MSA 2 -- Measurement System Analysis Method 2
The MSA Method 2 (also known as Procedure 2 or Gage R&R Study) is the most comprehensive method of measurement system analysis. It evaluates the repeatability and reproducibility of a measurement system while taking into account multiple appraisers and multiple parts.
Overview
Purpose and Application
MSA 2 answers the question: What is the proportion of measurement variation in the total variation -- and where does this variation come from?
While MSA 1 only considers the repeat precision of a single appraiser on a single part, MSA 2 examines the complete measurement system consisting of:
- Measurement Equipment (Equipment Variation, EV)
- Appraiser (Appraiser Variation, AV)
- Interaction between appraiser and part (Interaction)
Experimental Designs
my8data supports two different experimental designs for MSA 2:
Crossed Design
In the crossed design, each appraiser measures each part multiple times. This is the standard design and is recommended in most cases.
| Part 1 | Part 2 | Part 3 | ... | Part n | |
|---|---|---|---|---|---|
| Appraiser A | x measurements | x measurements | x measurements | ... | x measurements |
| Appraiser B | x measurements | x measurements | x measurements | ... | x measurements |
| Appraiser C | x measurements | x measurements | x measurements | ... | x measurements |
Typical Configuration: 3 appraisers, 10 parts, 2-3 replications = 60 to 90 measurements.
Tip: The crossed design provides the most complete information, as interactions between appraiser and part can be detected.
Nested Design
In the nested design, each appraiser measures their own, different parts. The parts are therefore not measured by all appraisers.
| Parts 1-3 | Parts 4-6 | Parts 7-9 | |
|---|---|---|---|
| Appraiser A | x measurements | -- | -- |
| Appraiser B | -- | x measurements | -- |
| Appraiser C | -- | -- | x measurements |
Use cases for the nested design:
- Destructive Testing -- When the part is destroyed during measurement
- Consumptive Testing -- When the part is no longer available after measurement
- Large Parts -- When transport between appraisers is not practical
Important: With the nested design, interactions between appraiser and part cannot be calculated, since no appraiser measures the same part. The validity is therefore somewhat limited.
Typical Procedure
- Select experimental design (crossed or nested)
- Define number of appraisers, parts, and replications
- Enter tolerance limits
- Perform measurements and enter measurement values
- Start calculation
- Evaluate ANOVA results and characteristic values
Input
Configure Experimental Design
Before entering data, define the experimental parameters:
| Parameter | Description | Recommendation |
|---|---|---|
| Design Type | Crossed or Nested | Crossed, if possible |
| Number of Appraisers | How many different appraisers measure | At least 2, recommended 3 |
| Number of Parts | How many different parts are measured | At least 5, recommended 10 |
| Number of Replications | How often each appraiser measures each part | At least 2, recommended 3 |
| Upper Tolerance Limit (USL) | Upper specification limit | According to drawing/specification |
| Lower Tolerance Limit (LSL) | Lower specification limit | According to drawing/specification |
Enter Measurement Values
The input table automatically adapts to the chosen configuration:
- Columns represent the individual parts
- Rows are grouped by appraisers, with replications as sub-rows
Tip: In the crossed design, ensure that appraisers measure the parts in random order and are unaware of the measurement values of other appraisers. This is crucial for the validity of the results.
Info: You can individually name appraisers and part numbers. By default, appraisers are designated as "Appraiser A, B, C, ..." and parts as "Part 1, 2, 3, ...".
ANOVA
ANOVA (Analysis of Variance) is the statistical core procedure of MSA 2. It decomposes the total variation into its individual components.
ANOVA Table
After calculation, my8data displays the complete ANOVA table:
| Source | df | SS | MS | F-Value | p-Value |
|---|---|---|---|---|---|
| Parts | n-1 | SS_Parts | MS_Parts | F_Parts | p_Parts |
| Operators | k-1 | SS_Operators | MS_Operators | F_Operators | p_Operators |
| Interaction | (n-1)(k-1) | SS_Interaction | MS_Interaction | F_Interaction | p_Interaction |
| Repeatability | nk(r-1) | SS_Repeat | MS_Repeat | -- | -- |
| Total | nkr-1 | SS_Total | -- | -- | -- |
Legend:
- df = degrees of freedom
- SS = sum of squares
- MS = mean square
- F-Value = test statistic of the F-test
- p-Value = significance level
Interpretation of ANOVA
The ANOVA helps you answer the following questions:
Is the appraiser variability significant? If the p-value for "Operators" is less than 0.05, the appraisers differ significantly from each other. Measures: Training, standardized work instructions.
Is there a significant interaction? If the p-value for "Interaction" is less than 0.05, certain appraisers measure certain parts systematically differently. This may indicate different measurement techniques.
Is the parts variation sufficient? The parts should show clear variation to make the study meaningful. Ideally, the parts cover at least 80 % of the tolerance.
Info: If the interaction is not significant (p > 0.25), it is automatically included in the repeatability (pooled model). This increases the accuracy of the other estimates.
Characteristic Values
The following characteristic values are derived from the ANOVA:
Variance Components
| Characteristic Value | Abbreviation | Description |
|---|---|---|
| Equipment Variation | EV | Variation due to the measurement equipment (repeatability). Portion of measurement variation attributable to the measurement equipment itself. |
| Appraiser Variation | AV | Variation due to appraisers (reproducibility). Portion of measurement variation resulting from different appraisers. |
| Gage R&R | GRR | Total measurement equipment variation (EV + AV). Combination of repeatability and reproducibility. |
| Part Variation | PV | Variation of parts. Represents the actual variation of the measured parts. |
| Total Variation | TV | Total variation (GRR + PV). |
Percentage Contributions
The characteristic values are presented as percentage contributions relative to tolerance (%Tolerance) and relative to total variation (%Contribution):
| Characteristic Value | Acceptable (green) | Marginal (yellow) | Not Acceptable (red) |
|---|---|---|---|
| %GRR (Tolerance) | <= 10 % | 10 % -- 30 % | > 30 % |
| %GRR (Contribution) | <= 1 % | 1 % -- 9 % | > 9 % |
| %EV | Small portion of GRR | -- | Dominates GRR |
| %AV | Small portion of GRR | -- | Dominates GRR |
Number of Distinct Categories (ndc)
The ndc value indicates how many distinguishable categories the measurement system can differentiate within the process variation.
| ndc | Assessment |
|---|---|
| >= 5 | The measurement system can adequately resolve the process. |
| 3 -- 4 | Limited resolution. Suitable for rough estimates. |
| < 3 | The measurement system is unsuitable. No meaningful distinctions can be made. |
Important: An ndc value less than 5 means that the measurement system is unable to reliably distinguish between good and bad parts. In this case, measures to improve the measurement system are urgently required.
Improvement Measures
Depending on whether EV or AV represents the larger portion of GRR, recommended measures differ:
| Problem Area | Possible Causes | Measures |
|---|---|---|
| EV Dominates (Equipment) | Wear, insufficient resolution, unsuitable measurement principle, environmental influences | Maintain/replace equipment, select higher resolution, stabilize environmental conditions |
| AV Dominates (Appraiser) | Different measurement techniques, insufficient training, unclear instructions | Train appraisers, standardize measurement instructions, use fixtures |
| Significant Interaction | Appraiser-dependent handling of certain part geometries | Standardize measurement technique, use fixtures |
Tip: Always consider both the percentage contributions and the ndc value. A measurement system with %GRR just above 10 % but ndc >= 5 may be acceptable if additional organizational measures are implemented.