A shaft-diameter study reports total study variation of 0.0199 mm. At first glance, that might look like the process is producing widely varying shafts. But the Gage Repeatability and Reproducibility (Gage R&R) analysis attributes 0.0060 mm, or 30.1%, to the measurement system.
That is variation created not by the manufacturing process, but by the way the parts are measured.
This distinction matters. If the measurement system cannot reliably separate good parts from bad ones, teams can make costly decisions based on measurement noise: adjusting a stable process, accepting nonconforming output, or rejecting parts that meet specification. In the realm of Lean Six Sigma, validating the measurement system is a foundation for trustworthy analysis, not an optional statistical extra.
What Gage R&R measures
Gage R&R is a Measurement System Analysis (MSA) method used to estimate how much observed measurement variation comes from the measurement process itself. It separates two main sources:
- Repeatability: variation when the same operator measures the same part repeatedly using the same equipment.
- Reproducibility: variation associated with different operators measuring the same parts. Depending on the model, this may include operator-by-part interaction.
The purpose is to distinguish measurement-system variation from part-to-part variation. A measurement system that contributes too much noise makes process conclusions less dependable.
A commonly used screening guide interprets total Gage R&R as a percentage of study variation: below 10% is generally considered acceptable; 10–30% may be acceptable depending on the application; and above 30% usually signals that improvement is needed. These are guidelines, not substitutes for considering risk, tolerance, customer impact, and the intended use of the measurement. See Minitab’s guidance on measurement-system acceptability.
The 10-part × 3-operator × 3-trial study
For this shaft-diameter example, the study design uses:
- 10 representative parts spanning the range of actual process output
- 3 operators
- 3 repeated trials per operator and part
That produces 90 measurements: 10 parts × 3 operators × 3 trials. It is a crossed study because each operator measures every part.
To make those readings meaningful, randomize the measurement sequence so operators are not simply repeating the same order. Where practical, have them measure without seeing previous readings. Use the same defined measurement method and equipment, and record the part, operator, trial, and result consistently.
The parts should represent the process variation the team needs to evaluate. If they are too similar, the study may understate the system’s ability to distinguish differences across the actual process range.
What the variation results say
The following are ANOVA-based standard-deviation components for the case, not a full ANOVA table of degrees of freedom, sums of squares, F-statistics, and p-values. The raw readings would be required to generate and verify that full inferential table.
| Variation source | Standard-deviation component |
|---|---|
| Repeatability | 0.0051 mm |
| Reproducibility | 0.0032 mm |
| Part-to-part | 0.0190 mm |
| Total study variation | 0.0199 mm |
Combining the repeatability and reproducibility components gives an estimated total Gage R&R of about 0.0060 mm:
[
\text{Gage R&R} \approx \sqrt{0.0051^2 + 0.0032^2} \approx 0.0060\text{ mm}
]
Comparing that with total study variation:
[
%GRR \approx \frac{0.0060}{0.0199}\times 100 = 30.1%
]
In practical terms, roughly three-tenths of the observed variation is associated with measurement, not just the manufacturing process. The component values are rounded, so calculations based on them are approximate. Also distinguish %Study Variation, which compares standard deviations, from %Contribution, which compares variance components; they are different measures and should not be treated as interchangeable.
The ndc warning, and a number worth checking
The case reports a number of distinct categories (ndc) of 3, below the commonly used minimum guideline of 5. Ndc estimates how many statistically distinguishable groups of parts the measurement system can resolve. An ndc of 3 means the system has limited ability to distinguish meaningful differences across the measured parts.
There is an important calculation check here. Using the displayed, rounded part-to-part and Gage R&R components, the common approximation
[
ndc \approx 1.41 \times \frac{\text{part-to-part variation}}{\text{Gage R&R}}
]
gives approximately 4.5. Since software convention and unrounded variance estimates affect the reported result, verify the ndc against the raw study output rather than assuming the rounded figures reproduce it exactly. The conclusion is unchanged: whether the verified result is 3 or approximately 4, it is below 5 and calls for attention. See Minitab’s explanation of ndc.
The quality cost hidden in the reject bin
In a single day’s sample, 4.2% of conforming parts were rejected. If those decisions are based on an inadequate measurement system, some parts recorded as scrap may in fact meet the specification. Annualized for this example, the value written off against parts that were actually good is estimated at $84,000.
That figure should be treated as an estimate to investigate, not automatic proof that every rejected part was conforming. Confirm the scale of the issue through traceable records, independent remeasurement, or a suitable reference method. Then assess the annual cost using the actual volume, reject rate, part value, and the proportion of rejects confirmed to be within specification.
The wider risk is not limited to scrap. Measurement noise can also mask process shifts, prompt unnecessary adjustments, and weaken conclusions during the Analyse and Control phases of DMAIC. MSA is therefore closely connected to data integrity and the reliability of improvement decisions.
The $0 fix list: improve the method before buying a gauge
Before approving a gauge purchase, test whether basic changes can improve the current measurement method. In this example, a focused, $0 improvement list reduces %GRR to 8.9% and raises ndc to 11:
- Stabilize the part. Use an existing V-block or other suitable fixture to prevent movement and help operators position the shaft consistently.
- Standardize lighting. Improve existing task lighting so operators can see the contact point, scale, and part condition clearly.
- Write an operational definition. Specify where and how to measure, how to orient the shaft, how much measuring force to apply, and how to record results.
- Coach and verify. Have all operators apply the definition, then repeat the study using the same parts and a randomized measurement order.
The results suggest the current setup can perform much better without immediately purchasing equipment. However, the post-improvement study should be checked carefully: confirm the 90 readings, model assumptions, variation estimates, ndc, and suitability against the engineering tolerance and decision risk. If the improved system still cannot support the required decisions, a gauge change may be justified, with evidence.
Make measurement validity part of the improvement plan
A Gage R&R study does more than evaluate a tool. It tests whether the measurement process (equipment, method, environment, and people) can produce data that support sound decisions. In this shaft example, 30.1% Gage R&R, a reported ndc of 3, and an estimated $84,000 annual scrap exposure all point to a practical priority: improve and validate the method before attributing every signal to the process.
If you are building these skills, explore Lean 6 Sigma Hub’s CSSC-accredited online training, including Green Belt and Black Belt pathways. The self-paced courses use practical case studies and worked examples to build capability in data-driven improvement.
Strengthen your measurement-analysis skills: pursue Lean Six Sigma training and professional certification, and validate your data before acting on it.
Kaizen. Kai-Care. Kai-Done. Lean Six Sigma.
