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MSA (Measurement System Analysis)¶
A measurement system analysis asks how much of the variation you see in your data comes from the parts and how much comes from the act of measuring them. It separates the two, and reports the measurement system's share as a set of components you can act on.
Find these tools on the ribbon at QXL Stat Tools > MSA / Gage R&R.
Start here: what did the appraisers write down?¶
Before anything else, one question splits the section in two.
A number on a measurement scale, such as 10.013 mm, sends you to the three variable studies below, which separate the variation in those numbers into its sources.
A judgement, such as pass or fail or grade B, sends you to Attribute MSA instead. Categories have no variation to separate, so that study measures agreement rather than variance.
Which variable study do you have?¶
For measured data, the next choice is not a preference. It is a question about what physically happened when the measurements were taken, and there is one right answer for a given set of data.
The choice between a crossed and a nested study is not a preference. It is a question about what physically happened when the measurements were taken, and there is only one right answer for a given set of data:
Did every operator measure the same parts, or did each operator measure parts that no other operator touched?
If the same parts went to every operator, the study is crossed. If each operator had their own parts, it is nested. The usual reason for a nested study is that measuring destroys or changes the part, so the same part cannot be handed to a second operator.
| Tool | Use it when |
|---|---|
| Crossed | every operator measured the same parts |
| Nested | each operator measured their own parts, and no part was measured by more than one operator |
| Extended | there is a factor besides part and operator, or nesting other than part within operator, or you need to set a factor as fixed, choose interactions by hand, or move a term's variation into part to part |
| Type 1 Gage Study | you have one part, one operator and one gage, and you want repeatability and bias before committing to a full study |
If you have not collected the data yet, Create MSA Template builds a worksheet laid out for the study, with the columns and instructions already in place, for a variable study or an attribute one.
The six tools¶
| Tool | What it does |
|---|---|
| Create MSA Template | Builds a blank data collection sheet for a study, sized to your number of operators, parts and replications |
| Crossed | Analyses a study in which every operator measured every part |
| Nested | Analyses a study in which parts are nested within operators |
| Extended | Analyses any study the other two cannot express, with a Model tab for declaring factors, nesting and interactions |
| Type 1 Gage Study | Analyses repeated measurements of one part on one gage, reporting repeatability, bias, Cg and Cgk |
| Attribute MSA | Analyses pass and fail or category data, reporting agreement, kappa and the two kinds of error |
Crossed, Nested and Extended are the same dialog with different parts shown, so once you know one you know all three. What changes between them is covered on each tool's own page. Type 1 and Attribute MSA are separate dialogs, because they ask different questions of different data.
Crossed and nested, side by side¶
In a crossed study every operator measures every part. Part 1 that operator A measured is the same physical part 1 that operator B measured:
Part 1 ── measured by ── Operator A, Operator B, Operator C
Part 2 ── measured by ── Operator A, Operator B, Operator C
Part 3 ── measured by ── Operator A, Operator B, Operator C
Because the same part appears under more than one operator, two operators can be compared on the same part. That is what makes two things possible that a nested study cannot offer:
- Reproducibility can be separated from part to part variation. A difference between operators measured on identical parts cannot be a difference between the parts.
- An operator by part interaction can be estimated, which is the question of whether the operators disagree more about some parts than about others.
In a nested study each operator measures their own parts, and no part is measured by more than one operator. The parts are said to be nested within the operators:
Operator A
└ Part 1, Part 2, Part 3
Operator B
└ Part 4, Part 5, Part 6
Operator C
└ Part 7, Part 8, Part 9
The part labels matter here in a way they do not in a crossed study. A part label in a nested study identifies a part only within its own operator. If the sheet happens to label all three of operator A's parts 1, 2, 3 and all three of operator B's parts 1, 2, 3, those are still six different physical parts, and the analysis treats them as six. It reports the total number of distinct nested parts, which is why that count can be larger than the number of distinct labels in the column: three labels reused by three operators are reported as nine observed parts.
The consequence is that it does not matter how you label them. A nested part label is read as a position within its own operator rather than as a name, so labelling every operator's parts 1, 2, 3 and giving all nine parts their own distinct labels describe the same study and produce the same report. You do not need to invent globally unique part numbers to run a nested study.
Because no part is shared, no operator by part interaction term exists, and no interaction chart is drawn. That is not a setting; there is nothing for the term to measure.
The two layouts can look identical on the worksheet, because both are a measurement column, a part column and an operator column. What separates them is whether a part label appears under more than one operator.
| Crossed | Nested | |
|---|---|---|
| the same part measured by several operators | yes | no |
| a part label means the same part everywhere | yes | no, only within its operator |
| operator by part interaction | can be estimated | does not exist |
| interaction chart drawn | yes | no |
| XbarR estimation method offered | yes | no |
| reason a study is usually run this way | the ordinary case | measuring destroys or changes the part |
Choosing the wrong one is not caught by an error message in every case. The same numbers analysed both ways answer different questions, so the choice has to come from how the data were collected.
What the choice changes¶
The study type is not only a label. Four things follow from it:
| Crossed | Nested | Extended | |
|---|---|---|---|
| Model tab | hidden | hidden | shown |
| Extended options | hidden | hidden | shown |
| additional factor columns | hidden | hidden | shown |
| confidence intervals | reported | reported | none reported |
| misclassification sweep charts | the two joint ones | the two joint ones | the two joint ones and probability the part is good |
| XbarR estimation method | offered | refused | refused |
The report names the study type at the top of the sheet and in the worksheet tab, so a finished report always says which of the three produced it.
What the three variable studies report¶
Whichever of Crossed, Nested and Extended you run, the report is laid out the same way, and anything your study did not produce is left out rather than shown empty. Type 1 and Attribute MSA each write their own kind of sheet, described on their own pages.
Every sheet is laid out in the same order, top to bottom:
- User Input, and the Gage Info block beside it
- Stats Advisor
- Notes, when there are any
- the Gage R&R results table, with the confidence interval table below it
- the analysis of variance table, beside them
- Probabilities of Misclassification
- the charts, with the bias and linearity tables inside that band
Anything the study did not produce is left out, and the sheet closes up rather than leaving a gap.
The full description of every table and chart is on each tool's own page, and the mathematics behind every number is under MSA Math.
The mathematics¶
| Page | What it covers |
|---|---|
| Variance Components | The model, the grouping rule, and the five aggregates every percentage is built from |
| Gage Evaluation | Every reported column, the tolerance width, and the number of distinct categories |
| Expected Mean Squares | The analysis of variance route to the components |
| Restricted Maximum Likelihood | The route used for unbalanced data |
| XbarR Method | The range based route, for crossed studies |
| Probabilities of Misclassification | What the system does to accept and reject decisions |
| Bias and Linearity | Whether the system reads correctly, not just consistently |
The mathematics of the other two tools¶
Type 1 and Attribute MSA share none of the pages above. Neither has variance components, so each carries its whole mathematics on its own Math Details page.
Other commands on the menu¶
The MSA / Gage R&R menu holds seven entries, in this order:
- Create MSA Template (Optional), described on Create MSA Template
- Crossed (REML, EMS, or XbarR), described on Crossed
- Nested (REML or EMS), described on Nested
- Extended (REML or EMS), described on Extended
- Type I MSA Gage Study (Repeatability Only), described on Type 1 Gage Study
- Attribute MSA - Crosstabulations Method, described on Attribute MSA Crosstabulations
- Attribute MSA - Analytic Method, which is from the previous version of Quantum XL and is not covered in this section
Every entry except the last has a page in this section.
Entries that used to be here and are gone. Type I MSA (Old) and Attribute MSA - Crosstabulations Method (Old) were removed once each had a v18 replacement beside it; use entries 5 and 6 above, which are those replacements. MSA Template (VBA) and the older ANOVA and XbarR entries were removed earlier. There is one template command now, entry 1, and it is the v18 one. A template sheet made by the older command in an earlier version still reads correctly, so an existing workbook is unaffected.