Measurement
Systems
Analysis
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Measurement Systems Analysis
Slide 1 , Printed 2/9/04
Don’t Let This Happen To YOU!
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Measurement Systems Analysis
Slide 2 , Printed 2/9/04
Variation
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Think of Measurement
as a Process
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Measurement Systems Analysis
Slide 3 , Printed 2/9/04
Definition
Measurement
The assignment of numbers to material
things to represent the relationships
among them with respect to particular
properties.
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C. Eisenhart (1963)
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Measurement Systems Analysis
Slide 4 , Printed 2/9/04
Measurement Systems Analysis
• Basic Concepts of Measurement Systems
A Process
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• Statistics and the Analysis of Measurement
Systems
• Conducting a Measurement Systems Analysis
• ISO - TC 69 is the Statistics Group
• Ensures high ‘Data Quality’ (Think of Bias)
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Measurement Systems Analysis
Slide 5 , Printed 2/9/04
Course Focus & Flow
Measurement as a Process
• Mechanical Aspects (vs Destructive)
Piece part
Continuous (fabric)
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• Features of a Measurement System
• Methods of Analysis
• Gauge R&R Studies
• Special Gauging Situations
Go/No-Go
Destructive Tests
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Measurement Systems Analysis
Slide 6 , Printed 2/9/04
Place Timeline Here
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Measurement Systems Analysis
Slide 7 , Printed 2/9/04
The Target & Goal
Continuous Improvement
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Production
Pre-Launch
Prototype
LSL
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USL
Measurement Systems Analysis
Slide 8 , Printed 2/9/04
Key Words
• Discrimination
Ability to tell things apart
• Bias
[per AIAG]
(Accuracy)
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• Repeatability [per AIAG] (Precision)
• Reproducibility
• Linearity
• Stability
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Measurement Systems Analysis
Slide 9 , Printed 2/9/04
Measurement as a Process
Basic Concepts
• Components of the Measurement System
• Requirements of a Measurement System
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• Factors Affecting a Measurement System
• Characteristics of a Measurement System
Features (Qualities) of a Measurement Number
• Units (Scale)
• Accuracy
• Precision (Consistency or Repeatability)
• Resolution (Reproducibility)
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Measurement Systems Analysis
Slide 10, Printed 2/9/04
Measurement Related Systems
Typical Experiences with
Measurement Systems
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Measurement Systems Analysis
Slide 11, Printed 2/9/04
Basic Concepts
• Every Process Produces a “Product”
• Every Product Possesses Qualities (Features)
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• Every Quality Feature Can Be Measured
• Total Variation
= Product Variation + Measurement Variation
• Some Variation Inherent in System Design
• Some Variation is Due to a Faulty Performance of
the System(s)
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Measurement Systems Analysis
Slide 12, Printed 2/9/04
The Measurement Process
What is the ‘Product’ of the Measurement Process?
What are the Features or Qualities of this Product?
How Can We Measure Those Features?
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Measurement Systems Analysis
Slide 13, Printed 2/9/04
Measurement Systems Components
• Material to be Inspected
Piece
Continuous
• Characteristic to be Measured
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• Collecting and Preparing Specimens
• Type and Scale of Measurement
• Instrument or Test Set
• Inspector or Technician
AIAG calls these ‘Appraiser’
• Conditions of Use
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Measurement Systems Analysis
Slide 14, Printed 2/9/04
Where Does It Start?
During the Design (APQP) Stage:
The engineer responsible for determining inspections
and tests, and for specifying appropriate equipment
should be well versed in measurement systems. The
Calibration folks should be part of the process as a
part of a cross-functional team.
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Variability chosen instrument must be small when
compared with:
Process Variability
Specification Limits
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Measurement Systems Analysis
Slide 15, Printed 2/9/04
Typical Progression
How will the data
be used?
Determine ‘Critical’
Characteristic
Product Engineer
Determine Required
Resolution
Product Engineer
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Consideration of the Entire
Measurement System for
the Characteristic
(Variables)
Determine What
Equipment is Already
Available
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Cross-Functional
Metrology
Measurement Systems Analysis
Slide 16, Printed 2/9/04
Measurement Systems Variables
Material
Inspector
Sample
Collection
Methods
Test Method
Training
Sample
Preparation
Workmanship
Parallax
Practice
Fixture
Eyesight
Air Pressure
Air Movement
Fatigue
Samples
Elsmar.com
Reproducibility
Ergonomics
Standards
Measurement
Discrimination
Vibration
Bias
Repeatability
Calibration
Linearity
Instrument
Temperature
Lighting
Humidity
Environment
These are some of the variables in a measurement
system. What others can you think of?
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Measurement Systems Analysis
Slide 17, Printed 2/9/04
Determining What To Measure
External
Requirements
Convert To
• Voice of the Customer
You Must Convert to Technical Features
• Technical Features
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Internal
Requirements
• Failure Modes Analysis
• Control Plan
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Measurement Systems Analysis
Slide 18, Printed 2/9/04
Voice of the Customer
Customer
may
specify
• External and
causes
Internal
rather than
output
Customers
• Stated vs Real
and Perceived
Needs
• Cultural Needs
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• Unintended
Uses
• Functional
Needs vs.
Technical
Features
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Measurement Systems Analysis
Slide 19, Printed 2/9/04
Convert to Technical Features
• Agreed upon
Measure(s)
• Related to
Functional Needs
• Understandable
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• Uniform
Interpretation
• Broad Application
• Economical
Y
Functional Need
Z
Technical Feature
• Compatible
• Basis for
Decisions
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Measurement Systems Analysis
Slide 20, Printed 2/9/04
Failure Modes Analysis
• Design
FMEA
• Process
FMEA
• Identify
Key
Features
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• Identify
Control
Needs
Critical Features are Defined Here!
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Measurement Systems Analysis
Slide 21, Printed 2/9/04
Automotive FMEA
Process Failure Mode And Effects Analysis
Other Div. Or People Involved:
Scheduled Production Released:
PFMEA Date:
Potential Failure
Mode
Potential Effects Of
Failure
Current Controls
Detection
1
Senior Advisor
RPN
SIR
Container
Quality Assurance Engineer
Operations Manager
Occured
Part Name
Operation
Number
Quality Assurance Manager
Severity
Approvals:
Material Certification
1
9
2
18
3
10 3
90
Recommended
Actions And
Status
1 - 10
Rev.
Actions
Taken
RPN
Part Number:
Detection
Engineer:
Model Year/Vehicle(s):
Occured
Outside Suppliers Affected:
Primary Process Responsibility:
Severity
Process:
Low - High
Responsible
Activity
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Process Function
Take TPPE
Wrong MaterialFragmented Container
Material Held In
Unpredictable Deployment
Storage Area
Potential Cause Of Failure
Insufficient Supplier Control
Improper Handling
Misidentified Material
Required With Each
Shipment
Release Verification
Out Of Spec
Material
Fragmented Container
Supplier Process Control
Unpredictable Deployment
Contaminated Fragmented Container
Material
Unpredictable Deployment
Material
Fragmented Container
Composition Unpredictable Deployment
Supplier Material
Open Boxes
Visual Inspection
1
9
7
63
Engineering Change
Release Verification
1
10 7
70
5
10 1
50
Supplier Change
Change
2
Move To
Unreleased
Periodic Audit Of
Green "OK" Tag
Customer Notification
Fragmentation
Approved
Storage
Untrained LTO
Untrained Personnel
Check For Green "OK"
Tag At Press
Trace Card
Check List
Training
Leading to MSA. Critical features are determined by the FMEA
(RPN indicators) and put into the Control Plan.
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Measurement Systems Analysis
Slide 22, Printed 2/9/04
Control Plan / Flow Diagram
• Inspection Points
• Inspection
Frequency
• Instrument
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• Measurement Scale
• Sample Preparation
• Inspection/Test
Method
• Inspector (who?)
• Method of Analysis
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Measurement Systems Analysis
Slide 23, Printed 2/9/04
GM Process Flow Chart
Process Flow Diagram
1
2
3
Inspect
Date: 4/5/93
Rev. : C
QA Manager
Operations Manager
Senior Advisor
QA Engineer
Store
Elsmar.com
Move
Step
Fabrication
Part Number:
Part Description:
Prepared By:
Approved By:
Operation Description
Item # Key Product Characteristic
Item #
Key Control Characteristic
Move "OK" Vinyl Material
From Storage Area and
Load Into Press.
1.0
Material Specs
1.0
Material Certification Tag
Auto Injection Mold Cover
In Tool #
2.0
Tearstrip In Cover
2.1
2.2
Tool Setup
Machine Setup
3.0
Hole Diameter In Cover
2.1
2.2
Tool Setup
Machine Setup
4.0
Flange Thickness In Cover
2.1
2.2
Tool Setup
Machine Setup
5.0
Pressure Control Protrusions
Height
2.1
2.2
Tool Setup
Machine Setup
6.0
Pressure Control Protrusions
Filled Out
2.1
2.2
Tool Setup
Machine Setup
Visually Inspect Cover
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Measurement Systems Analysis
Slide 24, Printed 2/9/04
Standard Control Plan Example
Control Plan Number
Key Contact / Phone
Date (Orig.)
Date (Rev.)
Part No./ Latest Change No.
Core Team
Customer Engineering Approval/Date
Part Name/Description
Supplier/Plant Apoproval/Date
Customer Quality Approval/Date
Elsmar.com
Supplier/Plant
Supplier Code
Other Approval/date (If Req'd)
Other Approval/date (If Req'd)
Characteristics
Part/
Process Name/
Process
Operation
Number
Description
Machine,
Device,
Jig, Tools
for Mfg.
No.
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Product
Process
Methods
Special
Char.
Class
Product/
Process
Spec/
Tolerance
Evaluation
Measurement
Technique
Measurement Systems Analysis
Size
Frequency
Control
Method
Reaction
Plan
This form is on
course
Slide
25,disk
Printed 2/9/04
Ford’s Dimensional Control Plan
(DCP)
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Measurement Systems Analysis
Slide 26, Printed 2/9/04
Measurement as a System
• Choosing the Right Instrument
Instrument Calibration Needs
Standards or Masters Needed
Accuracy and Precision
Elsmar.com
• Measurement Practices
Where
How Many Places
• Reported Figures
Significant Figures Rule
2 Action Figures
Rule of 10
Individuals, Averages, High-Lows
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Measurement Systems Analysis
Slide 27, Printed 2/9/04
Measurement Error
Measured Value (y)
=
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True Value (x) + Measurement Error
Deming says there is
no such thing as a
‘True’ Value.
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Consistent (linear)?
Measurement Systems Analysis
Slide 28, Printed 2/9/04
Sources of Measurement Error
• Sensitivity (Threshold)
Chemical Indicators
• Discrimination
• Precision (Repeatability)
Elsmar.com
• Accuracy (Bias)
• Damage
• Differences in use by Inspector (Reproducibility)
Training Issues
• Differences Among Instruments and Fixtures
• Differences Among Methods of Use
• Differences Due to Environment
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Measurement Systems Analysis
Slide 29, Printed 2/9/04
Types of Measurement Scales
• Variables
Can be measured on a continuous scale
Defined, standard Units of Measurement
Elsmar.com
• Attributes
No scale
Derived ‘Unit of Measurement’
Can be observed or counted
Either present or not
Needs large sample size because of low information content
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Measurement Systems Analysis
Slide 30, Printed 2/9/04
How We Get Data
• Inspection
Includes Sensory (e.g..: Beer)
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• Measurement
Magnitude of Quality
• Test
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Measurement Systems Analysis
Slide 31, Printed 2/9/04
Operational Definitions
• Is the container Round?
• Is your software Accurate?
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• Is the computer screen Clean?
• Is the truck On Time?
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Measurement Systems Analysis
Slide 32, Printed 2/9/04
Different Method = Different Results
Method 1
Method 2
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Out of Spec
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In Spec
Measurement Systems Analysis
Slide 33, Printed 2/9/04
Measurement System Variability
• Small with respect to Process Variation
• Small with respect to Specified
Requirements
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• Must be in Statistical Control
Measurement IS a Process!
Free of Assignable Causes of variation
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Measurement Systems Analysis
Slide 34, Printed 2/9/04
Studying the Measurement System
• Environmental Factors
• Human Factors
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• System Features
• Measurement Studies
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Measurement Systems Analysis
Slide 35, Printed 2/9/04
Standards
• National
In the US - Kept or Tracked by NIST
• Primary
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Copied directly from National Standard using ‘State-of-theArt’ Equipment
• Secondary
Transferred from Primary Standard
• Working
Used to calibrate laboratory and shop instruments
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Measurement Systems Analysis
Slide 36, Printed 2/9/04
Environmental Factors
• Temperature
• Humidity
• Vibration
• Lighting
Elsmar.com
• Corrosion
• Wear
Where is the study performed?
1. Lab?
2. Where used?
3. Both?
• Contaminants
Oil & Grease
Aerosols
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Measurement Systems Analysis
Slide 37, Printed 2/9/04
Human Factors
• Training
• Skills
• Fatigue
• Boredom
Elsmar.com
• Eyesight
• Comfort
• Complexity of Part
• Speed of Inspection (parts per hour)
• Misunderstood Instructions
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Measurement Systems Analysis
Slide 38, Printed 2/9/04
Human Measurement Errors
• Sources of Errors
Unaware of
problem
Inadvertent Errors
• Attentiveness
• Random
Good
Bad
Elsmar.com
• Good Mistake-Proofing Target
Training Technique Errors
Issue
• Consistent
Wilful Errors
Accept
OK!
beta
Reject
alpha
OK!
(Bad mood)
• Error Types (Can be machine or human)
Type I - Alpha Errors [ risk]
Type II - Beta Errors [ risk]
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Process in control,
but needs
adjustment, False
alarm
Measurement Systems Analysis
Slide 39, Printed 2/9/04
Measurement System Features
• Discrimination
Ability to tell things apart
• Bias
(Accuracy)
Elsmar.com
[per AIAG]
• Repeatability [per AIAG] (Precision)
• Reproducibility
• Linearity
• Stability
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Measurement Systems Analysis
Slide 40, Printed 2/9/04
Discrimination
• Readable Increments of Scale
• If Unit of Measure is too course: Process
variation will be lost in Rounding Off
Elsmar.com
• The “Rule of Ten”: Ten possible values
between limits is ideal
Five Possible Values: Marginally useful
Four or Less: Inadequate Discrimination
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Measurement Systems Analysis
Slide 41, Printed 2/9/04
Discrimination
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Measurement Systems Analysis
Slide 42, Printed 2/9/04
Range Charts & Discrimination
Elsmar.com
Indicates
Poor
Precision
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Measurement Systems Analysis
Slide 43, Printed 2/9/04
Bias and Repeatability
Precise
Imprecise
Accurate
Elsmar.com
Bias
Inaccurate
You can correct for Bias
You can NOT correct for Imprecision
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Measurement Systems Analysis
Slide 44, Printed 2/9/04
• Difference between
average of
measurements and an
Agreed Upon standard
value
Bias
• Known as Accuracy
Bias
Elsmar.com
Standard
Value
• Cannot be evaluated
without a Standard
Measurement Scale
• Adds a Consistent “Bias
Factor” to ALL
measurements
• Affects all measurements
in the same way
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Measurement Systems Analysis
Slide 45, Printed 2/9/04
Causes of Bias
• Error in Master
• Worn components
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• Instrument improperly calibrated
• Instrument damaged
• Instrument improperly used
• Instrument read incorrectly
• Part set incorrectly (wrong datum)
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Measurement Systems Analysis
Slide 46, Printed 2/9/04
Bias and QS9000
BIAS - The difference between the observed
Average of measurements and the master
Average of the same parts using precision
instruments. (MSA Manual Glossary)
Elsmar.com
The auditor may want evidence that the concept of
bias is understood. Remember that bias is nothing
more than an offset from ‘zero’. Bias is linked to
Stability in the sense that an instrument may be
‘zeroed’ during calibration verification. Knowing this
we deduce that the bias changes with instrument
use. This is in part the concept of Drift.
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Measurement Systems Analysis
Slide 47, Printed 2/9/04
Bias
• I choose a caliper (resolution 0.01) for
the measurement. I measure a set of
parts and derive the average.
Elsmar.com
• I take the same parts and measure
them with a micrometer (resolution
0.001). I then derive the average.
• I compare the two averages. The
difference is the Bias.
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Measurement Systems Analysis
Slide 48, Printed 2/9/04
Repeatability
• Variation among
repeated
measurements
• Known as Precision
• Standard NOT
required
• May add or subtract
from a given
measurement
Repeatability
Elsmar.com
• Affects each
measurement
randomly
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Measurement Scale
5.15
= 99%
Margin of Error
Doesn’t address Bias
Measurement Systems Analysis
Slide 49, Printed 2/9/04
Repeatability Issues
• Measurement Steps
Sample preparation
Setting up the instrument
Locating on the part
Elsmar.com
• How much of the measurement process
should we repeat?
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Measurement Systems Analysis
Slide 50, Printed 2/9/04
Using Shewhart Charts I
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Repeatability
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Measurement Systems Analysis
Slide 51, Printed 2/9/04
Using Shewhart Charts II
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Measurement Systems Analysis
Slide 52, Printed 2/9/04
Evaluating Bias & Repeatability
• Same appraiser, Same part, Same instrument
• Multiple readings (n≥10 with 20 to 40 better)
• Analysis
True
AIAG
Elsmar.com
Average minus Standard Value = Bias
5.15* Standard Deviation = Repeatability
or +/- 2.575
or +/- 2
[99% repeatability]
[95% repeatability]
• Histogram
• Probability
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Measurement Systems Analysis
Slide 53, Printed 2/9/04
Repeatability Issues
• Making a measurement may involve
numerous steps
Sample preparation
Setting up the instrument
Locating the part, etc.
Elsmar.com
• How much of the measurement process
should we repeat? How far do we go?
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Measurement Systems Analysis
Slide 54, Printed 2/9/04
Bias & Repeatability Histogram
Never include assignable cause errors
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Measurement Systems Analysis
Slide 55, Printed 2/9/04
Linearity
• The difference in the Bias or Repeatability across
the expected operating range of the instrument.
Elsmar.com
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Measurement Systems Analysis
Slide 56, Printed 2/9/04
Plot Biases vs. Ref. Values
Elsmar.com
Linearity = |Slope| * Process Variation = 0.1317*6.00 = 0.79
% Linearity = 100 * |Slope| = 13.17%
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Measurement Systems Analysis
Slide 57, Printed 2/9/04
Causes of Poor Linearity
• Instrument not properly calibrated at
both Upper and Lower extremes
• Error in the minimum or maximum
Master
Elsmar.com
• Worn Instrument
• Instrument design characteristics
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Measurement Systems Analysis
Slide 58, Printed 2/9/04
Reproducibility
• Variation in the
averages among
different
appraisers
repeatedly
measuring the
same part
characteristic
Elsmar.com
• Concept can also
apply to variation
among different
instruments
Includes repeatability which must be accounted for.
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Measurement Systems Analysis
Slide 59, Printed 2/9/04
Reproducibility Example
Elsmar.com
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Measurement Systems Analysis
Slide 60, Printed 2/9/04
Calculating Reproducibility (I)
• Find the range of the appraiser averages (R0)
• Convert to Standard Deviation using d2*
(m=# of appraisers; g=# of ranges used = 1)
Elsmar.com
• Multiply by 5.15
• Subtract the portion of this
repeatability
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due to
Measurement Systems Analysis
Slide 61, Printed 2/9/04
Calculating Reproducibility
People variance
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Times done
Trials
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Measurement Systems Analysis
Slide 62, Printed 2/9/04
Stability
• Variation in
measurements of a
single
characteristic
Elsmar.com
• On the same
master
• Over an extended
period of time
• Evaluate using
Shewhart charts
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Measurement Systems Analysis
Slide 63, Printed 2/9/04
Evaluate Stability with Run Charts
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Measurement Systems Analysis
Slide 64, Printed 2/9/04
Stability
Elsmar.com
Both gages are stable, but.....
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Measurement Systems Analysis
Slide 65, Printed 2/9/04
Importance of Stability
• Statistical stability, combined with subjectmatter knowledge, allows predictions of
process performance
• Action based on analysis of Unstable systems
may increase Variation due to ‘Tampering’
Elsmar.com
• A statistically unstable measurement system
cannot provide reliable data on the process
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Measurement Systems Analysis
Slide 66, Printed 2/9/04
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Methods of Analysis
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Measurement Systems Analysis
Slide 67, Printed 2/9/04
Analysis Tools
• Calculations of Average and Standard
Deviation
• Correlation Charts
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• Multi-Vari Charts
• Box-and-Whisker Plots
• Run charts
• Shewhart charts
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Measurement Systems Analysis
Slide 68, Printed 2/9/04
Average and Standard Deviation
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Measurement Systems Analysis
Slide 69, Printed 2/9/04
Correlation Charts
Describe Relationships
• Substitute measurement for desired
measurement
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• Actual measurement to reference value
• Inexpensive gaging method versus
Expensive gaging method
• Appraiser A with appraiser B
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Measurement Systems Analysis
Slide 70, Printed 2/9/04
Substitute Measurements
• Cannot directly
measure quality
• Correlate
substitute measure
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• Measure substitute
• Convert to desired
quality
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Measurement Systems Analysis
Slide 71, Printed 2/9/04
Comparing Two Methods
• Two
methods
Magnetic
• Measure
parts using
both
• Correlate
the two
Line of Perfect Agreement
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• Compare
to “Line of
No Bias”
• Investigate
differences
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Line of Correlation
Stripping
Measurement Systems Analysis
Slide 72, Printed 2/9/04
Measurements vs. Reference Data
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Measurement Systems Analysis
Slide 73, Printed 2/9/04
Measurements vs. Reference Correlation
Disparity
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Measurement Systems Analysis
Slide 74, Printed 2/9/04
Comparing Two Appraisers
Elsmar.com
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Measurement Systems Analysis
Slide 75, Printed 2/9/04
Run Charts Examine Stability
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Measurement Systems Analysis
Slide 76, Printed 2/9/04
Multiple Run Charts
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More than 3 appraisers confuses things...
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Measurement Systems Analysis
Slide 77, Printed 2/9/04
Multi-Vari Charts
• Displays 3 points
High Reading
• Length of bar; bar-to-bar;
Bar cluster to cluster
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• Plot High and Low
readings as Length of bar
Average Reading
• Each appraiser on a
separate bar
• Each piece in a separate
bar cluster
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Measurement Systems Analysis
Low Reading
Slide 78, Printed 2/9/04
Multi-Vari Type I
• Bar lengths
are long
• Appraiser
differences
small in
comparison
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• Piece-topiece hard to
detect
• Problem is
repeatability
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Measurement Systems Analysis
Slide 79, Printed 2/9/04
Multi-Vari Type II
• Appraiser
differences are
biggest source
of variation
Elsmar.com
• Bar length is
small in
comparison
• Piece-to-piece
hard to detect
• Problem is
reproducibility
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Measurement Systems Analysis
Slide 80, Printed 2/9/04
Multi-Vari Type III
• Piece-to-piece
variation is the
biggest source of
variation
• Bar length
(repeatability) is small
in comparison
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• Appraiser differences
(bar-to-bar) is small in
comparison
• Ideal Pattern
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Measurement Systems Analysis
Slide 81, Printed 2/9/04
Multi-Vari Chart Example
Normalized Data
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Measurement Systems Analysis
Slide 82, Printed 2/9/04
Multi-Vari Chart, Joined
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Look for similar pattern
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Measurement Systems Analysis
Slide 83, Printed 2/9/04
Using Shewhart Charts
• Subgroup = Repeated measurements,, same piece
• Different Subgroups = Different pieces and/or
appraisers
Elsmar.com
• Range chart shows precision (repeatability)
• Average chart “In Control” shows reproducibility
If subgroups are different appraisers
• Average chart shows discriminating power
If subgroups are different pieces
(“In Control” is BAD!)
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Measurement Systems Analysis
Slide 84, Printed 2/9/04
Shewhart Charts
Elsmar.com
This is not a good way to plot this data
Too many lines
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Measurement Systems Analysis
Slide 85, Printed 2/9/04
Shewhart Chart of Instrument
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Measurement Systems Analysis
Slide 86, Printed 2/9/04
Gage R&R Studies
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Measurement Systems Analysis
Slide 87, Printed 2/9/04
Gauge R&R Studies
• Developed by Jack Gantt
• Originally plotted on probability paper
• Revived as purely numerical
calculations
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• Worksheets developed by AIAG
• Renewed awareness of Measurement
Systems as ‘Part of the Process’
Consider Numerical vs. Graphical Data Evaluations
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Measurement Systems Analysis
Slide 88, Printed 2/9/04
Terms Used in R&R (I)
Minimum of 5.
2 to 10 To accommodate
worksheet factors
• n = Number of Parts [2 to 10]
Parts represent total range of process variation
Need not be “good” parts. Do NOT use consecutive pieces.
Screen for size
Elsmar.com
• a = Number of Appraisers
Each appraiser measures each part r times
Study must be by those actually using
• R - Number of trials
– Also called “m” in AIAG manual
1
2
3
4
5
1 Outside Low/High
1 Inside Low/High
Target
• g = r*a [Used to find d2* in table 2, p. 29 AIAG manual]
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Measurement Systems Analysis
Slide 89, Printed 2/9/04
Terms Used in R&R (II)
• R-barA = Average range for appraiser A, etc.
• R-double bar = Average of R-barA, R-barB
• Rp = Range of part averages Process Variation
Elsmar.com
• XDIFF = Difference between High & Low appraiser
averages
Also a range, but “R” is not used to avoid confusion
• EV = 5.15 = Equipment variation (repeatability)
• EV = 5.15 = Equipment variation (reproducibility)
• PV = Part variation
• TV = Total variation
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Measurement Systems Analysis
Slide 90, Printed 2/9/04
R&R Calculations
Left over
Repeatability
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Remember Nonconsecutive
Pieces
Left over
Repeatability
Measurement
System Variation
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Product Process
Variation
Measurement Systems Analysis
Slide 91, Printed 2/9/04
Accumulation of Variances
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Measurement Systems Analysis
Slide 92, Printed 2/9/04
Evaluating R&R
• %R&R=100*[R&R/TV] (Process Control)
• %R&R=100*[R&R/Tolerance] (Inspection)
Elsmar.com
• Under 10%: Measurement System Acceptable
• 10% to 30%: Possibly acceptable,
depending upon use, cost, etc.
• Over 30%: Needs serious improvement
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Measurement Systems Analysis
Slide 93, Printed 2/9/04
Analysis of Variance I
• Mean squares and Sums of squares
• Ratio of variances versus expected F-ratio
• Advantages
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Any experimental layout
Estimate interaction effects
• Disadvantages
Must use computer
Non-intuitive interpretation
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Measurement Systems Analysis
Slide 94, Printed 2/9/04
Analysis of Variance II
• The n*r measurements must be done in
random sequence [a good idea anyway]
• Assumes that EV [repeatability] is normal
and that EV is not proportional to
measurement [normally a fairly good
Elsmar.com
assumption]
• Details beyond scope of this course
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Measurement Systems Analysis
Slide 95, Printed 2/9/04
Special Gauging Situations
• Go/No-Go
• Destructive Testing
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Measurement Systems Analysis
Slide 96, Printed 2/9/04
If Gauges were Perfect
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Measurement Systems Analysis
Slide 97, Printed 2/9/04
But Repeatability Means We Never
Know The Precise Value
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Measurement Systems Analysis
Slide 98, Printed 2/9/04
So - Actual Part Acceptance Will Look Like
This:
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Measurement Systems Analysis
Slide 99, Printed 2/9/04
The Effect of Bias on Part Acceptance
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Measurement Systems Analysis
Slide 100, Printed 2/9/04
Go/No-Go gauges
• Treat variables like attributes
• Provide less information on the process,
but...
Elsmar.com
• Are fast and inexpensive
• Cannot use for Process Control
• Can be used for Sorting purposes
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Measurement Systems Analysis
Slide 101, Printed 2/9/04
“Short” Go/No-Go Study
• Collect 20 parts covering the entire
process range
• Use two inspectors
Elsmar.com
• Gage each part twice
• Accept gauge if there is agreement on
each of the 20 parts
* May reject a good measuring system
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Measurement Systems Analysis
Slide 102, Printed 2/9/04
Destructive Tests
• Cannot make true duplicate tests
• Use interpenetrating samples
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• Compare 3 averages
• Adjust using √n
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Measurement Systems Analysis
Slide 103, Printed 2/9/04
Destructive Tests: Interpreting Samples
AIAG does not address
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Measurement Systems Analysis
Slide 104, Printed 2/9/04
Summary
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Measurement Systems Analysis
Slide 105, Printed 2/9/04
Measurement Variation
• Observed variation is a combination of
the production process PLUS the
measurement process
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• The contribution of the measurement
system is often overlooked
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Measurement Systems Analysis
Slide 106, Printed 2/9/04
Types of Measurement Variation
• Bias (Inaccuracy)
• Repeatability (Imprecision)
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• Discrimination
• Linearity
• Stability
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Measurement Systems Analysis
Slide 107, Printed 2/9/04
Measurement Systems
• Material
• Characteristic
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• Sampling and Preparation
• Operational Definition of Measurement
• Instrument
• Appraiser
• Environment and Ergonomics
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Measurement Systems Analysis
Slide 108, Printed 2/9/04
Measurement Systems Evaluation Tools
• Histograms
• Probability paper
• Run Charts
Elsmar.com
• Scatter diagrams
• Multi-Vari Charts
• Gantt “R&R” analysis
• Analysis of Variance (ANOVA)
• Shewhart “Control” Charts
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Measurement Systems Analysis
Slide 109, Printed 2/9/04
Shewhart Charts
• Range chart shows repeatability
• X-bar limits show discriminating power
Elsmar.com
• X-double bar shows bias
(if a known standard exists)
• Average chart shows stability
(sub-groups overtime)
• Average chart shows reproducibility
(sub-groups over technicians/instruments)
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Measurement Systems Analysis
Slide 110, Printed 2/9/04
Conclusion
• Rule of Ten
• Operating Characteristic Curve
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• Special Problems
Go/No-Go Gages
Attribute Inspection
Destructive Testing
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Measurement Systems Analysis
Slide 111, Printed 2/9/04