Two operators, one part, two values
A part is measured by two operators with the same type of gauge. One gets a value close to nominal, the other a value close to the limit. Neither has made an obvious mistake. Which value should be trusted, and does the process need adjusting?
The answer starts with seeing the measurement as a process in its own right. Gauge, fixture, method, person and environment together produce a result, and that result varies too.
What measurement system analysis looks at
An MSA describes a measurement system with a few well-defined properties:
- Bias: the difference between the average of repeated measurements and a reference value.
- Linearity: how the bias changes across the gauge’s operating range.
- Stability: how bias and spread change over time.
- Repeatability: the variation when one person measures the same part several times with the same gauge. Also called equipment variation (EV).
- Reproducibility: the variation between different people measuring the same parts with the same gauge. Also called appraiser variation (AV).
Why measurement variation matters
The variation you observe is the sum of the process variation and the measurement variation. If the two are independent, their variances add: observed variance = process variance + measurement variance.
That has three practical consequences. A process may be adjusted unnecessarily, because measurement noise looks like a change. Parts near the limits may be wrongly accepted or rejected. And capability indices such as Cp and Cpk come out lower than the process deserves, because measurement variation is counted as process spread.
For a single value, the related idea is measurement uncertainty, described in the GUM (JCGM 100:2008): an interval around the result within which the true value can reasonably be expected. Near a limit it decides whether “accepted” really means accepted.
How a Gage R&R study is done
Gage R&R, short for gauge repeatability and reproducibility, is the most common study for variable measurements. A typical design is that three operators each measure the same ten parts two or three times, in random order and without seeing their earlier results. The parts are chosen to cover the normal process variation.
The combined measurement variation is
GRR = √(EV² + AV²)
and it is compared with the total variation TV, or with the tolerance. Results are calculated either with the average and range method or with analysis of variance (ANOVA). ANOVA also shows whether there is an interaction between operator and part, for example one operator measuring some parts differently.
Worked example (illustrative values). A study gives EV = 0.006 mm and AV = 0.008 mm. Then GRR = √(0.006² + 0.008²) = √0.0001 = 0.010 mm. With a total variation TV = 0.040 mm, %GRR = 100 × 0.010 / 0.040 = 25%. The part variation is PV = √(TV² - GRR²) ≈ 0.0387 mm, and the number of distinct categories ndc = 1.41 × PV / GRR ≈ 5.5, rounded down to 5. Compared with a tolerance of 0.20 mm, 6 × GRR uses 30% of it.
What is good enough?
The AIAG MSA manual (4th edition, 2010) gives general guidelines for %GRR:
- under 10%: generally acceptable
- 10 to 30%: may be acceptable depending on the importance of the application, the cost of the gauge and the cost of improvement
- over 30%: not acceptable; the measurement system needs improving
- the number of distinct categories (ndc) should be at least 5
The example above, at 25%, would be in the grey zone.
Against the process or against the tolerance?
The same study can be expressed relative to process variation or to the tolerance. If the measurement is used to control the process, for example on a control chart, the comparison with process variation is the relevant one. If it is used to accept or reject parts, the comparison with the tolerance is relevant. Always state which one a result is based on. Customers may set stricter requirements than the general guidelines.
MSA before capability
Because measurement variation is part of the spread that process capability is calculated on, the measurement system should be known before a capability study. Otherwise you cannot tell whether a low Cpk comes from the process or from the gauge. This applies equally to manual gauges and to a coordinate measuring machine.
For go/no-go gauges, such as plug and snap gauges, attribute methods are used instead: they examine how consistently different appraisers reach the same verdict, and how well it agrees with a reference.
When to do a study, and what to do with the result
- when a new gauge, fixture or measuring method is introduced
- before a capability study
- when the customer requires it, for example for a new part approval
- after repair, or when results start to be questioned
If repeatability dominates, look at the gauge, the fixture and maintenance. If reproducibility dominates, look at the method, the instructions and training.
In short
Measure the measurement before you trust it. A Gage R&R study tells you how much of what you see is the gauge, and where to improve if it is too much.
