💻 computer science

Tolerance-Dependent Inspection Disagreement Between a Fixed CMM and a Portable Articulated-Arm CMM

This study demonstrates that the average difference between fixed and portable CMMs is insufficient to assess substitution risk, proposing instead a tolerance-dependent analysis to identify specific feature-tolerance combinations where instrument choice can alter inspection pass/fail decisions.

Original authors: Md Manjurul Ahsan, Hamidreza Samadi, Shivakumar Raman

Published 2026-08-25

📖 5 min read🧠 Deep dive

CC BY 4.0

Original authors: Md Manjurul Ahsan, Hamidreza Samadi, Shivakumar Raman

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

In the world of manufacturing, a part is only as good as the measurement that proves it fits. When a factory makes a metal block or a cylinder, it must check that the dimensions fall within a specific range, known as a tolerance. If the part is too big or too small, it is rejected; if it is just right, it is accepted. To do this, shops use machines called coordinate measuring machines. Some are large, fixed units that sit in a climate-controlled room, offering extreme stability. Others are portable arms that can be wheeled right up to a massive engine or a difficult-to-move component on the factory floor. The goal of both machines is the same: to tell the truth about the part's size. But a persistent question haunts quality control: if a factory switches from the big, fixed machine to the portable one, will the decision change? Will a part that passed on the first machine suddenly fail on the second? The answer is not found in the machines' official specifications, which describe how well they perform under ideal test conditions. Instead, the answer depends on the specific part, the specific measurement, and how close that measurement sits to the edge of the allowed limit.

Researchers at the University of Oklahoma set out to solve this puzzle by looking at real data collected from both types of machines. They examined measurements of simple shapes—cylinders, cubes, and spheres—taken under two different temperature conditions, one at twenty degrees Celsius and another at thirty degrees Celsius. The team did not try to prove which machine was more accurate or which one was "correct." Instead, they asked a more practical question: at what point does the difference between the two machines become big enough to flip a pass/fail decision? They analyzed the data to find the exact range of tolerance where the two machines would disagree. If a factory sets a tolerance that falls inside this specific range, the choice of machine becomes critical. If the tolerance is wider or narrower than this range, the machines will likely agree on the verdict, even if their numbers differ slightly.

The study revealed a consistent pattern in the numbers. Across all the shapes and temperatures tested, the fixed machine consistently recorded values that were higher than the portable arm. To understand how small this is, imagine a human hair; the difference between the two machines is less than one-sixth of a single hair's width. While this gap seems tiny, it is not the whole story. The researchers found that the danger of a wrong decision depends entirely on where the part sits relative to its target size. For the six dimensional measurements they studied, there was a specific "danger zone" of tolerance widths where the two machines would give opposite labels. At the cooler temperature, this zone of disagreement spanned a range. At the warmer temperature, the zone narrowed. This means that if a factory sets a tolerance limit that falls within these narrow bands, one machine might say "pass" while the other says "fail," simply because of the inherent difference in how they measure.

The situation was even more stark for the measurements of shape, such as how round a cylinder is or how flat a surface lies. For these four form profiles, the fixed machine and the portable arm landed on opposite sides of the ten-micrometer limit in every single case. One machine recorded a value that exceeded the limit, while the other stayed below it. This resulted in a direct conflict: the fixed machine would reject the part, while the portable arm would accept it. The researchers noted that without a known, perfect reference standard to compare against, they could not say which machine was right. They could only confirm that the choice of instrument would change the outcome. This finding highlights a crucial reality: a simple average difference between two machines does not tell you if they are interchangeable. Two machines can be very close in their average readings, yet still disagree on the fate of a part if that part is measured near the edge of its tolerance.

The researchers concluded that swapping one machine for another is not a simple matter of checking a spec sheet. It requires a careful look at the specific part and its tolerance. If the tolerance is wide, the machines will likely agree. If the tolerance is extremely tight, the machines might both agree to reject the part. But if the tolerance falls into that middle ground—the disagreement interval identified in the study—the decision becomes unstable. In these cases, a factory cannot simply swap tools without first conducting a deeper study to understand the risks. They must map out the specific uncertainty of the task and ensure that the new machine will not accidentally reject good parts or accept bad ones. The study provides a clear map for manufacturers, showing exactly where the risk lies and reminding them that in the world of precision measurement, the tool you choose can be just as important as the part you are making.

Technical Summary: Tolerance-Dependent Inspection Disagreement in Coordinate Metrology

Problem Statement
In coordinate metrology, fixed Coordinate Measuring Machines (CMMs) and portable articulated-arm CMMs are often used interchangeably for inspection tasks. However, manufacturers face a critical uncertainty: does substituting one instrument for another preserve the disposition (accept/reject decision) of a part? Current standards (e.g., ISO 10360, ISO 14253-1) and instrument specifications describe performance under test conditions or provide uncertainty frameworks, but they do not directly identify the specific tolerance ranges where two different systems would assign conflicting labels to the same feature. The central problem is that the mean difference between instruments is an insufficient metric for substitution risk; the decision outcome depends on the position of the measured values relative to the nominal value and the tolerance boundary.

Methodology
The study analyzed a consolidated dataset from a broader digital-twin project involving a Brown & Sharpe fixed CMM and a FARO Quantum S articulated-arm CMM. The data included measurements of cylindrical, cubic, and spherical features under nominal condition labels of 20 °C and 30 °C.

Data Selection: From an initial set of 81 rows, the authors consolidated repeated values within geometry-characteristic groups to avoid pseudoreplication. Two surface roughness profiles were excluded due to insufficient acquisition metadata (profilometer, stylus, filter details). This left six dimensional profiles and four form profiles (cylindricity, flatness, perpendicularity, sphericity).
Analytical Approach: The authors calculated the mean of two recorded values for each system and condition. They defined a "direct arithmetic label" ( $q$ ) based on whether the absolute deviation from nominal ( $e$ ) fell within a bilateral tolerance half-width ( $t$ ).
Disagreement Interval: For each dimensional feature, the study identified the tolerance interval $D = [\min(e_C, e_A), \max(e_C, e_A))$ where the two systems would receive opposite labels (one "in," one "out"). The width of this interval ( $WD$ ) represents the range of tolerances where instrument choice alters the inspection decision.
Form Analysis: For form characteristics, the analysis compared the system means against a recorded one-sided upper limit of 10 μm to determine if they fell on opposite sides of the threshold.
Constraints: The study explicitly noted the lack of independent setup repetitions, traceable reference values, and task-specific uncertainty budgets. Consequently, the analysis was confined to the decision consequences of the recorded values rather than a verification of instrument accuracy or thermal response.

Key Results

System Separation: The fixed-CMM stream consistently yielded higher values than the articulated-arm stream. The mean difference was approximately 11.2 μm at both 20 °C (11.175 μm) and 30 °C (11.202 μm).
Form Characteristics: All four form profiles resulted in opposite direct labels for the two systems at both temperature conditions. In every case, the fixed-CMM mean exceeded the 10 μm upper limit, while the articulated-arm mean remained below it.
Dimensional Disagreement Intervals: The six dimensional features produced overlapping disagreement intervals.
- At 20 °C, the mean width of the disagreement intervals was 6.573 μm.
- At 30 °C, the mean width decreased to 4.995 μm.
- The study found that while the raw inter-system difference remained nearly constant (~11.2 μm), the width of the tolerance range causing decision disagreement narrowed. This occurred because the results straddled the nominal value, meaning part of the separation did not contribute to the disagreement range.
Aggregate Regions: The study defined specific tolerance ranges where at least one characteristic, or all six characteristics, would yield conflicting labels. For example, at 20 °C, all six dimensional characteristics would disagree if the tolerance half-width fell between 2.335 μm and 8.825 μm.

Significance and Claims
The paper claims to clarify why the average difference between instruments is not, by itself, a measure of substitution risk. The primary contribution is the proposal of a tolerance map (or disagreement interval) that identifies specific feature-tolerance combinations where instrument choice can change the recorded inspection label.

The authors assert that:

Decision Sensitivity: Substitution is only safe when it preserves the decision for the specific feature. If a part's drawing tolerance falls within the calculated disagreement interval, a controlled equivalence study and a task-specific uncertainty budget are required before substitution.
Limitations of Current Data: The results do not identify the "correct" instrument, nor do they certify interchangeability. The findings describe a small, deterministic record and cannot be generalized across different instruments, operators, parts, or facilities without further validation.
Practical Application: The methodology provides a straightforward calculation for manufacturing engineers to determine if a specific drawing tolerance is "decision-sensitive" relative to the observed system difference. If the tolerance is inside the interval, substitution is risky; if outside, the systems share the same arithmetic label, though this is not proof of equivalence.

The paper concludes that while established uncertainty and capability methods remain essential for defensible conformity decisions, this tolerance-dependent approach addresses a specific planning question: identifying where observed differences are large enough relative to assigned tolerances to justify deeper validation.

Technical Summary: Tolerance-Dependent Inspection Disagreement in Coordinate Metrology

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