Every number in a quality system passes through a measurement before anyone looks at it. The control chart, the capability index, the PPAP dimensional report, the accept or reject decision at the end of the line — each one is a reading taken by a person or a machine with an instrument, and each one is wrong by some amount. Measurement systems analysis, MSA, is the discipline of finding out by how much, and whether that amount is small enough for the decision you are using the number to make.
It is the least glamorous of the core tools and the one most often faked. The control plan article in this series put it bluntly: a plan built on a gauge nobody has studied is a plan that produces confident numbers of unknown quality. The control plan names the gauge; the PFMEA rates the detection that gauge provides; the PPAP submits the results it produced. If the gauge cannot tell a good part from a bad one, all three documents are describing a control that does not exist.
A measurement is not a fact about the part. It is the part plus the gauge plus the person plus the method plus the day. MSA is how you find out how much of the number you are looking at is actually the part.
This is the fourth article in the Core Tools series. The worked example continues the welded pump mounting bracket from the free Control Plan Template: its formed height of 24.5 ± 0.30 mm, checked with height gauge HG-003, and its 8.20 mm special-characteristic hole, checked with a go/no-go plug gauge.
The vocabulary, in one place
Measurement error comes in two families, and confusing them is behind most bad MSA decisions.
Accuracy is about where the readings sit relative to the true value:
- Bias — the difference between the average of repeated readings and a reference value. A gauge that reads 0.003 mm high on a certified master has a bias of +0.003 mm.
- Linearity — whether that bias stays the same across the operating range, or grows at one end. A gauge can be perfect at nominal and drift at the limits, which is exactly where accept and reject decisions are made.
- Stability — whether bias and spread stay the same over time. Checked by measuring the same master at intervals and plotting the readings on a control chart.
Precision is about how much the readings scatter:
- Repeatability — the variation when the same person measures the same part with the same gauge several times. Often called equipment variation, EV, because it is mostly the instrument and its fixturing.
- Reproducibility — the variation between different people (or set-ups, or locations) measuring the same parts. Often called appraiser variation, AV.
- Gage R&R — repeatability and reproducibility combined, the total precision error of the measurement system.
And two more ideas complete the set. Resolution (or discrimination) is the smallest change the instrument can display; the common rule of thumb is that it should be no coarser than a tenth of the tolerance or the process spread, whichever is the tighter test. The number of distinct categories, ndc, is a way of expressing how many groups of genuinely different parts the measurement system can tell apart within the spread of the parts studied.
What the standards ask for
For IATF 16949 suppliers, clause 7.1.5.1.1 is explicit. In plain English: statistical studies must be carried out on every type of inspection, measurement and test equipment system named in the control plan; the analytical methods and acceptance criteria must follow the customer's reference manuals for MSA, which in practice means the AIAG MSA manual (4th edition, 2010) or, for many German-heritage customers, VDA Volume 5; other methods are allowed only with customer acceptance, and that acceptance has to be on record. Quote the wording from your licensed copy when you write a procedure or a finding.
Two words in that requirement carry a lot of weight. "Every type" means that a family of identical micrometers can be studied as a type rather than one by one — but a height gauge on a fixture and a height gauge on a granite table are not the same system. "In the control plan" means the scope of your MSA programme is defined by your control plans; a gauge named in a control plan with no study behind it is a finding waiting to happen.
ISO 9001 users have a gentler version of the same idea in clause 7.1.5: measuring resources must be suitable for the measurement being made and maintained to stay fit for purpose — and "suitable" is exactly the question MSA answers.
Start with the instrument: resolution and a type 1 study
Before involving three operators and ten parts, check the instrument itself.
HG-003 reads to 0.01 mm. The formed height tolerance is 0.60 mm (24.20 to 24.80), so the resolution is one sixtieth of the tolerance — comfortably inside the one-tenth rule.
Then a type 1 gauge study: one operator, one reference part with a known value, the same feature measured repeatedly — 50 readings is common practice, 25 a minimum — under normal conditions, lifting and replacing the part between readings. The study is not in the AIAG manual's main toolkit; it comes from European practice and VDA Volume 5, but many customers ask for it and it is the quickest way to find a gauge that is hopeless before wasting a full study on it. It produces two indices, both comparing a slice of the tolerance with the gauge's own scatter:
- Cg compares 20% of the tolerance with six standard deviations of the repeated readings.
- Cgk does the same with 10% of the tolerance, minus the bias, against three standard deviations — so it penalises a gauge that is precise but off-centre.
A common acceptance target for both is at least 1.33.
Worked example. The reference part has a certified height of 24.512 mm. Fifty readings on HG-003 average 24.515 mm with a standard deviation of 0.0058 mm (0.005803 unrounded). So the bias is +0.003 mm — statistically detectable over fifty readings, but only 0.5% of the 0.60 mm tolerance — and:
- Cg = (0.2 × 0.60) ÷ (6 × 0.005803) = 0.12 ÷ 0.0348 = 3.45
- Cgk = (0.1 × 0.60 − 0.003) ÷ (3 × 0.005803) = 0.057 ÷ 0.0174 = 3.27
Both pass easily. Hold on to that 0.0058 mm, because the next study is going to tell a different story — and the gap between the two is the most useful thing the example teaches.
The crossed Gage R&R study
The workhorse of variable MSA is the crossed study: several appraisers each measure the same set of parts several times, in random order, without seeing each other's results or their own earlier readings. The classic design is 10 parts × 3 appraisers × 3 trials = 90 readings. "Crossed" means every appraiser measures every part, which is only possible when measuring does not destroy or change the part; destructive tests need a nested design, which is beyond this article.
Three design decisions matter more than the arithmetic.
Who measures. The people who measure in production, with the production method, at the production location. A study run by the metrology technician in the lab tells you about the metrology technician.
How it is blinded. Number the parts underneath, randomise the order for every trial, and have someone else record the readings. An appraiser who remembers that part 4 read 24.62 last time will, without meaning to, read 24.62 again.
Which parts. This is the decision that quietly decides the result. The parts must represent the full range of the process variation — not ten consecutive parts from one hour. The reason becomes obvious in the numbers below.
Analysing it: ANOVA or average and range
There are two accepted ways to turn 90 readings into a verdict.
The average and range method is the older one, designed to be done by hand. It uses the average range of each appraiser's repeated readings to estimate repeatability, the spread of the appraiser averages to estimate reproducibility, and the range of the part averages to estimate part variation, each multiplied by a published constant that depends on the number of trials, appraisers or parts. For 3 trials, 3 appraisers and 10 parts the constants are 0.5908, 0.5231 and 0.3146.
The ANOVA method splits the total variation into parts, appraisers, the part-by-appraiser interaction and pure repeatability, using the mean squares of a two-way analysis of variance. It is the preferred method whenever software is available, for two reasons: it uses all the data rather than ranges, so its estimates are more efficient, and it can detect an interaction — an appraiser who measures some parts differently from others, typically because of where they place the instrument on a feature with form error. The average and range method cannot see an interaction at all; it simply hides it inside the other components. The usual convention is that if the interaction is not significant (a p-value above 0.25 is the common threshold), it is pooled back into repeatability.
The worked example: HG-003 on the formed height
Ten brackets were chosen from a week of production to span the process, from about 24.37 to 24.63 mm. Three setters each measured all ten, three times, in random order. The ANOVA, using six standard deviations as the spread of each component:
- Interaction p-value 0.40 — not significant, so pooled into repeatability.
- Repeatability (EV): standard deviation 0.0178 mm, which is 6 × 0.0178 ÷ 0.60 = 17.8% of tolerance.
- Reproducibility (AV): 0.0114 mm, 11.4% of tolerance.
- Gage R&R: √(0.0178² + 0.0114²) = 0.0211 mm, so 6 × 0.0211 = 0.127 mm, which is 21.1% of tolerance.
- Part variation (PV): 0.0858 mm. Total variation: √(0.0211² + 0.0858²) = 0.0883 mm, so %GRR against total variation is 0.0211 ÷ 0.0883 = 23.9%.
- ndc = 1.41 × 0.0858 ÷ 0.0211 = 5.7, which is 5 — ndc is always truncated to a whole number, never rounded up.
The average and range method on the same 90 readings gives an average range of 0.0293 mm and a gap of 0.0237 mm between the highest-reading and lowest-reading appraisers, leading to EV 0.0173 mm, AV 0.0120 mm, GRR 0.0211 mm and PV 0.0811 mm — 21.1% of tolerance, 25.1% of total variation, ndc 5. Close to the ANOVA here, because there was no interaction for it to miss; when there is one, the two methods can disagree by a lot more.
Reading the verdict: three bands, two denominators
The acceptance guidance in the AIAG manual is the most quoted rule in quality engineering:
- Under 10% — generally acceptable.
- 10% to 30% — may be acceptable, depending on the importance of the application, the cost of the gauge, the cost of repairs and the customer's agreement.
- Over 30% — not acceptable; improve the measurement system.
- And ndc of 5 or more for a measurement system used to control or analyse a process.
What the rule does not tell you on its face is what the percentage is a percentage of, and the answer depends on what the gauge is for.
- If the gauge is used to accept or reject parts against a specification, compare the GRR with the tolerance. The question is whether the measurement error is small relative to the window the part has to fall in.
- If the gauge is used to control the process — feeding an SPC chart, a capability study, a set-up adjustment — compare it with the process variation, either the total variation from the study (when the parts genuinely represent the process) or a known process standard deviation from long-term data. The question is whether the gauge can see the process moving.
HG-003 is used for both: the control plan line is a first-off approval and an X-bar/R chart. Against both denominators it lands in the middle band — 21.1% of tolerance, 23.9% of process variation — with ndc exactly at the minimum of 5. That is a "may be acceptable" result, and it should be recorded as a decision, with reasons, not as a pass.
The trap in part selection
Now see what happens if the study had been run the lazy way, on ten consecutive parts from one hour. Suppose those parts vary with a standard deviation of only 0.015 mm. The gauge is exactly as good as before — same GRR of 0.0211 mm — but:
- %GRR against total variation = 0.0211 ÷ √(0.0211² + 0.015²) = 81.5%
- ndc = 1.41 × 0.015 ÷ 0.0211 = 1.002, which is 1
The same gauge now "fails" catastrophically against process variation, purely because the parts studied were nearly identical, while its %tolerance is unchanged at 21.1%. Teams that meet this result often respond by buying a better gauge, when the honest fix was ten better-chosen parts. The reverse trap is as common: hand-picking parts from the extremes of the tolerance inflates the part variation and makes any gauge look excellent against total variation. Choose parts that look like the process — or use the process standard deviation from long-term data as the denominator instead.
Finding the cause: repeatability or reproducibility?
The split between EV and AV is diagnostic, and it is the part of a study most reports skip.
Repeatability larger than reproducibility points at the instrument, the fixturing, or the interaction between the gauge and the part: worn contacts, a stylus landing on a different spot each time, a part that rocks on its datums, form error on the surface being measured. Reproducibility larger than repeatability points at the people and the method: training, technique, how hard they press, where they take the reading, how they read a vernier.
HG-003 is repeatability-dominated — 17.8% against 11.4%. And here the type 1 study earns its keep. On a smooth certified master, the gauge's own scatter was 0.0058 mm. On real formed brackets it was 0.0178 mm, three times larger. The instrument is fine. The extra scatter comes from measuring a formed, slightly springy part on an open surface plate, where the height depends on exactly where along the flange the stylus lands and how the part sits. The fix is not a new height gauge; it is a simple locating nest that seats the bracket on its datums, and a defined measuring point marked on the work instruction. The 0.024 mm difference between the highest- and lowest-reading setters points at the same cause: each has a slightly different habit of where to measure. Fix the method, re-run the study, and expect both numbers to fall.
What measurement error does to your Cpk
Measurement variation does not sit beside process variation; it adds to it. What you observe is the process plus the gauge:
observed variance = process variance + measurement variance
So a measurement system eats capability. Take a process whose true standard deviation is 0.050 mm on the 0.60 mm formed-height tolerance — a true Cp of 0.60 ÷ (6 × 0.050) = 2.00. Measured with HG-003 as it stands, the observed standard deviation is √(0.050² + 0.0211²) = 0.0543 mm, and the observed Cp is 0.60 ÷ (6 × 0.0543) = 1.84. With a gauge sitting at the 30% limit — a GRR standard deviation of 0.30 × 0.60 ÷ 6 = 0.030 mm — the observed figure drops to 0.60 ÷ (6 × √(0.050² + 0.030²)) = 1.71.
In other words, a capable process can be reported as marginal purely because of the gauge, and a team can spend months trying to improve a process when the variation they are chasing lives in the measurement. Before anyone launches a capability project on a characteristic, check its MSA first. The free Cpk Calculator will give you the index from your readings; it cannot tell you how much of the spread belongs to the gauge — only the study can. Cp vs Cpk vs Ppk explains the indices themselves, and the control charts article explains why a chart fed by a gauge with ndc below 5 tends to show a staircase of repeated values and produce false out-of-control signals.
Attribute gauges: agreement, not %GRR
A go/no-go plug gauge does not produce a number, so it has no %GRR in the variable sense. Its study is an attribute agreement analysis: a set of parts with known reference decisions — deliberately including parts close to both limits, because that is where gauges and people disagree — each judged several times by several appraisers, blind and in random order. The results are expressed as the appraisers' agreement with themselves, with each other, and with the reference.
The AIAG manual's guidance for the per-appraiser measures, paraphrased: effectiveness (correct decisions as a share of all decisions) of 90% or more is acceptable and below 80% is not; miss rate (bad parts accepted) of 2% or less is acceptable and above 5% is not; false alarm rate (good parts rejected) of 5% or less is acceptable and above 10% is not; and Cohen's kappa, the agreement corrected for chance, above 0.75 indicates good agreement while below 0.40 indicates poor agreement.
Worked example — the plug gauge on the 8.20 mm hole. Fifty parts — 30 good and 20 bad by CMM reference, many of the bad ones only a few hundredths undersize or oversize — are judged three times each by three operators: 150 decisions per operator, 90 on good parts and 60 on bad. Operator C accepts 4 of the 60 bad decisions and rejects 7 of the 90 good ones:
- Effectiveness = (150 − 4 − 7) ÷ 150 = 139 ÷ 150 = 92.7% — acceptable.
- Miss rate = 4 ÷ 60 = 6.7% — unacceptable.
- False alarm rate = 7 ÷ 90 = 7.8% — marginal.
- Kappa against the reference: observed agreement 0.927; chance agreement (87/150 × 90/150) + (63/150 × 60/150) = 0.348 + 0.168 = 0.516; kappa = (0.927 − 0.516) ÷ (1 − 0.516) = 0.85 — good.
Two of the four numbers say this operator is fine. The one that matters most for a special characteristic says four undersize holes in sixty reached the next operation. That is why every measure has to be read, and why the miss rate is the one to put in front of management. On a special characteristic, the honest conclusion is usually that the attribute check should not be the primary control at all: measure the feature with a variable gauge, or error-proof it so it cannot be made wrong — the poka-yoke article covers the options.
Bias, linearity and stability — the accuracy side
Gage R&R says nothing about whether the gauge is right on average. Three smaller studies cover that.
- Bias study. Measure a reference part with a known value — ideally near the middle of the range — ten or more times; the average minus the reference is the bias, and a simple t-test tells you whether it is statistically different from zero. HG-003's +0.003 mm bias from the type 1 study is 0.5% of tolerance — negligible for this characteristic.
- Linearity study. Repeat the bias study with several reference parts spread across the operating range — five is common — and plot bias against reference value. A slope that is not flat means the gauge is accurate at one end and not the other; for a characteristic whose decisions sit near the limits, that is the end that matters.
- Stability study. Measure the same master at regular intervals — at the start of every shift, say — and plot the readings on an X-bar and R chart. A shift or a trend shows the measurement system changing over time between calibrations, and the chart doubles as your interim check between calibrations.
When to study, and when to study again
The first study belongs in the launch — it is element 8 of the PPAP — and the studies that matter most are those on gauges controlling special characteristics. After that, MSA is event-driven, like the rest of the core tools:
- A new gauge, a replacement, or a repair that could affect its performance.
- A new fixture, a new measuring method or a moved gauge.
- A change in the tolerance or the process variation — the denominator changed, so the verdict may have too.
- A stability chart that goes out of control.
- A customer complaint involving a characteristic the gauge checks — the first question in any escape investigation is whether the measurement could have seen it.
- A control plan revision that adds a characteristic or changes the evaluation method.
Seven ways MSA fails an audit
- The gauge in the control plan is not the gauge in the study. A "same type" study on a different instrument, in a different location, with a different fixture.
- The parts did not represent the process. Ten consecutive parts, or ten hand-picked extremes, so the %GRR against process variation means nothing.
- No denominator stated. A report that says "GRR 12%" without saying whether it is a percentage of tolerance or of process variation.
- Studies done by the wrong people. Lab technicians in ideal conditions instead of the operators who measure in production.
- Not blinded. Appraisers measuring parts in sequence, with their previous readings in front of them.
- Marginal results with no recorded decision. A 10–30% result filed as a pass, with no reason, no customer agreement where required and no improvement action.
- Attribute gauges with no study at all, or with a %GRR figure quoted for a go/no-go gauge that cannot produce one.
Start this week
Take one control plan for a part with a special characteristic and list the evaluation method on every line. Then pull the MSA file for each gauge on that list. For each study, check four things: is it the same gauge, in the same place, with the same fixture; were the appraisers the people who measure in production; is the denominator stated and right for how the gauge is used; and what does the split between repeatability and reproducibility say about where the error lives. Most plants find at least one gauge with no study, one study on the wrong denominator, and one marginal result nobody decided anything about.
The free MSA / Gage R&R Study Template below does the arithmetic from this article for you: an ANOVA Gage R&R for 10 parts × 3 appraisers × 3 trials with the interaction test, %tolerance, %study variation and ndc, alongside the average and range method; a type 1 gauge study; and the height gauge worked example, pre-filled. For the control plan that names the gauges, the free Control Plan Template has the bracket example line by line, and the PFMEA Toolkit is where a gauge's real capability belongs in the detection rating. The clause explorer has the full IATF requirement behind it.
Frequently asked questions
What is the difference between calibration and MSA? Calibration checks the instrument against a traceable standard at a point in time. MSA checks the whole measurement system — instrument, fixture, method, people and environment — on real parts, for the decision it is used to make. A freshly calibrated gauge can still fail a Gage R&R.
Should %GRR be calculated against the tolerance or the process variation? It depends on use. For accept or reject decisions, compare with the tolerance. For process control, SPC and capability studies, compare with the process variation. Many studies report both, and a good report says which one the decision was based on.
Is 10–30% acceptable? It may be. The AIAG guidance makes it conditional on the importance of the measurement, the cost of improving it and, where required, customer agreement. Record the decision and the reasons; do not file it as a pass.
Why must ndc be at least 5? Below 5 the gauge cannot split the parts studied into enough distinct groups to show the process moving within its spread — a control chart fed by it will show repeated values and false signals. An ndc of 1 means the gauge cannot tell the parts apart at all.
Do we need MSA if we are only certified to ISO 9001? Not by name. ISO 9001 clause 7.1.5 asks for measuring resources suitable for the purpose. A Gage R&R on the gauges behind your critical decisions is the most direct evidence that they are.
Does a type 1 study replace a Gage R&R? No. A type 1 study checks the instrument's own repeatability and bias on a reference part. A Gage R&R checks the full system on real parts with real operators — as the worked example shows, the two can differ by a factor of three.
Interpretive guidance only — not a substitute for the AIAG MSA reference manual, VDA Volume 5, IATF 16949 or ISO 9001. Work from your licensed copies, and follow your customer-specific requirements, which take precedence throughout. The worked example's numbers are illustrative. Clause numbering follows ISO 9001:2015 and IATF 16949:2016. ISO 9001:2026 was published on 16 September 2026; clause 7.1.5 carries over in the published text.