and examples
For continual improvement, 1/10th tolerance may beinadequate.MSA recommends 1/10th of six sigma (total)manufacturing standard deviation.
Chapter 3c
Bias, Linearity and StabilityBias, Linearity and Stability
64
APPLICATION OF MSA
65
Accuracy & Precision
AccuracyHow close is the measured value to the reference value
ASTM includes the effect of location and width errorsMSA evaluates bias instead of accuracy
Precision
Closeness of repeated readings to each otherMSA evaluates repeatability and reproducibility
Accuracy and Precision are not calculated as part of aMSA Analysis
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Accuracy & Precision Example
A has best AccuracyB has best PrecisionC has better Accuracy than B
Compare the performance of A & CCompare the performance of A & C
Contestant A
Contestant B
Contestant C
Average for Contestant A
Average for Contestant B
Average for Contestant C
67
The Nature of Process Variation
Precise but not AccuratePrecise but not Accurate
Accurate but not PreciseAccurate but not Precise
. . . . . .Test equipment MUST be a least 10 times
more accurate & precise then whats being tested
Rule of thumb:
68
Work Around Gage Error
If you want to decrease your measurement error takeadvantage of the standard error square root of the sample:
Example: A measurement error of 50% can be cut in
halfif your point estimate is a sample of 4 data points.
Example: A measurement error of 50% can be cut in
halfif your point estimate is a sample of 4 data points.
THIS CAN BE USED AS A SHORT TERM APPROACH TO PERFORM
A STUDY, BUT YOU MUST FIX THE GAGE.
n = sample sizess
xx
n=
69
Terminology
True value:
Theoretically correct value unknown andunknowable
Reference standards
Traceable to NIST standards
Bias
Distance between average value of allmeasurements and reference value
Amount gage is consistently off target
Systematic error or offset
Reference Value
70
Reference Value
A value that serves as an agreed upon referencefor comparisonA reference value can be determined by averaging severalmeasurements with a higher level of measuring equipment
Sometimes known as:master valueaccepted valueconventional valueassigned valuebest estimate of the valuemaster measurementmeasurement standard
71
Reference Material
A material or substance with one or moreproperties which are sufficiently wellestablished to be used for the calibrationof an apparatus, assessment of a
measurement method, or for assigningvalues to materials
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National / International
Measurement StandardsA material measure, measuring instrument, reference material or system
intended to define, realize, conserve or reproduce a unit, or one or more
values of a quantity, in order to transmit them to other measuring
instruments by comparison.These standards are recognized by an official national decision or by an
international agreement to serve i nternationally, as the basis for fixing
the value of all other standards of the quantity concerned.
Some Examples:
solution of cortisol in human serum as a standard of concentration
Iodi ne-Sta bi lize d H eli um 100 W standard resistor
Neon laser length Standard 1 Kg mass
Weston Standard cel l caesium atomic f requency standard
Standard gage b lock Josephson Ar ray Vo ltage Standard
73
National / International
Measurement Standards
Using a traceable standard provides:
common point for comparisonmeasurement system validity
measurement system accuracy estimates
conflict management between parties
most direct line of verification
74
Traceable Standard Limitations
Difficult to use in destructive testing
Some product characteristics and process resultshave no defined industry or national standards
Some tests have no defined industry or nationalstandards
Discuss limitations during design and development,contract review and APQP; managementresponsibility issue
75
Options
For calibration you may need to use GoldenUnits, other in house verification units and/ormutual consent standards. These are the bestproduct evaluated by the highest level ofmeasurement equipment.
Comparative analysis resulting in precise datathat will define amount of adjustment neededfor calibrating
Inter-laboratory Comparisons: organization,performance and evaluation of equipment onthe same or similar items by 2 or more labs inaccordance with predetermined conditions.
76
BIAS Is the difference between theobserved average of the measurement and thereference value.
The reference value can be determined byaveraging several measurements with a higherlevel (e.g., metrology lab) of measuring
equipment.
Warning: Dont assume your metrologyreference is gospel.
Observed
Average Value
Reference
Value
BIAS is often referred to as ACCURACY
BIAS Definition
77
Why Do a Gage Bias Study?
Because it is required
To determine if the bias is acceptablei.e. statistically zero
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Bias
Test of hypothesis approach.
Expanded the analysis to include control chartmethod.
79
Analysis of Bias
Average
Confidence Band
ReferenceValue
80
Calculating Bias
1
n
i
i
x
Xn
==
where is taken from Appendix C
withg= 1 and m = n
( ) ( )*2
max mini ix x
drepeatabilitys
-=
*
2d
bias = observed average measurement reference value
rb
n= ss
b
biast=
s
where are found in MSA Appendix C
withg= 1 and m = n andis found using the standard ttables.
( ) ( )b b, 1 , 12 2
Bias t zero Bias t a an n- - - +
*
2 2, andd d n
,12
t an -
81
TheThe aa level which is used depends on the level oflevel which is used depends on the level ofsensitivity which is needed to evaluate/controlsensitivity which is needed to evaluate/control
the process and is associated with the lossthe process and is associated with the loss
function (sensitivity curve) of thefunction (sensitivity curve) of the
product/process. Customer agreement should beproduct/process. Customer agreement should be
obtained if anobtained if an aa level other than the default valuelevel other than the default valueof .05 (95% confidence) is used.of .05 (95% confidence) is used.
82
Gage Bias Work Instruction
1. Obtain accepted reference value using a master ormeasuring equipment of higher level, such as layoutequipment to create a golden unit or master partto use as a reference value.
2. Measure same part by same appraiser minimum of10 times using gage under evaluation
83
Gage Bias Work Instruction
3. Analysis:plot the histogram of all the readings
Determine if any special causes are present
calculateaverage of all the readingsbias = average of all the reading - reference valuesd(bias) = standard deviation of all the readings dividedby the square root of the sample sizeThe t-statistic and/or confidence bounds.
determine if the bias is statistically zero; i.e.The t-statistic is less than the critical valueZero is contained within the confidence bounds
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Bias Calculation- Example
Reference
Value = 6.00Bias
1 5.8 -0.2
2 5.7 -0.33 5.9 -0.1
T 4 5.9 -0.1
R 5 6.0 0.0
I 6 6.1 0.1
A 7 6.0 0.0
L 8 6.1 0.1
S 9 6.4 0.4
10 6.3 0.3
11 6.0 0.0
12 6.1 0.1
13 6.2 0.2
14 5.6 -0.4
15 6.0 0.0
85
Bias Calculation- Example
5.6 5.7 5.8 5.9 6.0 6.1 6.2 6.3 6.4
0
1
2
3
4
F r e q u e n c y
Measured value
86
Bias Calculation- Example Range Method
Reference
Value = 6.00Bias
1 5.8 -0.2
2 5.7 -0.3
3 5.9 -0.1
T 4 5.9 -0.1
R 5 6.0 0.0
I 6 6.1 0.1
A 7 6.0 0.0
L 8 6.1 0.1
S 9 6.4 0.4
10 6.3 0.3
11 6.0 0.0
12 6.1 0.1
13 6.2 0.2
14 5.6 -0.4
15 6.0 0.0
1 90.16.0067
15
n
i
i
x
Xn
== = =
n = 15
( ) ( )*2
max min
6.4 5 .6.2254
3.55
i ix x
drepeatabilitys
-=
-= =
.2254.0582
15r
bn
ss = = =
.0067.1151
.0582b
biast
s= = =
bias = observed average measurement
reference value = 6.0067 6.00 = .006787
Bias Calculation- Example Range Method
Given: m = n = 15 g=1
d2* = 3.55 d2 = 3.47 df = 10.8
t.975, 10.8 = 2.2060
.1151t=.0582bs =
( ) ( )b b, 1 , 12 2
Bias t zero Bias t a an n- - - +
( ) ( )3.47*.05813 3.47*.05813
.0067 2.2060 0 .0067 2.20603.55 3.55
- +
.1186 0 .1320-
88
Bias - Control Chart Method
bias = reference valueX
*2
repeatability
R
ds =
where is based on the subgroup size
(m) and the number of subgroups in thechart (g).
*
2d
rb
gm
ss =
b
bias
t = s
( ) ( )b b, 1 , 12 2
Bias t zero Bias t a an n- - - +
Where are found in
MSA Appendix C and is
found using the standard ttables.
*2 2, andd d n
,12
t an -
89
Bias- Control Chart Example
0Subgroup 10 20
5.7
5.8
5.9
6.0
6.1
6.2
6.3
SampleMean
6.021
UCL=6.297
LCL=5.746
0.0
0.5
1.0
SampleRange
0.4779
UCL=1.010
LCL=0
Xbar/R Chart for Stability
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90
BIAS EXAMPLE
OD VALUES
TRIALS (inches)
1 0.726602 0.72440
3 0.72535
4 0.726305 0.72710
6 0.72745
7 0.72630
8 0.725159 0.72525
10 0.72570
Average (X-bar) = 0.72596
Bias = Observed Average - Reference Value= 0.72596 - 0.72650 = - 0.00054
The observed measurements on the averagewill be 0.00054 smaller than the reference
value
The outside diameter of a shaft is measured ten times by the sameoperator. The data is given below.
The process variation is estimated as 0.00310.
The reference value is 0.72650.
91
BIAS EXAMPLE
Average = 0.72596
Bias = - 0.00054
Overall StdDev = 0.000954
StdDev Bias = 0.000954/sqrt(10) = 0.000302
Critical tvalue = 2.26216 for df = 9 (from ttable)
Calculated t = abs(-0.00054)/0.000302 = 1.79
Confidence Bounds = (-0.001223, 0.000143)
Analysis
Since Calculated tis less than theCritica l tvalue
And zero is contained within the Confidence Bounds
Accept the hypothesis that the bias is zero
The bias is statistically zero
92
BREAKOUT 1
Bias
93
Cause of Unacceptable Bias
Error in measuring instrument
Instrument:
worn, dirty, broken
improper design
made to wrong dimension
worn, dirty, broken
improper discrimination
improper calibration
improper use by operator
94
2 3 4 5 6 7 98 10
LINEARITY EXAMPLELINEARITY EXAMPLE Y = 0.736667 - 0.131667X R-Sq = 71.4
reference values
Linearity StudyLinearity Study -- Graphical AnalysisGraphical Analysis
bias
bias
1
0
-1
bias = 0bias = 0
Regression95% ClBias Average
Linearity
Difference in the bias values of a measurementsystem through its expected operating range
95
Linearity
Test of hypothesis approach.
Added examples and more explanation oninterpretation of results.
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96
LinearityDifference in the bias values of a measurementsystem through its expected operating range
2 3 4 5 6 7 8 9 10
0.0
0.5
1.0
Master
-bias-
-bias-= -0.0000433+0.0000083 Master
S =0.232676 R-Sq= 0.0% R-Sq(adj) = 0.0%
Regression
95% CI
Good LinearityUnacceptable LinearityAcceptable Linearity
97
Gage Linearity
Gage linearity can be determined by conducting biasstudies through expected operating range
Minimum of two bias studies should be conducted,one at each end of operating range
Middle of range should also be considered
98
Gage Linearity Study
Gage Linearity Work Instruction
1. Select five to eight parts that can be measured atdifferent operating ranges of measurement system
2. Determine reference value for each part usinglayout inspection or use a set of standards
3. Use one appraiser and the same instrument tomeasure parts
4. Take 5 or more repeated measurements on eachpart
5. Calculate each part s bias
bias = observed average - reference value
99
Gage Linearity Study(continued)
6. Create a scatter plot by putting the reference valuesfrom smallest to largest on the x-axis, and thecorresponding bias values on the y-axis.
7. Calculate the 95% confidence intervals for the controllimits.
Note: you will find it helpful to graph all of the actual
groups of readings stacked vertically at the related
reference value points
100
Gage Linearity Study(continued)
8. To analyze the graph:
a. The bias = 0 line must fall entirely within the CI foracceptable linearity
b. Watch for individual readings that do not follow
the pattern of the groups (e.g. outliers). Also watchfor other patterns indicating unusual variation orabnormal behavior.
9. Remember that a measurement system with large(i.e. unacceptable) repeatability can indicate anstatistically acceptable bias even if it practicallyunacceptable.
101
Gage Linearity Study(continued)
10. If measurement system has a linearity problem,use problem-solving methods to determinemodifications necessary to achieve zero linearity
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102
102 3 4 5 6 7 98
PARTREFERENCE
VALUE
1
2.00
2
4.00
3
6.00
4
8.00
5
10.00
1 2 .70 5.10 5.8 0 7.60 9.10
2 2 .50 3.90 5.7 0 7.70 9.30
3 2 .40 4.20 5.9 0 7.80 9.504 2 .50 5.00 5.9 0 7.70 9.30
5 2 .70 3.80 6.0 0 7.80 9.40
6 2 .30 3.90 6.1 0 7.80 9.50
7 2 .50 3.90 6.0 0 7.80 9.50
8 2 .50 3.90 6.1 0 7.70 9.50
9 2 .40 3.90 6.4 0 7.80 9.60
10 2 .40 4.00 6.3 0 7.50 9.20
11 2 .60 4.10 6.0 0 7.60 9.30
12 2 .40 3.80 6.1 0 7.70 9.40
LINEARITY STUDY DATALINEARITY STUDY DATA
TT
RR
IIAA
LL
SS
PARTREFERENCE
VALUE
1
2.00
24.00
36.00
48.00
510.00
1 0.7 1.1 -0.2 -0.4 -0.9
2 0.5 -0.1 -0.3 -0.3 -0.7
3 0.4 0.2 -0.1 -0.2 -0.5
4 0.5 1 -0.1 -0.3 -0.7
5 0.7 -0.2 0.0 -0.2 -0.6
6 0.3 -0.1 0.1 -0.2 -0.5
7 0.5 -0.1 0.0 -0.2 -0.5
8 0.5 -0.1 0.1 -0.3 -0.5
9 0.4 -0.1 0.4 -0.2 -0.4
10 0.4 0.0 0.3 -0.5 -0.8
11 0.6 0.1 0.0 -0.4 -0.7
12 0.4 -0.2 0.1 -0.3 -0.6
BIAS AVG 0 .4 91 66 7 0 .1 25 0 .0 25 - 0. 29 16 7 - 0.6 16 67
BB
II
AA
SS
Charting Linearity
LINEARITY EXAMPLELINEARITY EXAMPLE
1
-1
0
Y = 0.736667 -0.131667X R-Sq = 71.4
Linearity StudyLinearity Study -- Graphical AnalysisGraphical Analysis
bias
=0
bias
=0
reference values
95%Cl
Regression
Bias Average
103
Breakout 2Linearity
104
Causes of Non-linearity
Improper calibration of the gage at the lowerand upper end of operating range
Error in the master used at the minimum andmaximum range
Instrument wear
Design characteristics of the instrument
105
Stability
A Measurement System isStable if there are nospecial cause variationaffecting the measurementsystem s bias over time
106
Stability
Stability (or drift) in ameasurement systemevaluated bymeasuring the samemaster(s) or part(s) on
a single characteristicover an extended timeperiod(a time periodis days, not hours)
107
Measurement System Stability
Typically not as large a problem as GRR
Useful to help determine calibration intervals
Should track from test to test and chart (or at leastrecord actual readings and other pertinent data inthe gage record)
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108
Affects On Gage Stability
Time long idle periods or intermittent use
Very large or very small number of measurements
taken between stability testsEnvironment or system changes, such as: humidity;air pressure
potential confusion with statistical stabilityfactors, such as warm up effects, rate of wear,lack of maintenance, untrained operators orlab technicians
109
Cause of Gage Stability Error
Infrequent or too frequent calibration
Lack of air pressure regulator or filter
Warm-up period for electronic or other gages
Lack of maintenance
Wear or damage not readily observable
Oxidization (corrosion)
110
Gage Stability Study
Stability Analysis Instructions
1. Use a standard set of parts or reference/mastermaterials as sample
Retain these as appropriate (life of product) in aprotected environment
Label them with name and number for trackingand further studies include samples at the low,mid and high range.
111
Gage Stability Study (continued)
2. (Recommended) Perform a Bias or Linearity study onthe sample. Use this information to establish the controlchart parameters
3. Measure part(s) three to five times (based onknowledge of measurement system) at different timesof the day.Plot data on X-bar and R or X-bar and S chart
3. Evaluate per normal SPC requirements
Note: Maintain a chart for each part/master
4. Evaluate the within sample standard deviation(repeatability) of measurements to determine suitabilityfor the application
112
Analyzing Stability Charts
0Subgroup 10 205.7
5.8
5.9
6.0
6.1
6.2
6.3
SampleMean
6.021
UCL=6.297
LCL=5.746
0.0
0.5
1.0
SampleRange
0.4779
UCL=1.010
LCL=0
Xbar/R Chart for Stability
113
Analyzing Stability Charts
If stability is not acceptable, the X-bar and possibly S
or R charts will show a shift or out-of-control condition
out-of-control chart conditions indicatemeasurement system not measuring consistently
Check for:bias changed - determine cause of change andcorrect
if cause is wear - may be fixed by re-calibration
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Chapter 3d
GRR StudiesGRR Studies
115
APPLICATION OF MSA
116
GRR
Intent
provide an understanding of GRR using theMSA 3rd edition
Note that:
repeatability and reproducibility deal with thewidth or spread of the measurement systemvariation
bias, stability and linearity deal w ith the locationof the measurement system variation
117
Repeatability
Variation in measurements obtained with onemeasurementinstrumentwhen used several times byone appraiserwhile measuring the same characteristicon the same part
118
Repeatability
The inherent variability of the measurementsystem
Variation in measurements obtained with agage when used several times by one
appraiser while measuring a characteristic onone part.
Estimated by the pooled standard deviation ofthe distribution of repeated measurements
Repeatability is less than the total variation ofthe measurement system
sG
s GR
d=
2
*
119
Repeatability Example
Contestant A
Contestant B
Contestant CAverage for Contestant A
Average for Contestant B
Average for Contestant C
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120
Reproducibility
Variation in average of measurements made bydifferentappraisers using same measuringinstrumentwhen measuring the same characteristic onthe same parts
121
Reproducibility
Appraiser variability of the measurement
systemVariation in the average of the measurements
made by different appraisers using the same
measurement system when measuring the
same characteristic on one part
Must be adjusted for repeatability
Reproducibility is less than the total variation
of the measurement system
As
122
Reproducibility Example
Contestant A
Contestant B
Contestant C
Average for Contestant A
Average for Contestant B
Average for Contestant C
to Reproducibility between A & B
to Reproducibility between A & C
to Reproducibi lity between B & C
123
Possible Sources of Process Variation
Long-term
Process Variation
Short-term
Process Variation
Variation
w/i sample
Actual Process Variation
Stabi lity LinearityRepeatability Bias
Variation due
to instrument
Variation due
to appraisers
Measurement Variation
Observed Process Variation
We look at repeatability and reproducibility as these
are the usually primary contributors to measurement error.
We look at repeatability and reproducibility as these
are the usually primary contributors to measurement error.
Reproducibility
124
Preparation for a Measurement Study
Determine if reproducibility is an unknown or a concern. If it is,select the number of appraisers to participate.
Appraisers selected should normally use the measurement system.
Select samples that represent the entire operating range.
Gage must have graduations that allow at least one-tenth of theexpected process variation.
Insure defined gaging procedures are followed.
Measurements should be made in random order.
Study must be observed by someone who recognizes theimportance of conducting a reliable study.
Determine if reproducibility is an unknown or a concern. If it is,select the number of appraisers to participate.
Appraisers selected should normally use the measurement system.
Select samples that represent the entire operating range.
Gage must have graduations that allow at least one-tenth of theexpected process variation.
Insure defined gaging procedures are followed.
Measurements should be made in random order.
Study must be observed by someone who recognizes theimportance of conducting a reliable study.
125
GRR Study
GRR Study Instructions
1. Select two or three appraisers who are users of themeasurement system
2. Obtain a sample of n (10 or more) parts that
represent actual or expected range of processvariation
3. Number parts 1 through n so that numbers are notvisible to appraisers
4. Calibrate gage if this is part of the normal gagingprocedures
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126
GRR Study (continued)
5. Measure the n parts in random order by appraiserA, with an observer recording results
6. Repeat step 5 with other appraisers conceal otherappraisers readings
7. Repeat step 5 and 6 using a different random orderof measurement
8. Using the Average and Range approach, enter thedata onto the form and follow the form instructions
calculate the average and ranges for all readingsfor each appraiser
127
Plot the average and Range charts and analyze forstability
GRR Study (continued)
128
GRR
Repeatability
variation in measurementsobtained with onemeasurement instrument
when used several timesby one appraiserwhilemeasuring the samecharacteristic on samepart
graph on Rchart
Reproducibility
variation in average ofmeasurements made bydifferentappraisers usingsame measuringinstrumentwhenmeasuring the samecharacteristic on samepart
graph on average chart
129
Range Chart Example
130
Range Chart Conclusion
There appears to be differences among assessors
A reading of one appraiser is outside the controllimits; the conclusion is that the appraiser s methoddiffers from other appraisers
In general if all appraisers have some points outsidecontrol limit, then conclusion is measurement systemsensitive to appraiser technique and needsimprovement to obtain useful data
131
Average Chart Example
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132
Average Chart Conclusion
Used to determine
Consistency between appraisers
Adequacy to detect part variation
Adequacy of resolution
Adequacy of sample
In this study, 22 out of 30 points are outside thecontrol limit
Since this is more than half of the points, theconclusion is that the measurement system isadequate to detect part-to-part variations
133
Misc:
Tolerance:
Reported by:
Dateof study:
Gage name:
1.11.00.90.8
0.70.6
0.50.40.3
321
Xbar Chart by Operator
SampleM
ean
X=0.80753.0SL=0.8796
-3.0SL=0.7354
0.15
0.10
0.05
0.00
321
R Chart by Operator
SampleRange
R=0.03833
3.0SL=0.1252
-3.0SL=0.000
10987654321
1.1
1.0
0.9
0.8
0.7
0.6
0.5
0.4
Gasket
OperatorOperator*Gasket Interaction
Avera
ge
1
2
3
321
1.1
1.0
0.9
0.8
0.7
0.6
0.5
0.4
Operator
Response by Operator
10987654321
1.1
1.0
0.9
0.8
0.7
0.6
0.5
0.4
Gasket
Response by Gasket
%TotalVar
%Study Var
Part-to-PartReprodRepeatGageR&R
100
50
0
Components of Variation
Percent
Gage R&R (Xbar/R) for Thickness
Example of MSA Graphics
134
Breakout 3
Graphing GRR
135
Calculate the overall average and range, part range,and maximum difference between appraiser averages
Calculate repeatability for equipment variation:
Calculate reproducibility for appraiser variation
Calculate GRR
Calculate part variation
Calculate total variation
Calculate the percent indices for above
Calculate the ndc
Analyze the numerical results
GRR Study (continued)
136
Breakout 4
Calculating GRR
137
Gasket Thickness Study
PT1 PT2 PT3 PT4 PT5 PT6 PT7 PT8 PT9 PT10 AP/TRIAL
0.65 1.00 0.85 0.85 0.55 1.00 0.95 0.85 1.00 0.60 A1
0.60 1.00 0.80 0.95 0.45 1.00 0.95 0.80 1.00 0.70 A2
0.55 1.05 0.80 0.80 0.40 1.00 0.95 0.75 1.00 0.55 B1
0.55 0.95 0.75 0.75 0.40 1.05 0.90 0.70 0.95 0.50 B2
0.50 1.05 0.80 0.80 0.45 1.00 0.95 0.80 1.05 0.85 C1
0.55 1.00 0.80 0.80 0.50 1.05 0.95 0.80 1.05 0.80 C2
Xbar & R Example
Specification: 0.6 - 1.0 mm
Process Variation: 1.6 mm
Reference: Measurement System Analysis Manual, 2nd Edition
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138
Gage R&R Study for Thickness XBar/R Method
Source Variance StdDev 5.15*Sigma
Total Gage R&R 2.08E-03 0.045650 0.235099
Repeatability 1.15E-03 0.033983 0.175015
Reproducibility 9.29E-04 0.030481 0.156975Part-to-Part 3.08E-02 0.175577 0.904219
Total Variation 3.29E-02 0.181414 0.934282
Source %Contributio n %Study Var
Total Gage R&R 6.332 25.164
Repeatability 3.509 18.733Reproducibility 2.823 16.802
Part-to-Part 93.668 96.782
Total Variation 100.000 100.000
Number of distinct categories = 5
139
Calculation Explanation
5.15 Sigma = 5.15 the factor standard deviation.5.15 was developed empirically to approximate the gage populationdistribution variation. (99% area for Normal forms)
% Contribution = Percent contribution of each factor based uponthe variance.Repeatability = 100 repeatability variance/ total variationvariance.
% Study Variation = the factor standard deviation divided by thetotal variation s tandard deviation.Repeatability = 100 repeatability standard deviation/ totalvariation standard deviation.
5.15 Sigma = 5.15 the factor standard deviation.5.15 was developed empirically to approximate the gage populationdistribution variation. (99% area for Normal forms)
% Contribution = Percent contribution of each factor based uponthe variance.Repeatability = 100 repeatability variance/ total variationvariance.
% Study Variation = the factor standard deviation divided by thetotal variation s tandard deviation.Repeatability = 100 repeatability standard deviation/ totalvariation standard deviation.
140
Calculation Explanation
% Tolerance = the factor standard deviation divided by thetolerance/6.Repeatability = 100 repeatability standard deviation/(tolerance/6)
% Process Variation = the factor standard deviation divided bythe process variation.
Repeatability = 100 x repeatability standard deviation/ processvariation.
Number of Distinct Categories = part standard deviation dividedby the total measurement standard deviation times 1.41.
% Tolerance = the factor standard deviation divided by thetolerance/6.Repeatability = 100 repeatability standard deviation/(tolerance/6)
% Process Variation = the factor standard deviation divided bythe process variation.
Repeatability = 100 x repeatability standard deviation/ processvariation.
Number of Distinct Categories = part standard deviation dividedby the total measurement standard deviation times 1.41.
141
GRR Acceptance Guidelines
Acceptance criteria based on estimated value of R&R(%R&R) of system
if % GRR < 10%, system is acceptable
if 10% < % GRR < 30%, system may beacceptable based on application, cost of gage, costof repair, etc.
if % GRR > 30%, system needs improvement orcorrective action
Note: THE SUM OF THE PERCENT CONSUMED BYEACH FACTOR WILL NOT EQUAL 100%.
142
Analysis with MSA Pro
Show percentages
Show charts
Draw conclusions
143
Application of GRR
When repeatability is large compared to reproducibility:
instrument needs maintenance
redesign gage for more rigidity
improve clamping or location of gauging
excessive within-part variation
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144
Application of GRR (continued)
When reproducibility is large compared to repeatability:
Appraisers need better gage use training
Need better operational definition
Incremental divisions on instrument are not readable
Need fixture to provide consistency in gage use
Chapter 4a
Advanced Analysis - ANOVAAdvanced Analysis - ANOVA
146
Advanced Analysis
Intent
provide an understanding of how to evaluatemeasurement systems using Analysis of variance (ANOVA)
Scope
ANOVA is a standard statistical technique and can be usedto analyze the measurement error and other sources ofvariability of data in a measurement systems study.
the variance can be decomposed into four categories:
parts,
appraisers,
interaction between parts and appraisers, and
replication error due to the gage.
147
When To Use ANOVA
Product cannot be usedagain, such as destructivetests
pull test
tensile strength test
chemical compositiontest
Product changed byevaluation equipment
Requires knowledge ofvariation contributed by:
equipment
appraisers
units measured
their interaction
other sources of variation
148
ANOVA table
The ANOVA table here is composed of fivecolumns
Source column is the cause of variation.
DFcolumn is the degree of freedom
associated with the source.SSor sum of squares column is the deviationaround the mean of the source.
MSor mean square column is the sum ofsquares divided by degrees of freedom.
F-ratio column, calculated to determine thestatistical significance of the source value.
149
ANOVA table
Source DF SS MS F
Appraiser 2 3.1673 1.58363 34.44*
Parts 9 88.3619 9.81799 213.52*
Appraiser
by Part
18 0.3590 0.01994 0.434
Equipment 60 2.7589 0.04598
Total 89 94.6471
* Significant at = 0.05 level
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150
Estimate of
Variance
Std.
Dev. (s)% Total
Variation
%
Contribution
2t = 0.039973(Repeatability)
EV= 0.199933 18.4 3.4
2w = 0.051455
(Appraiser)
AV= 0.226838 20.9 4.4
2g = 0
(Interaction)
INT= 0 0 0
System = 0.09143
( 2 2 2t g w+ + )GRR = 0.302373 27.9 7.8
2s = 1.086446
(Part)
PV= 1.042327 96.0 92.2
Total Variation TV=1.085 100.0
Note: % Total Variation for Repeatability = (EV/TV) x 100
% Contribution for Repeatability = (EV/TV)2 x 100
Chapter 4b
Attribute MeasurementsAttribute Measurements
152
lVariable Gage R&R
Numbers
Units of measure
lAttribute Gage R&R
Subjective (visual defects)
Scatter of defects
feel/visual
Types of R&R Studies
153
Attribute Measurement
An attribute gage:
compares each part to a specific set of limits andaccepts the part if the limits are satisfied
is designed to accept/reject a set of master parts
cannot indicate how good or how bad a part is, onlywhether the part is accepted or rejected (pass/fail)
154
Analyzing Attribute Data
Always Try To Convert Attribute To VariablesAlways Try To Convert Attribute To Variables
Examples:l End Disk Height
l Likert Scale
l Leak Rate (go/no go)
l Mass Spec
Then use Variable Data Analysis TechniquesThen use Variable Data Analysis Techniques
155
The Inspection Exercise
The Necessity of Training Farm Hands for First
Class Farms in the Fatherly Handling of Farm Live
Stock is Foremost in the Eyes of Farm Owners.
Since the Forefathers of the Farm Owners Trainedthe Farm Hands for First Class Farms in the
Fatherly Handling of Farm Live Stock, the Farm
Owners Feel they should carry on with the Family
Tradition of Training Farm Hands of First Class
Farmers in the Fatherly Handling of Farm Live
Stock Because they Believe it is the Basis of Good
Fundamental Farm Management.
Task: Count the number of times the 6th letter of the alphabet
appears in the following text. One minute time limit
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156
The Inspection Exercise
The Necessity ofTrainingFarm HandsforFirst
Class Farms in the Fatherly Handling of Farm Live
Stock is Foremost in the Eyes of Farm Owners.
Since the Forefathers of the Farm Owners Trained
the Farm HandsforFirst Class Farms in the
Fatherly Handling ofFarm Live Stock, the Farm
Owners Feel they should carry on with the Family
Tradition ofTrainingFarm Hands of First Class
Farmers in the Fatherly Handling of Farm Live
Stock Because they Believe it is the Basis of Good
FundamentalFarm Management.
Task: Count the number of times the 6th letter of the alphabet
appears in the following text. One minute time limit
157
Operational Definitions
An operational definition is one that people can dobusiness with. An operational definition of safe, round,reliable, or any other quality [characteristic] must be
communicable, with the same meaning to vendor as to thepurchaser, same meaning yesterday and today to theproduction worker. Example:
1. A specific test of a piece of material or an assembly
2. A criterion (or criteria) for judgment
3. Decision: yes or no, the object or the material did ordid not meet the criterion (or criteria)
W. E. Deming, Out of the Crisis (1982, 1986), p. 277.
158
Attribute MSA Study 3rd Edition
2nd Edition Short and Long Term Methods
Short Term Method: no longer referenced
Long Term Method: Name changed (to Analytic)
Approaches:
Risk Analysis Method
Contingency table analysis/Multiple Tests of Hypothesis
Signal detection theory
Analytic Method
159
RISK ANALYSIS METHODS
In some attribute situations it is not feasible to get sufficientparts with variable reference values. In such cases, the risksof making wrong or inconsistent decisions can be evaluatedby using
Hypothesis Test Analyses
Signal Detection Theory
These methods do notquantify the measurement systemvariability, they should be used only with the consent of thecustomer.
Selection and use of such techniques should be based ongood statistical practices, an understanding of the potentialsources of variation which can affect the product andmeasurement processes, and the effect of an incorrectdecision on the remaining processes and the final customer
The sources of variation of attribute systems should be
minimized by using the results of human factors andergonomic research.
160
Attribute MSA Study
Used when measurements are subjective classifications or ratings by people.
Attribute data can be ORDINAL orNOMINAL.
Ordinal Data are categorical variables that have three or more possible levelswith a natural ordering, such as strongly disagree, disagree, neutral, agree, and
strongly agree. Or, you can use a numeric scale such as 1-5.
Kendalls Coefficients are used.
----- to measure nonparametric correlations.
Nominal Data are categorical variables that have two or more possible levels
with no natural ordering.
Pass, Fail
Crunchy, Mushy, and Crispy(Food tasting study).
161
Nominal Data
Kappa Coefficients are used.
Kappa is an indicator of inter-rater agreement; i.e., the ratioof the proportion of agreement (corrected for chance)divided by the maximum number of times they could agree(corrected for chance).
Where Pr (agreement ) = Proportion(Agreement)Pr (error) = Proportion (Error)
A Kappa coefficient of 90% may be interpreted as 90%agreement.
Pr( ) Pr( )1 Pr( )
agreement errorKerror
-=-
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162
Kappa CoefficientsKappa CoefficientsBased onBased on an article by Altman, 1991 recommends the followingan article by Altman, 1991 recommends the following
kappa interpretation scale. The definition of the interpretationkappa interpretation scale. The definition of the interpretations,s,
such assuch as PoorPoor, must be agreed upon by the customer and the, must be agreed upon by the customer and the
supplier.supplier.
Kappa ValueKappa Value InterpretationInterpretation
< 0.20< 0.20 PoorPoor
0.210.21--0.400.40 FairFair
0.410.41--0.600.60 ModerateModerate
0.610.61--0.800.80 GoodGood
0.810.81--1.001.00 Very GoodVery Good
In addition, Gardner (1995) recommends that kappa exceed .70In addition, Gardner (1995) recommends that kappa exceed .70
before you proceed with additional data analyses.before you proceed with additional data analyses.
163
Hypothesis Test Analyses
A * B Crosstabulation
44 6 50
15.7 34.3 50.0
3 97 100
31.3 68.7 100.0
47 103 150
47.0 103.0 150.0
Count
Expected Count
Count
Expected Count
Count
Expected Count
.00
1.00
A
Total
.00 1.00
B
Total
164
Count & Expected Count CalculationsCount & Expected Count Calculations
A * B Crosstabulation
44 6 50
15.7 34.3 50.0
3 97 100
31.3 68.7 100.0
47 103 150
47.0 103.0 150.0
Count
Expected Count
Count
Expected Count
Count
Expected Count
.00
1.00
A
Total
.00 1.00
B
Total
165
There are 34 times where
A-1 = 1 and B-1 = 1(that is, of the 50 parts checked
there were 34 matches by A and Bon their FIRST check)
Table 12: Attribute Study Data SetTable 12: Attribute Study Data Set
MSA 3MSA 3rdrd, pg 127, pg 127
Part A- 1 A - 2 A -3 B- 1 B - 2 B - 3 C - 1 C -2 C- 3 Reference
1 1 1 1 1 1 1 1 1 1 1
2 1 1 1 1 1 1 1 1 1 1
3 0 0 0 0 0 0 0 0 0 0
4 0 0 0 0 0 0 0 0 0 0
5 0 0 0 0 0 0 0 0 0 0
6 1 1 0 1 1 0 1 0 0 1
7 1 1 1 1 1 1 1 0 1 1
8 1 1 1 1 1 1 1 1 1 1
9 0 0 0 0 0 0 0 0 0 0
10 1 1 1 1 1 1 1 1 1 1
11 1 1 1 1 1 1 1 1 1 1
12 0 0 0 0 0 0 0 1 0 0
13 1 1 1 1 1 1 1 1 1 1
14 1 1 0 1 1 1 1 0 0 1
15 1 1 1 1 1 1 1 1 1 1
16 1 1 1 1 1 1 1 1 1 1
17 1 1 1 1 1 1 1 1 1 1
18 1 1 1 1 1 1 1 1 1 1
19 1 1 1 1 1 1 1 1 1 1
20 1 1 1 1 1 1 1 1 1 1
21 1 1 0 1 0 1 0 1 0 1
22 0 0 1 0 1 0 1 1 0 0
23 1 1 1 1 1 1 1 1 1 1
24 1 1 1 1 1 1 1 1 1 1
25 0 0 0 0 0 0 0 0 0 0
26 0 1 0 0 0 0 0 0 1 0
27 1 1 1 1 1 1 1 1 1 1
28 1 1 1 1 1 1 1 1 1 1
29 1 1 1 1 1 1 1 1 1 1
30 0 0 0 0 0 1 0 0 0 0
31 1 1 1 1 1 1 1 1 1 1
32 1 1 1 1 1 1 1 1 1 1
33 1 1 1 1 1 1 1 1 1 1
34 0 0 1 0 0 1 0 1 1 0
35 1 1 1 1 1 1 1 1 1 1
36 1 1 0 1 1 1 1 0 1 1
37 0 0 0 0 0 0 0 0 0 0
38 1 1 1 1 1 1 1 1 1 1
39 0 0 0 0 0 0 0 0 0 0
40 1 1 1 1 1 1 1 1 1 1
41 1 1 1 1 1 1 1 1 1 1
42 0 0 0 0 0 0 0 0 0 0
43 1 0 1 1 1 1 1 1 0 1
44 1 1 1 1 1 1 1 1 1 1
45 0 0 0 0 0 0 0 0 0 0
46 1 1 1 1 1 1 1 1 1 1
47 1 1 1 1 1 1 1 1 1 1
48 0 0 0 0 0 0 0 0 0 0
49 1 1 1 1 1 1 1 1 1 1
50 0 0 0 0 0 0 0 0 0 0
ATTRIBUTE GAGECALCULATIONS FOR
COUNTS
166
ATTRIBUTE GAGECALCULATIONS FOR
COUNTS
There are 32 times whereA-2 = 1 and B-2 = 1
(that is of the 50 parts checked
there were 32 matches by A and Bon their SECOND check)
Part A -1 A -2 A - 3 B - 1 B- 2 B-3 C - 1 C -2 C- 3 Reference
1 1 1 1 1 1 1 1 1 1 1
2 1 1 1 1 1 1 1 1 1 1
3 0 0 0 0 0 0 0 0 0 0
4 0 0 0 0 0 0 0 0 0 0
5 0 0 0 0 0 0 0 0 0 0
6 1 1 0 1 1 0 1 0 0 1
7 1 1 1 1 1 1 1 0 1 1
8 1 1 1 1 1 1 1 1 1 1
9 0 0 0 0 0 0 0 0 0 0
10 1 1 1 1 1 1 1 1 1 1
11 1 1 1 1 1 1 1 1 1 1
12 0 0 0 0 0 0 0 1 0 0
13 1 1 1 1 1 1 1 1 1 1
14 1 1 0 1 1 1 1 0 0 1
15 1 1 1 1 1 1 1 1 1 1
16 1 1 1 1 1 1 1 1 1 1
17 1 1 1 1 1 1 1 1 1 1
18 1 1 1 1 1 1 1 1 1 1
19 1 1 1 1 1 1 1 1 1 1
20 1 1 1 1 1 1 1 1 1 1
21 1 1 0 1 0 1 0 1 0 1
22 0 0 1 0 1 0 1 1 0 0
23 1 1 1 1 1 1 1 1 1 1
24 1 1 1 1 1 1 1 1 1 1
25 0 0 0 0 0 0 0 0 0 0
26 0 1 0 0 0 0 0 0 1 0
27 1 1 1 1 1 1 1 1 1 1
28 1 1 1 1 1 1 1 1 1 1
29 1 1 1 1 1 1 1 1 1 1
30 0 0 0 0 0 1 0 0 0 0
31 1 1 1 1 1 1 1 1 1 1
32 1 1 1 1 1 1 1 1 1 1
33 1 1 1 1 1 1 1 1 1 1
34 0 0 1 0 0 1 0 1 1 0
35 1 1 1 1 1 1 1 1 1 1
36 1 1 0 1 1 1 1 0 1 1
37 0 0 0 0 0 0 0 0 0 0
38 1 1 1 1 1 1 1 1 1 1
39 0 0 0 0 0 0 0 0 0 0
40 1 1 1 1 1 1 1 1 1 1
41 1 1 1 1 1 1 1 1 1 1
42 0 0 0 0 0 0 0 0 0 0
43 1 0 1 1 1 1 1 1 0 1
44 1 1 1 1 1 1 1 1 1 1
45 0 0 0 0 0 0 0 0 0 0
46 1 1 1 1 1 1 1 1 1 1
47 1 1 1 1 1 1 1 1 1 1
48 0 0 0 0 0 0 0 0 0 0
49 1 1 1 1 1 1 1 1 1 1
50 0 0 0 0 0 0 0 0 0 0167
ATTRIBUTE GAGECALCULATIONS FOR
COUNTS
There are 31 times where
A-3 = 1 and B-3 = 1(that is of the 50 parts checkedthere were 31 matches by A and B
on their THIRD check)
Total : where A-x =1 and B-x =1= 34+32+31= 97
Part A - 1 A - 2 A- 3 B - 1 B - 2 B - 3 C - 1 C - 2 C - 3 Reference
1 1 1 1 1 1 1 1 1 1 1
2 1 1 1 1 1 1 1 1 1 1
3 0 0 0 0 0 0 0 0 0 0
4 0 0 0 0 0 0 0 0 0 0
5 0 0 0 0 0 0 0 0 0 0
6 1 1 0 1 1 0 1 0 0 1
7 1 1 1 1 1 1 1 0 1 1
8 1 1 1 1 1 1 1 1 1 1
9 0 0 0 0 0 0 0 0 0 0
10 1 1 1 1 1 1 1 1 1 1
11 1 1 1 1 1 1 1 1 1 1
12 0 0 0 0 0 0 0 1 0 0
13 1 1 1 1 1 1 1 1 1 1
14 1 1 0 1 1 1 1 0 0 1
15 1 1 1 1 1 1 1 1 1 1
16 1 1 1 1 1 1 1 1 1 1
17 1 1 1 1 1 1 1 1 1 1
18 1 1 1 1 1 1 1 1 1 1
19 1 1 1 1 1 1 1 1 1 1
20 1 1 1 1 1 1 1 1 1 1
21 1 1 0 1 0 1 0 1 0 1
22 0 0 1 0 1 0 1 1 0 0
23 1 1 1 1 1 1 1 1 1 1
24 1 1 1 1 1 1 1 1 1 1
25 0 0 0 0 0 0 0 0 0 0
26 0 1 0 0 0 0 0 0 1 0
27 1 1 1 1 1 1 1 1 1 1
28 1 1 1 1 1 1 1 1 1 1
29 1 1 1 1 1 1 1 1 1 1
30 0 0 0 0 0 1 0 0 0 0
31 1 1 1 1 1 1 1 1 1 1
32 1 1 1 1 1 1 1 1 1 1
33 1 1 1 1 1 1 1 1 1 1
34 0 0 1 0 0 1 0 1 1 0
35 1 1 1 1 1 1 1 1 1 1
36 1 1 0 1 1 1 1 0 1 1
37 0 0 0 0 0 0 0 0 0 0
38 1 1 1 1 1 1 1 1 1 1
39 0 0 0 0 0 0 0 0 0 0
40 1 1 1 1 1 1 1 1 1 1
41 1 1 1 1 1 1 1 1 1 1
42 0 0 0 0 0 0 0 0 0 0
43 1 0 1 1 1 1 1 1 0 1
44 1 1 1 1 1 1 1 1 1 1
45 0 0 0 0 0 0 0 0 0 0
46 1 1 1 1 1 1 1 1 1 1
47 1 1 1 1 1 1 1 1 1 1
48 0 0 0 0 0 0 0 0 0 0
49 1 1 1 1 1 1 1 1 1 1
50 0 0 0 0 0 0 0 0 0 0
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168
A* BCrosstabulation
44 6 50
15.7 34.3 50.0
3 97 100
31.3 68.7 100.0
47 103 150
47.0 103.0 150.0
Count
Expected Count
Count
Expected Count
Count
Expected Count
.00
1.00
A
Total
.00 1.00
B
Total
"EXPECTED COUNTS""EXPECTED COUNTS"
The expected counts is calculated using the the followingThe expected counts is calculated using the the following
formula (based on Chiformula (based on Chi--Square)Square)
Expected Count = Column Total x [Row Total/Grand Total]Expected Count = Column Total x [Row Total/Grand Total]
From the A*BFrom the A*B CrosstabulationCrosstabulation Table (pg 128)Table (pg 128)
Column Total = 103Column Total = 103
Row Total = 100Row Total = 100
The Grand Total = 150The Grand Total = 150
HenceHenceFor A=1 and B=1For A=1 and B=1
the Expected Count = 103 x [100/150] = 68.7the Expected Count = 103 x [100/150] = 68.7
97 from previous
slide
169
o
e
1
where p = Sum of the observed proportions in the diagonal cells (left to right direction)
p = Sum of the expected proportions in the diagonal cells (left to right direction)
o e
e
p pkappa
p-=
-
44 97 15.7 68.70.94 0.56150 150o e
p p+ += = = =
0.94 0.560.86
1 1 0.56o e
e
p pkappa
p- -= = =
- -
A * B Crosstabulation
44 6 50
15.7 34.3 50.0
3 97 100
31.3 68.7 100.0
47 103 150
47.0 103.0 150.0
Count
Expected Count
Count
Expected Count
Count
Expected Count
.00
1.00
A
Total
.00 1.00
B
Total
170
Miss Rate & False Alarm Rate For Appraiser A
Miss Rate1: Calling aBAD part GOOD.
= 3/48 = 6.3%
1 Type II error, Consumer s risk2 Type I error, Producer s risk
False Alarm Rate2:
Calling a GOOD
part BAD.
= 5/102 = 4.9%
171
Signal Detection Theory
Not Covered in TI class
172
Attribute Risk Analysis Workshop
lDetermine the operational definition for visual defects for
M&M's
e.g. clear markings (M's), no chips, roundness, etc.
lPerform attribute risk analysis study using M&M's.
Use 3 operators/inspectorsUse a random sample of 25 M&Ms
lComplete attribute risk analysis and report results
lDetermine the Defects Per Unit of the sample
lSwitch with another team and determine the DPU of the
new sample using your operational definition
lDetermine the operational definition for visual defects for
M&M's
e.g. clear markings (M's), no chips, roundness, etc.
lPerform attribute risk analysis study using M&M's.
Use 3 operators/inspectors
Use a random sample of 25 M&Ms
lComplete attribute risk analysis and report results
lDetermine the Defects Per Unit of the sample
lSwitch with another team and determine the DPU of the
new sample using your operational definition
Chapter 4c
Automated SystemsAutomated Systems
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174
Automatic Test Systems
Address during APQP - highest importance
Program measurement system identification
Determination of limits, ranges, targets, thresholdsCompensate for settling times, rise and fall times
of equipment, mechanical and environmentalphenomena
Determine discrimination level needed and Plan forProcess Control
Choose an appropriate set of nominal values for theIC process
175
Identify product parametric yield loss such as 2.9-3.9or 3.8-4.0 for the Process Controls
Do Bias, Linearity and GR&R studies on themeasurement/test system for that product with theselimits
Use capability of the equipment to read out variabledata or at least to store it for retrieval when needed
Analyze for improvement in each variable and/oridentified range
Automatic Test Systems
176
Test Setup
Optimize measurement window delay andmeasurement window length
Plan testing sequences carefully
MSA cannot be done on test fixtures or loadboards separately. It has to be done as part of thesystem
Do studies consideringAllnormal variables,Where the tests are done, Bythe personnelassigned to set up and run them.
Automatic Test Systems
Chapter 4d
Non-Replicable SystemsNon-Replicable Systems
178
Non-Replicable Analysis-Guidelines
Tightly control all variables
Use a large sample from a stable process
Take samples from a homogeneous lot
Use multiple lots to represent the parts
The part is not expected to age during the studyEach trail is conducted with a new sample
Use standard GRR techniques
ANOVA can be used to highlight variation fromappraisers, materials, day-to-day, etc
179
Non-Replicable GRR Case Study
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180
Non-Replicable
Replication: the action or process of reproducing;performance of an experiment or procedure morethan once
Not always Destructive
Another R - sorry
181
Standardize Conditions
Qualified appraisers
Adequate lighting, environment
Proper work instructions
Equipment properly maintained
Failure modes understood
etc., etc., etc.
182
Assumptions/Prerequisites
Only looking at Repeatability
ANOVA (nested) software
Samples
homogeneous within
heterogeneous between
Pre-research on process
stable
nature of variation understood
183
Aside
If process is Stable
And if process is Capable
May be no need to do study
process variation includes measurement
this requires some process history/research
184
Process Information
A
B C
D
E
F G
H
I
J K
L
M
N O
P
Q
R S
T
U
V W
X
Welders
Press
1
2
3
4
5
6
7
8
9
10
Rods
RawMaterial
185
Standard GRR Layout
Appraiser 1 Appraiser 2
Part # Trial 1 Trial 2 Trial 3 Trial 1 Trial 2 Trial 3
1 1 1 1 1 1 1
2 2 2 2 2 2 2
3 3 3 3 3 3 3
4 4 4 4 4 4 4
5 5 5 5 5 5 5
6 6 6 6 6 6 6
7 7 7 7 7 7 7
8 8 8 8 8 8 8
9 9 9 9 9 9 9
10 10 10 10 10 10 10
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186
Non-Replicable GRR Layout
Appraiser 1 Appraiser 2
Part # Trial 1 Trial 2 Trial 3 Trial 1 Trial 2 Trial 3
1 1-1 1-2 1-3 1-4 1-5 1-62 2-1 2-2 2-3 2-4 2-5 2-6
3 3-1 3-2 3-3 3-4 3-5 3-6
4 4-1 4-2 4-3 4-4 4-5 4-6
5 5-1 5-2 5-3 5-4 5-5 5-6
6 6-1 6-2 6-3 6-4 6-5 6-6
7 7-1 7-2 7-3 7-4 7-5 7-6
8 8-1 8-2 8-3 8-4 8-5 8-6
9 9-1 9-2 9-3 9-4 9-5 9-6
10 10-1 10-2 10-3 10-4 10-5 10-6
187
Randomize Presentation
Each part has equal chance of being selected
Not haphazard
Not convenience
188
Randomize Presentation
Appraiser 1 Appraiser 2
Part # Trial 1 Trial 2 Trial 3 Trial 1 Trial 2 Trial 3
1-1R 1-6R 1-6R53 1-5R25 1-3R7 1-4R40 1-1R34 1-2R32
2-1P 2-6P 2-2P27 2-6P35 2-5P57 2-4P12 2-3P43 2-1P17
3-1H 3-6H 3-1H21 3-2H36 3-6H1 3-5H56 3-4H10 3-3H264-1G 4-6G 4-4G46 4-6G42 4-3G8 4-2G28 4-1G55 4-5G305-1E 5-6E 5-4E5 5-3E20 5-1E13 5-6E54 5-2E39 5-5E50
6-1F 6-6F 6-1F52 6-3F3 6-4F37 6-5F29 6-2F51 6-6F457-1M 7-6M 7-6M16 7-4M11 7-1M23 7-2M6 7-3M15 7-5M14
8-1O 8-6O 8-6O49 8-3O60 8-1O33 8-5O41 8-2O44 8-4O199-1Q 9-6Q 9-5Q31 9-6Q59 9-3Q24 9-2Q4 9-4Q9 9-1Q2
10-1T 10-6T 10-2T22 10-5T18 10-3T47 10-4T58 10-1T48 10-6T38
189
Process Information
A
B C
D
E
F G
H
I
J K
L
M
N O
P
Q
R S
T
U
V W
X
Welders
Press
1
2
3
4
5
6
7
8
9
10
Rods
RawMaterial
190
Results
8500
9000
9500
10000Appr1 Appr2
Xbar Chart by Appr No.
SampleMean
Mean=9156
UCL=9525
LCL=8787
0
500
1000 Appr1 Appr2
R Chart by Appr No.
SampleRange
R=360.7
UCL=928.6
LCL=0
Appr1 Appr2
8000
9000
10000
Appr No
By Appr No.
1 2 3 4 5 6 7 8 9 10 1 2 3 4 5 6 7 8 9 10Appr1 Appr2
8000
9000
10000
Part2Appr No
By "Part" (Appr No.)
%Contribution
%StudyVar
Ga ge R &R R ep ea t R ep ro d P ar t- to -P ar t
0
50
100
Components of Variation
Percent
1
2
3
4
5
40% GR&R
FlatIn Control
50% Out of Control
191
Case Study Summary
Doing SOMETHING is Better than doingNOTHING (with customer approval)
Develop approach for each situation
Focus on learning
Be careful conducting study and interpretingresults
Consult statistical resources
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Chapter 5
Measurement PlanningMeasurement Planning
193
Where To Start?
Evaluate the components of the measuring systemand control variation as much as possible to ensurethat an item of measuring equipment is in a state ofcompliance with requirements for its intended use
Expand our consideration of Measurement ProcessVariation to Measurement System StatisticalProperties and Measurement Uncertainty
Follow the basics of SPC
194
Measurement Planning
MSA Plan is the output of APQP (NPD) Phase 3, the ProcessDevelopment
At TI, this plan should originate in process development and becompleted by the production verification team.
It starts with the customer requirements and ends withconfidence of determination that these requirements are metand result in customer satisfaction
Is repeated as often as appropriate to control new equipment,new processes, new methods, new personnel, changes or anyvariables that may effect our ability to make accurate decisions
195
Measurement System Data
Define data needed, how to use the measurementsystem at APQP
Determine if measurement system statistical propertiesmeet needed limits and requirements and are worth timeand cost of using the system
The quality of a Measurement System is determined bythe statist ical properties of data produced:
Bias and Linearity, < 10%
R&R < 10%; 10-30% marginal and
total measurement uncertainty < 30%
196
Common Properties
Measurement System
Must be in a state of statistical control
Variation must be small compared to the
manufacturing process variation and specificationlimits
Increments no greater than 1/10th or smaller ofeither process variability or specification limits
Worst variation must be small relative to smallerof either process variation or specification limits
197
Measurement Systems must be in a state of statisticalcontrol i.e., free of special causes, as is true of allprocesses
1. In general, the absence of points in
the special cause region indicatesthe process is in a state of statistical
control.
2. If there is no trend or shift in the dataas explained in SPC, then along with(1) we could say that the process is
in a state of statistical control.
Statistical Control
COMM
ONCA
USER
EGION
SPECIAL CAUSE REGION
SPECIAL CAUSE REGION
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198
Measurement Planning
The Data
What is to be measured: physical, contact, electrical,condition, dynamic
How important is this data
What will be done with the results
Who cares about the results
Process capability
Data range
What is the acceptance criteria
199
Measurement Planning
The Appraisers
Operators, engineers, inspectors
Training or certificationInstructions: Selection, set up, execution,
Automated vs manual
Can they influence results
Will attitude, stress affect results
Will the environment allow them to read the same results
Special handling, storage
200
Measurement Planning
Defining the physical system
Dedicated or flexible
Contact vs non-contact
Destructive
Measurement points
Fixturing
Part orientation
Part preparation
Transducer location
Resolution, sensitivity
Environment
201
Measurement Planning
Supporting Activities
What is the objective of the study
Has an equipment and MS FMEA been done
Do the equipment/fixtures have to be built
How have we defined the specifications
Is the source selected and proven
How will acceptance be conducted
202
Measurement Planning
Supporting Activities (continued)
Is the cost in the budget
Is there a preventative maintenance plan
Is there a user/troubleshooting guide
What are the utility requirements
What is the calibration plan
Can results be correlated with others: same
gage, same method, same measurements
What inputs are required
Chapter 6
Analysis of ResultsAnalysis of Results
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204
Analysis of Results
Methods to determine problems are discussed in Chap. 3. Thistext is to be specific to TI per the intended procedures.
Chapter 7
Conducting a GR&R StudyConducting a GR&R Study
206
Measurement System Study
Typical preparation includes:
Work Instruction for the study
Number of appraisers andsample parts
Number of repeated readingsor trials
Criticality of dimension
Part configuration
Operators who use measurementEquipment as part of their work
Sample parts that represententire operating range
Is the equipment ready
Measurement equipment musthave discrimination thatallows at least 1/10th ofprocess variation ofcharacteristic to be read
Chapter 8
MSA Application to Continual
Improvement
MSA Application to Continual
Improvement
208
Continual Improvement Applications
Reduce Calibration or Maintenance Events
Based on stability studies and traditional percentageof error, calibration or maintenance intervals may
be extended.
Of course the studies could point to the need for moremaintenance or calibration events to keep thesystem capable.
209
Continual Improvement Applications
Measure Appraiser Competence
TS requires the demonstration of competence forall personnel performing work affecting product
quality. An unacceptable MSA on a repeated basiscan point out the need for more capability ortraining or automation.
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210
Continual Improvement Applications
Increase process tolerance
Show how gray area reduction expands good/good
areaReduce false accepts or rejects
211
Continual Improvement Applications
Improve selection of Measurement Systems
Retire incapable systems
212
Continual Improvement Applications
Benchmark and compare to other fabs
213
Do You Understand?
l The language of Measurement ?
l The importance of Measurement?
l How to perform a Gage R&R Study and
how to interpret results ?
l Use MSAPro to analyze GRR results?
l The language of Measurement ?
l The importance of