Measurement uncertainty is the range of possible values that a measured quantity could reasonably be, given the limitations of the measurement process. To put it in plain language: when you measure a part’s feature—say, the diameter of a hole, the length of a slot, or the flatness of a surface—you never get the “true” value of that feature. Instead, you get a measured value, and uncertainty tells you how far that measured value might be from the true value.
Uncertainty is not a “mistake” or “error” (though errors contribute to it); it is a quantified statement of confidence in a measurement. For example, if you measure a hole’s diameter as 10.000 mm with an uncertainty of ±0.002 mm, you are stating that the true diameter is almost certainly between 9.998 mm and 10.002 mm.
A core tool for managing uncertainty is an uncertainty budget: a structured breakdown of all sources of uncertainty in a measurement process, their individual magnitudes, and how they combine to produce the total uncertainty. It is essentially a “risk assessment” for measurements, ensuring you account for every factor that could skew your results.
Measurement uncertainty directly impacts part function, assembly compatibility, and production costs—often in ways that are not obvious at first glance.
For critical features, even small deviations from the true value can cause failure. Consider a high-precision aerospace component with a hole designed to fit a 10.000 mm pin with a maximum clearance of 0.003 mm. If you measure the hole as 10.001 mm with an uncertainty of ±0.002 mm, the true diameter could be as small as 9.999 mm—too tight for the pin to fit, leading to assembly failure.
In multi-part assemblies, uncertainty propagates across all components. For example, if you are assembling a shaft into a bearing, both the shaft’s diameter and the bearing’s inner diameter have their own measurement uncertainties. If each has an uncertainty of ±0.002 mm, the combined uncertainty of their fit is larger, increasing the risk of a misfit.
Uncertainty drives two types of costs:
Measurement uncertainty is quantified by identifying all sources of variation in the measurement process, calculating their individual contributions, and combining them statistically. Below are practical shop-floor methods for measuring uncertainty, along with their accuracy limits, using Gree CNC machine specifications as context.
First, two critical specifications for CNC machines that directly impact uncertainty:
Uncertainty is typically expressed as an expanded uncertainty (U), which is the range of values that contains the true value with a high level of confidence (usually 95%, corresponding to a coverage factor k=2). Below are common methods, their typical expanded uncertainty, and how they relate to CNC machining:
Direct measurement with hand tools (calipers, micrometers)
On-machine measurement (OMM)
Coordinate Measuring Machine (CMM)
Optical measurement (laser scanners, vision systems)
All sources of uncertainty fall into two categories: random error and systematic error. Random error causes measurements to vary around the true value (e.g., a technician’s inconsistent hand pressure when using a caliper), while systematic error causes measurements to be consistently biased in one direction (e.g., a caliper that is 0.001 mm too large across all measurements).
Below are the most common sources of uncertainty in CNC machining and measurement processes:
Machine tool error
Measurement tool error
Part-related error
Environmental error
Human error
Uncertainty budgets and measurement processes have critical limitations that are often overlooked, leading to overconfidence in results:
Uncertainty budgets do not account for unforeseen errors An uncertainty budget only includes sources of error that you identify. If you forget to account for thermal expansion in a large part machined on the GA-GF4028 heavy-duty gantry machining center (4200 mm X-axis travel), your budget will underestimate the total uncertainty, leading to incorrect measurements.
Uncertainty is only valid for the conditions under which it was measured The uncertainty of an OMM process on the GA-UHD500 is calculated for a specific temperature range, part material, and feature size. If you use the same OMM process to measure a titanium part (which has a different thermal expansion coefficient) in a shop with a 5°C temperature variation, the original uncertainty value is no longer valid.
Overconfidence in machine specifications Manufacturers specify positioning accuracy and repeatability under ideal conditions (e.g., constant temperature, new tools, no load). In real-world shop conditions, these values are often worse. For example, the GA-MV856’s 0.010 mm positioning accuracy may degrade to 0.015 mm after 6 months of use due to tool wear and thermal variation.
Uncertainty does not account for process drift An uncertainty budget is a snapshot in time. Over weeks or months, a machine’s positioning accuracy may drift due to wear, leading to a gradual increase in uncertainty that is not captured in the original budget.
Confusion between accuracy and repeatability Many users assume that a machine with high repeatability (e.g., the GA-DV750’s 0.0024 mm repeatability) also has high accuracy. Repeatability only measures consistency, not correctness. A machine could consistently position 0.010 mm away from the intended position (high repeatability, low accuracy), leading to biased measurements.
| Measurement Method | Typical Expanded Uncertainty (k=2) | Effort (Low/Medium/High) | Typical Use Case |
|---|---|---|---|
| Hand Tools (Calipers/Micrometers) | ±0.002 mm to ±0.010 mm | Low | Non-critical features, in-process checks |
| On-Machine Measurement (OMM) | ±0.003 mm to ±0.020 mm | Medium | In-process inspection, medium-tolerance features |
| Coordinate Measuring Machine (CMM) | ±0.001 mm to ±0.005 mm | High | Final inspection of high-precision parts |
| Optical Measurement | ±0.002 mm to ±0.010 mm | Medium | Soft/delicate parts, high-volume inspection |
Use this checklist to apply measurement uncertainty correctly in your shop:
What is the difference between uncertainty and error? Error is the difference between a measured value and the true value of a quantity. Uncertainty is a quantified range that describes how confident you are that the true value falls within that range. Error is a specific deviation, while uncertainty is a measure of confidence in your measurement.
Can uncertainty be eliminated? No. All measurement processes have inherent limitations (e.g., machine positioning error, thermal expansion) that make it impossible to measure the true value of a feature. Uncertainty can only be reduced, not eliminated.
How do I calculate the combined uncertainty in an uncertainty budget? Combined uncertainty is calculated by taking the square root of the sum of the squares of each individual uncertainty contribution. For example, if you have two sources of uncertainty: u1 = 0.002 mm and u2 = 0.003 mm, the combined uncertainty is √(0.002² + 0.003²) ≈ 0.0036 mm.
What is a coverage factor, and why is it important? A coverage factor (k) is a multiplier used to convert combined uncertainty into expanded uncertainty. A coverage factor of k=2 means the expanded uncertainty range contains the true value with a 95% confidence level. This is important because it allows you to compare uncertainty values across different processes and make risk-based decisions.
How does machine size affect measurement uncertainty? Larger machines typically have higher positioning error and are more sensitive to thermal expansion, leading to higher measurement uncertainty. For example, the GA-GF4028 (4200 mm X-axis travel) has a positioning accuracy of 0.020 mm, which is much higher than the GA-DV750’s 0.003 mm positioning accuracy. This means measurements on larger machines will have higher uncertainty, all else being equal.
Send us your part, batch size and target port. We reply with a configuration, a binding lead window and a total-cost comparison.
Request a quote →