A measurement system that cannot produce repeatable results is worse than no measurement at all — it gives false confidence or false alarms. In deep hole drilling, where hole diameter tolerances of 0.025 mm are common, the measurement system must be capable of detecting those differences reliably. A measurement repeatability study (GR&R) determines whether the measurement system is up to the task.
Measurement System Variation
Sources of Variation
| Variation Source | Type | Description | Typical Contribution |
|---|
| Repeatability (Equipment Variation) | Random | Variation when the same operator measures the same part multiple times with the same gage | 20–50% of total GR&R |
| Reproducibility (Operator Variation) | Random | Variation when different operators measure the same part with the same gage | 10–30% of total GR&R |
| Part Variation | Expected | Actual variation between different parts | 60–80% of total observed variation |
| Gage Calibration Error | Systematic | Gage reads consistently high or low | Corrected by calibration |
| Environmental Variation | Random | Temperature, humidity, vibration | 5–15% |
| Measurement Procedure Variation | Systematic | Different techniques used by operators | 10–20% |
GR&R Components
| Component | Definition | Contribution to GR&R |
|---|
| Repeatability | Variation from repeated measurements by one operator, same part, same gage | EV — Equipment Variation |
| Reproducibility | Variation from different operators measuring same parts with same gage | AV — Appraiser Variation |
| GR&R Total | Combined repeatability and reproducibility | R&R = √(EV² + AV²) |
GR&R Study Methods
Method Comparison
| Method | Description | Number of Parts | Number of Operators | Number of Trials | Output |
|---|
| Range Method (Short) | Quick estimate — uses part ranges | 2–3 | 2 | 2–3 | Range-based %GR&R |
| Average and Range Method (Standard) | Most common — standard | 5–10 | 2–3 | 2–3 | %GR&R, ndc |
| ANOVA Method (Advanced) | Statistical — detects interactions | 5–10 | 2–3 | 2–3 | %GR&R, ndc, interaction effects |
Recommended Method for Deep Hole Drilling
| Application | Recommended Method | Why |
|---|
| Bore diameter (plug gage, air gage) | Average and Range Method | Standard — widely accepted |
| Bore diameter (CMM) | ANOVA Method | Detects operator × part interactions |
| Surface roughness | Average and Range Method | Standard |
| Hole depth measurement | Average and Range Method | Standard |
| Runout measurement | Average and Range Method | Standard |
| Quick check — new gage | Range Method | Fast — initial assessment |
Study Procedure
Preparation
| Step | Action | Detail |
|---|
| 1 | Select parts for study | 5–10 parts covering full tolerance range |
| 2 | Number parts | 1 through N — markings that operators cannot see |
| 3 | Select operators | 2–3 operators who normally perform measurements |
| 4 | Prepare data collection form | Standard GR&R form or digital data collection |
| 5 | Verify gage is calibrated | Within calibration date |
| 6 | Define measurement procedure | Written — all operators follow same procedure |
| 7 | Ensure parts are at stable temperature | Allow parts to reach room temperature |
Part Selection
| Criterion | Requirement | Why |
|---|
| Number of parts | 5–10 minimum | Provides adequate part variation |
| Part range | Cover 80% of tolerance band | Must include near-min and near-max |
| Part identification | Blind to operators | Prevents bias |
| Part condition | Production-representative | Surface finish, cleanliness |
Data Collection
| Step | Action | Detail |
|---|
| 1 | Operator A measures all parts in random order | Record results — do not share with other operators |
| 2 | Operator B measures all parts in random order | Different random order |
| 3 | Operator C (if using 3) measures all parts | Different random order |
| 4 | Repeat all trials | Same procedure — new random order each trial |
| 5 | Repeat for minimum 2–3 trials | — |
| 6 | Collect completed data form | — |
Measurement Rules During Study
| Rule | Why |
|---|
| Operators must not see each other's results | Prevents bias |
| Parts must not be identified by value | Prevents memorization |
| Gage must be zeroed per normal procedure | Represents actual use |
| Operators use normal measurement technique | Represents actual use |
| Record all results — no editing | Honest assessment |
GR&R Interpretation
Acceptance Criteria
| %GR&R | ndc (Number of Distinct Categories) | Decision |
|---|
| < 10% | ≥ 10 | Excellent — measurement system acceptable |
| 10–20% | 5–9 | Marginal — acceptable for some applications |
| 20–30% | 3–4 | Conditional — may be acceptable based on application |
| > 30% | < 3 | Unacceptable — measurement system needs improvement |
GR&R Calculation (Simplified)
| Step | Calculation | Notes |
|---|
| 1 | Calculate average range (R̄) for each operator | Average of ranges across parts |
| 2 | Calculate Repeatability (EV) | EV = R̄ × K₁ (K₁ depends on number of trials) |
| 3 | Calculate Reproducibility (AV) | AV = √[(X̄diff × K₂)² - (EV² / (nr))] |
| 4 | Calculate GR&R | GR&R = √(EV² + AV²) |
| 5 | Calculate Part Variation (PV) | PV = Rp × K₃ |
| 6 | Calculate Total Variation (TV) | TV = √(GR&R² + PV²) |
| 7 | Calculate %GR&R | %GR&R = GR&R / TV × 100 |
Common GR&R Problems
| Problem | Possible Cause | Corrective Action |
|---|
| %GR&R > 30% (high repeatability error) | Gage not sensitive enough | Use more precise gage |
| Gage not properly maintained | Calibrate or repair gage |
| Measurement technique inconsistent | Standardize procedure — train operators |
| Part fixturing not repeatable | Improve part positioning |
| High reproducibility error (operator-to-operator) | Measurement procedure not standardized | Write clear procedure — train all operators |
| Gage design requires skill to use | Consider different gage type |
| Part features difficult to access | Improve part setup |
| Low ndc (< 3) | Part range too narrow | Select parts covering wider range |
| Gage resolution insufficient | Use higher-resolution gage |
Corrective Actions
Improving Measurement System
| Action | When | Expected Improvement |
|---|
| Calibrate gage | If calibration overdue | Reduces systematic error |
| Repair or replace gage | If worn or damaged | Reduces random error |
| Standardize measurement procedure | If high operator variation | Reduces reproducibility error |
| Train operators | If technique differs | Reduces reproducibility error |
| Improve part fixturing | If positioning varies | Reduces repeatability error |
| Control environment | If temperature variation | Reduces environmental error |
| Use higher-resolution gage | If ndc < 5 | Increases discrimination |
When to Rerun the Study
| Condition | Action |
|---|
| After gage repair or replacement | Rerun full study |
| After procedure change | Rerun full study |
| After operator training | Rerun study with trained operators |
| Annually (routine) | Rerun study |
| When new part types are introduced | Rerun study for new feature |
FAQ
What is a GR&R study and why is it important for deep hole drilling?
GR&R (Gage Repeatability and Reproducibility) is a study that measures the variation in a measurement system. Repeatability is the variation when the same operator measures the same part multiple times with the same gage. Reproducibility is the variation when different operators measure the same part. In deep hole drilling, where tolerances of 0.025 mm are common, the measurement system must be 10× more precise than the tolerance. A GR&R study confirms whether the gage, operator, and procedure can reliably detect the required tolerance.
Select 5–10 parts that cover the full tolerance range (from minimum to maximum). Have 2–3 operators measure each part in random order, 2–3 times each, using the same gage and same procedure. Use a standard GR&R data collection form. Calculate the average range, repeatability, reproducibility, and %GR&R. The %GR&R should be below 20% for the measurement system to be acceptable — below 10% is excellent.
What is an acceptable GR&R percentage?
%GR&R below 10% is excellent — the measurement system is capable for any application. 10–20% is marginal — acceptable for general inspection but may not detect small changes. 20–30% is conditional — may be acceptable for wide tolerances but not for precision work. Above 30% is unacceptable — the measurement system needs improvement. The ndc (Number of Distinct Categories) should be 5 or more — ideally 10 or more. These criteria apply directly to deep hole drilling dimensional measurements.
Why did my GR&R study fail?
The most common causes: gage resolution too low for the tolerance (rule of thumb: gage must resolve 1/10 of tolerance), gage not calibrated or maintained, measurement procedure not standardized between operators (each operator uses a different technique), part fixturing inconsistent (part moves between measurements), or operators not properly trained. Identify which component (repeatability or reproducibility) is driving the high %GR&R and address that source first.
Perform a GR&R study: annually (routine schedule), whenever a new gage is introduced, after gage repair or recalibration, after measurement procedure changes, after operator training on the measurement method, or when introducing a new part that the measurement system has not been tested on. Annual studies confirm that the measurement system remains capable — measurement systems degrade over time from wear, contamination, and operator drift.
A measurement system that passes a GR&R study can be trusted to make correct accept/reject decisions. A system that fails produces scrap (good parts rejected) or escapes (bad parts accepted). Run GR&R studies annually, after any gage change, and whenever measurement problems are suspected. A capable measurement system is the foundation of quality control in deep hole drilling. This article reflects industry practice as of 2026.
