# Intro to Measurement System Analysis (MSA) of Continuous Data – Part 3: Linearity

#### Miner

##### Forum Moderator
Staff member
This is the third in a series of articles about MSA. The focus of this article will be on measurement linearity.

Linearity is simply measurement bias throughout the entire range of the measurement device. For this reason bias and linearity are often combined into a single study.

A good calibration system will check the calibration of a measurement device at a minimum of three locations (both extremes and the middle of the measurement range). A thorough linearity study will check at least five locations (e.g., both extremes, and at 25%, 50% and 75% of the measurement range). Standards such as used in calibration should be used instead of actual parts unless the parts can be measured with less measurement variation with a different measurement device. Each standard is measured repeatedly at least ten times. All measurements must be made randomly to minimize the appraiser recalling previous results. The results can be analyzed using statistical software such as Minitab, or with the attached file as shown.
• Calculate the bias for each individual measurement and the average bias for each reference standard (or part).
• Plot the individual and average biases on the y-axis of a scatter plot versus the values of the standards on the x-axis.
• Perform a regression analysis using the individual biases as the response and the reference values as the predictor variable.
• Plot the regression line and the 95% confidence limits for the regression line on the scatter plot.
• Plot the bias = 0 line for all reference values.
• Verify that the Bias = 0 line lies within the +/- 95% confidence limits of the regression line.
• The y – intercept and slope of the regression equation should each be approximately equal to zero. These values may be statistically evaluated if desired per the formulae in the AIAG MSA 3rd edition manual. For practical purposes the graphical analysis is sufficient. The statistical analysis is only necessary for borderline cases.
Ideally, linearity will be statistically equal to zero. However, this will not always be the case. There are several possible scenarios:
• [Constant bias – All measurements are offset by the same amount regardless of size. This is essentially a calibration issue. Calibrate the measurement device and repeat the linearity study.
• ]Non-constant, linearly increasing/decreasing bias –The bias either increases or decreases as the location within the measuring range increases. Possible causes: measurement scale is proportionally small/large (gage issue), thermal bias (thermal expansion/contraction is proportional to the size of the dimension), pressure bias (deflection under pressure is proportional to size), etc.
[Non-constant, nonlinear bias – The bias changes in a nonlinear fashion throughout the measurement range. Possible cause: measurement scale is nonlinear (gage issue, particularly with electronics), gage wear in one section of the measurement range, worn standards.

If the linearity is acceptable within the range actually used for measurement, the gage may be accepted for a specified range of measurement. This must be clearly noted on the gage and the practice documented in the appropriate quality procedures.

The next article will be:
Intro to Measurement System Analysis (MSA) of Continuous Data – Part 4: Stability

Last edited by a moderator:

#### Ron Rompen

Trusted Information Resource
Thanks for the update, Marc, and of course to Miner for posting the article in the first place.

G

#### Guest

I got a situation where the No of Parts are 5, No appraisers 3 and No of trials 3, Can I conduct MSA for this situation ? if so what are Values of Constants Like D2,D3,D4? and K1, K2, K3 for this situation as per MSA edition 3? can some one Help on this Urgently Please?

#### Miner

##### Forum Moderator
Staff member
dsvkannagi;bt514 said:
I got a situation where the No of Parts are 5, No appraisers 3 and No of trials 3, Can I conduct MSA for this situation ? if so what are Values of Constants Like D2,D3,D4? and K1, K2, K3 for this situation as per MSA edition 3? can some one Help on this Urgently Please?
Yes
K1 = 0.5908
K2 = 0.5231
K3 = 0.4030
d2 = 1.693
d3 = 0.888
D4 = 2.58

G

#### Guest

hello Miner,

I've been using MSA since 2nd Ed., in which the linearity test were far more simple... the linear regression were based on mean bias values, not on individual values (which is the case since 3rd Ed)...

in fact, my concern is about the R-sq value, which is (by consequence) derived from individual values.. the way I see it, the estimation of residuals based on individuals will be testing not only the bias variation (over op. range) itself, but also repeatability of the MS... in other words, based on individuals, this index will not be usefull to caracterize true linearity error.. by 'true linearity error' I mean the variation of the gain (slope) error over the op. range, not the slope of the mean line itself (MSA mixes these two different errors in only one).. with residuals based on means, it was possible to state if there is a true linearity error on the MS (by observing how good the mean bias values fit in a line)...

Last edited:
G

#### Guest

Hello Guys,
I was wondering if someone can help me out with my deliemma. I am trying to create an Uncertainty Budget for the optical microscope that we have in our lab. I am following the VDA German Automotive standards which make alot of refrences to AIAG MSA. I cannot figure out how to derive the linearity uncertainty. Does anybody have an suggestions? Formulas/ Explaination would help alot.
Thanks

#### Miner

##### Forum Moderator
Staff member
Hello Guys,
I was wondering if someone can help me out with my deliemma. I am trying to create an Uncertainty Budget for the optical microscope that we have in our lab. I am following the VDA German Automotive standards which make alot of refrences to AIAG MSA. I cannot figure out how to derive the linearity uncertainty. Does anybody have an suggestions? Formulas/ Explaination would help alot.
Thanks
I am not an expert in Uncertainty. I recommend that you post your question in the ISO 17025 forum, but expert responses.

#### Miner

##### Forum Moderator
Staff member
Francisco Augusto;bt556 said:
hello Miner,

I've been using MSA since 2nd Ed., in which the linearity test were far more simple... the linear regression were based on mean bias values, not on individual values (which is the case since 3rd Ed)...

in fact, my concern is about the R-sq value, which is (by consequence) derived from individual values.. the way I see it, the estimation of residuals based on individuals will be testing not only the bias variation (over op. range) itself, but also repeatability of the MS... in other words, based on individuals, this index will not be usefull to caracterize true linearity error.. by 'true linearity error' I mean the variation of the gain (slope) error over the op. range, not the slope of the mean line itself (MSA mixes these two different errors in only one).. with residuals based on means, it was possible to state if there is a true linearity error on the MS (by observing how good the mean bias values fit in a line)...

Intro to Measurement System Analysis (MSA) of Continuous Data – Part 5b: R&R Imported Legacy Blogs 14
Intro to Measurement System Analysis (MSA) of Continuous Data – Part 5a: R&R Imported Legacy Blogs 5
Intro to Measurement System Analysis (MSA) of Continuous Data – Part 4: Stability Imported Legacy Blogs 2
Intro to Measurement System Analysis (MSA) of Continuous Data – Part 2: Bias Imported Legacy Blogs 4
Intro to Measurement System Analysis (MSA) of Continuous Data – Part 1: What and Why? Imported Legacy Blogs 22
Intro to MSA of Continuous Data - Part 10: Creating gauge families Imported Legacy Blogs 10
Intro to MSA of Continuous Data - Part 9: %Tolerance for One-sided Specs Imported Legacy Blogs 3
Intro to MSA of Continuous Data – Part 8: Comparison of Two Gages Imported Legacy Blogs 3
Intro to MSA of Continuous Data – Part 7: R&R using Wheeler’s Honest Gage Study Imported Legacy Blogs 17
Intro to MSA of Continuous Data – Part 6: R&R for Non-Replicable Measurements Imported Legacy Blogs 18
T Intro & ISO 9001:2006 Question - Is ISO 9001:2006 Released? ISO 9000, ISO 9001, and ISO 9004 Quality Management Systems Standards 1
E French Intro to Quality - Introducing ISO 9001 to New Employees Book, Video, Blog and Web Site Reviews and Recommendations 1
QMS monitoring, measurement, analysis and evaluation requirement - Template ISO 9000, ISO 9001, and ISO 9004 Quality Management Systems Standards 5
Physical Part Measurement General Measurement Device and Calibration Topics 6
Measurement Uncertainty in Optical Microscopy Measurement Uncertainty (MU) 1
ISO 6508 and portable hardness measurement instruments General Measurement Device and Calibration Topics 0
How to Establish the Calibration & Measurement Capability (CMC)? ISO 17025 related Discussions 1
Measurement of residual magnetism General Measurement Device and Calibration Topics 2
Surgical angle measurement guide device with an application software Medical Device and FDA Regulations and Standards News 1
Disabling measurement data during fault conditions IEC 60601 - Medical Electrical Equipment Safety Standards Series 5
Most versatile measurement device General Measurement Device and Calibration Topics 2
Surface scratch measurement General Measurement Device and Calibration Topics 1
Drawing tolerance vs. Measurement device General Measurement Device and Calibration Topics 7
MSA on automated measurement system - Multiple Step Vision System Gage R&R (GR&R) and MSA (Measurement Systems Analysis) 3
Thermo-Hygrometer - Measurement of 10DegC @10%RH ISO 17025 related Discussions 4
GDT Flatness measurement question Inspection, Prints (Drawings), Testing, Sampling and Related Topics 10
Software Validation for Measurement Tools used in Process Validation ISO 13485:2016 - Medical Device Quality Management Systems 2
Best Measurement Systems Demos in California? General Measurement Device and Calibration Topics 1
Measurement Error - How to determine what is acceptable? Gage R&R (GR&R) and MSA (Measurement Systems Analysis) 3
Process Mapping - Inputs/Outputs/Detail Activities/Control points/Measurement? Process Maps, Process Mapping and Turtle Diagrams 4
IEC 60601-2-10 - Accuracy of Pulse Parameters - Required Measurement Uncertainty IEC 60601 - Medical Electrical Equipment Safety Standards Series 3
Program or application for standard time measurement in industry from video surveillance? Human Factors and Ergonomics in Engineering 1
Defining frequency of measurement tools callibration Calibration and Metrology Software and Hardware 3
How to “validate/qualify” a new measurement equipment? Gage R&R (GR&R) and MSA (Measurement Systems Analysis) 4
Verification and Validation of Measurement Systems Misc. Quality Assurance and Business Systems Related Topics 0
How do you add accuracies for tools with different measurement devices? General Measurement Device and Calibration Topics 1
Viable count Measurement ISO Standard Other Medical Device Related Standards 1
Gauge R&R on a torque measurement Gage R&R (GR&R) and MSA (Measurement Systems Analysis) 11
Air Quality Measurement Hardware and Software General Measurement Device and Calibration Topics 11
Dimension Measurement Tool Recommendation General Measurement Device and Calibration Topics 21
Does pitch/increment/resolution of a ruled scale apply to measurement uncertainty as line item? Measurement Uncertainty (MU) 10
Plane measurement with a 3D touch machine like a CMM. Calibration and Metrology Software and Hardware 3
Diameters measurement with 3D touch machine like a CMM Calibration and Metrology Software and Hardware 4
Uncertainty in measurement larger than tolerance Measurement Uncertainty (MU) 2
Measurement Uncertainties Budget for Thermometer Measurement Uncertainty (MU) 6
Performance Measurement ISO 9001: 2015 ISO 9000, ISO 9001, and ISO 9004 Quality Management Systems Standards 2
Monitoring performance - How do I determine performance measurement basis within my organization? Misc. Quality Assurance and Business Systems Related Topics 4
What information to put on measurement Dimensional Results APQP and PPAP 7
O Ring capability and measurement - What is the automotive 'norm' for capability studies on O Rings? General Measurement Device and Calibration Topics 3
Electrical Metrology (Source/Generation and Measurement) General Measurement Device and Calibration Topics 1