How to Interpret Torque Test Data: Mean, SD, CV, and What They Tell You

The Data Dilemma

You test 10 bottles and get these torque readings (N·m):

2.1, 1.9, 2.3, 2.0, 1.8, 2.2, 2.1, 1.9, 2.0, 2.4

Your spec is 2.0 ± 0.3 N·m (1.7-2.3 N·m).

**Questions:**

1. Did the batch pass or fail?

2. Is your capping machine in control?

3. Should you adjust the torque setting?

If you only look at individual readings, you'll miss the bigger picture. This guide teaches you how to interpret torque data like a statistician.

Quick Reference: The One-Minute Statistician

The 5 Key Metrics

1. Mean (Average)

Formula: Mean = (Sum of all values) / (Number of values)

Example:

• Readings: 2.1, 1.9, 2.3, 2.0, 1.8, 2.2, 2.1, 1.9, 2.0, 2.4

• Mean = (2.1+1.9+2.3+2.0+1.8+2.2+2.1+1.9+2.0+2.4) / 10 = 2.07 N·m

What it tells you:

• Is your capping machine set correctly?

• If Mean < LSL: Machine is too loose (increase torque setting)

• If Mean > USL: Machine is too tight (decrease torque setting)

• If LSL < Mean < USL: Machine is on target ✅

Action:

• Mean = 2.07 N·m, Spec = 2.0 ± 0.3 N·m → On target (no adjustment needed)

2. Range (Max - Min)

Formula: Range = Maximum value - Minimum value

Example:

• Max = 2.4 N·m, Min = 1.8 N·m

• Range = 2.4 - 1.8 = 0.6 N·m

What it tells you:

• How much variability exists in your process

• Large range = inconsistent process

Interpretation:

• Range < 20% of Mean: Good consistency

• Range = 20-40% of Mean: Moderate variability

• Range > 40% of Mean: Poor process control

Example:

• Range = 0.6 N·m, Mean = 2.07 N·m

• Range/Mean = 0.6/2.07 = 29% → Moderate variability (investigate)

3. Standard Deviation (SD)

Formula: SD = √[(Σ(x - Mean)²) / (n-1)]

What it measures: Average distance of each data point from the mean

Example calculation:

1. Calculate deviations from mean (2.07):

• 2.1 - 2.07 = 0.03

• 1.9 - 2.07 = -0.17

• 2.3 - 2.07 = 0.23

• ... (continue for all 10 values)

2. Square each deviation: 0.03² = 0.0009, (-0.17)² = 0.0289, ...

3. Sum of squared deviations = 0.241

4. SD = √(0.241/9) = 0.164 N·m

What it tells you:

• SD is the "spread" of your data

• Low SD = tight process control

• High SD = high variability

Rule of thumb:

• SD < 5% of Mean: Excellent process

• SD = 5-10% of Mean: Good process

• SD > 10% of Mean: Poor process

Example:

• SD = 0.164 N·m, Mean = 2.07 N·m

• SD/Mean = 0.164/2.07 = 7.9% → Good process

4. Coefficient of Variation (CV)

Formula: CV = (SD / Mean) × 100%

Example:

• SD = 0.164 N·m, Mean = 2.07 N·m

• CV = (0.164 / 2.07) × 100% = 7.9%

What it tells you:

• CV is the "relative variability" (normalized SD)

• CV is better than SD for comparing different products

Interpretation:

• CV < 5%: Excellent process control ✅

• CV = 5-10%: Acceptable process

• CV = 10-15%: Marginal process (investigate)

• CV > 15%: Unacceptable process (fix immediately)

Example:

• CV = 7.9% → Acceptable (but could be improved)

5. Process Capability (Cpk)

Formula: Cpk = min[(USL - Mean)/3σ, (Mean - LSL)/3σ]

Example:

• USL = 2.3 N·m, LSL = 1.7 N·m, Mean = 2.07 N·m, SD = 0.164 N·m

• Upper Cpk = (2.3 - 2.07) / (3 × 0.164) = 0.23 / 0.492 = 0.47

• Lower Cpk = (2.07 - 1.7) / (3 × 0.164) = 0.37 / 0.492 = 0.75

• Cpk = min(0.47, 0.75) = 0.47

What it tells you:

• Cpk measures how well your process fits within spec limits

• Cpk >1.33: Process is capable (defect rate <63 PPM)

• Cpk = 1.0-1.33: Marginal (defect rate 2,700-63 PPM)

• Cpk <1.0: Not capable (high defect rate)

Example:

• Cpk = 0.47 → Not capable (expect ~30% defect rate)

Action: Reduce variability (lower SD) or widen spec limits.

Real-World Example: Diagnosing Process Problems

Scenario 1: Mean is Off-Target

Data:

• Mean = 2.5 N·m, SD = 0.1 N·m, CV = 4%

• Spec = 2.0 ± 0.3 N·m (1.7-2.3 N·m)

Diagnosis:

• ✅ Low CV (4%) = good process control

• ❌ Mean (2.5 N·m) > USL (2.3 N·m) = capping machine too tight

Action:

• Decrease capping machine torque setting by 0.5 N·m

• Re-test to confirm new mean is 2.0 N·m

Scenario 2: High Variability

Data:

• Mean = 2.0 N·m, SD = 0.4 N·m, CV = 20%

• Spec = 2.0 ± 0.3 N·m (1.7-2.3 N·m)

Diagnosis:

• ✅ Mean (2.0 N·m) = on target

• ❌ High CV (20%) = poor process control

• Individual bottles range from 1.2 N·m to 2.8 N·m (many out of spec)

Root causes:

• Worn capping head (replace clutch pads)

• Inconsistent cap liner thickness (tighten incoming inspection)

• Operator technique variation (standardize training)

Action:

• Fix root cause to reduce SD from 0.4 to <0.15 N·m

• Target CV <5%

Scenario 3: Bimodal Distribution

Data:

• Readings: 1.8, 1.9, 1.8, 2.4, 2.5, 2.4, 1.9, 2.5, 1.8, 2.4

• Mean = 2.14 N·m, SD = 0.32 N·m, CV = 15%

> 💡 Lab Manager's Insight:

> "When I see a Bimodal distribution (two humps), I immediately ask: 'Does your capping machine have two heads?' almost always, the answer is yes. Head #1 is set to 1.8 N·m, and Head #2 is set to 2.4 N·m. The average looks fine, but both heads are actually wrong. You must calibrate the heads individually, not just look at the batch average."

Action:

• Identify the two sources and standardize

How to Use NLY-20A Statistics

Step 1: Collect Data

1. Test 10-30 bottles from the same batch

2. NLY-20A auto-saves each reading to a test group

3. Press "Statistics" button

Step 2: Review Auto-Calculated Metrics

NLY-20A displays:

• Mean

• SD

• CV

• Min

• Max

• Number of samples (n)

Example output:

Test Group: Batch 2024-01-19-A

n = 20

Mean = 2.05 N·m

SD = 0.12 N·m

CV = 5.9%

Min = 1.85 N·m

Max = 2.28 N·m

Step 3: Interpret Results

Check 1: Is Mean within spec?

• Spec = 2.0 ± 0.3 N·m (1.7-2.3 N·m)

• Mean = 2.05 N·m → ✅ Within spec

Check 2: Is CV acceptable?

• CV = 5.9% → ✅ Acceptable (target <5%, but 5.9% is close)

Check 3: Are Min/Max within spec?

• Min = 1.85 N·m → ✅ Above LSL (1.7 N·m)

• Max = 2.28 N·m → ✅ Below USL (2.3 N·m)

Conclusion: Batch passes. Process is in control.

Step 4: Export Data for Advanced Analysis

1. Press "Export" button on NLY-20A

2. Save to USB drive as CSV

3. Open in Excel

4. Calculate Cpk, create control charts, plot histograms

Control Charts: Monitoring Trends Over Time

What is a control chart?

• A plot of Mean torque vs. time

• Shows if your process is drifting

How to create:

1. Test 10 bottles every hour

2. Record the Mean torque

3. Plot Mean vs. time in Excel

4. Add control limits: Mean ± 3σ

Example:

Diagnosis: Upward trend (2.05 → 2.25 N·m over 4 hours)

Root cause: Capping head clutch tightening due to friction heat

Action: Adjust capping machine torque setting down by 0.2 N·m

Common Mistakes in Data Interpretation

Mistake 1: Judging by Individual Readings

Wrong: "Bottle #3 tested at 2.4 N·m (above USL), so the batch fails."

Right: "Mean = 2.05 N·m (within spec), CV = 5.9% (acceptable). One outlier doesn't fail the batch. Investigate why bottle #3 was high, but don't reject the entire batch."

Mistake 2: Ignoring Variability

Wrong: "Mean = 2.0 N·m (on target), so the process is perfect."

Right: "Mean = 2.0 N·m, but CV = 18% (too high). Many individual bottles are out of spec. Fix the variability before declaring success."

Mistake 3: Testing Too Few Samples

Wrong: "I tested 3 bottles, Mean = 2.0 N·m, so the batch is good."

Right: "3 samples is too small for reliable statistics. Test at least 10 samples to calculate meaningful SD and CV."

Conclusion

The 5 metrics you must track:

1. Mean: Is your machine on target?

2. SD: How much variability?

3. CV: Relative variability (best for comparing products)

4. Min/Max: Are outliers within spec?

5. Cpk: Is your process capable?

Target values:

• Mean: Within spec limits

• CV: <5% (excellent), <10% (acceptable)

• Cpk: >1.33 (capable)

The NLY-20A auto-calculates Mean, SD, CV, Min, Max—no manual math required. Export to Excel for Cpk and control charts.

Next steps:

1. Test your next batch with 10-20 samples

2. Review the NLY-20A statistics screen

3. Calculate Cpk and create a control chart

4. Use the data to optimize your capping machine