## VALIDATION REPORT 
**SigmaExacta Taguchi DOE Calculator & Analyzer**  
Test Date: April 2, 2026  
Location: Vigo, Galicia, Spain  
Conducted By: Quality Engineering Team  

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### 1. EXECUTIVE SUMMARY

This report documents the validation testing of the SigmaExacta Taguchi DOE tool using a standard academic dataset (L9 Orthogonal Array) to verify the accuracy of Signal‑to‑Noise (S/N) ratio calculations, Analysis of Variance (ANOVA), and optimal result predictions.

The tool was compared against the chemical engineering case study “Adhesion Strength Optimization,” referenced in standard academic literature (LibreTexts Engineering / York University).

**Verdict:** The tool demonstrated 100% accuracy in identifying critical factors and showed less than 0.01% deviation in arithmetic calculations compared to the theoretical reference.

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### 2. OBJECTIVE

The objective of this validation was to:

- Verify correct generation of the L9 orthogonal array (4 factors, 3 levels).
- Validate the accuracy of main‑effects mean calculations.
- Confirm the logic of “Larger is Better” S/N ratio selection.
- Evaluate the handling of saturated designs in the ANOVA table (where error degrees of freedom equal 0).
- Validate the prediction equation for the optimal result.

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### 3. TEST DATA

**Reference Source:** LibreTexts Engineering – Design of Experiments via Taguchi Methods  

**Experiment Configuration:**

- Design: L9 (9 runs)
- S/N Objective: Larger is Better (maximize adhesion)
- Factors: 4 (Temperature, Pressure, Time, Voltage)

**Input Values (Corrected):**

| Run | Temperature (A) | Pressure (B) | Time (C) | Voltage (D) | Response (Output) |
|-----|----------------|--------------|----------|-------------|---------------------|
| 1   | 150            | 10           | 5        | 1           | 15.0                |
| 2   | 150            | 20           | 10       | 2           | 17.2                |
| 3   | 150            | 30           | 15       | 3           | 16.5                |
| 4   | 200            | 10           | 10       | 3           | 14.8                |
| 5   | 200            | 20           | 15       | 1           | 15.5                |
| 6   | 200            | 30           | 5        | 2           | 18.1                |
| 7   | 250            | 10           | 15       | 2           | 16.2                |
| 8   | 250            | 20           | 5        | 3           | 19.0                |
| 9   | 250            | 30           | 10       | 1           | 17.8                |

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### 4. VALIDATION RESULTS

The results calculated by SigmaExacta were compared with expected values derived from manual calculations and the reference source.

#### 4.1 Main Effects Analysis (Means)

The tool’s ability to average responses per level was verified.

**Critical Factor: Pressure**

- Level 1 (SigmaExacta): 15.333  
- Level 1 (Theoretical): 15.33  
- Level 3 (SigmaExacta): 17.467 (correctly identified as optimal)  
- Level 3 (Theoretical): 17.47  
- Deviation: < 0.01% (attributable to display rounding)

**Critical Factor: Temperature**

- Level 1 (SigmaExacta): 16.233  
- Level 1 (Theoretical): 16.23  
- Deviation: 0.00% – EXACT

#### 4.2 Analysis of Variance (ANOVA)

The test presented a specific challenge: a saturated design where error degrees of freedom (DF) are zero (DF_total = 8, DF_factors = 8).

- **Tool Behavior:** Correctly reported Error DF = 0 and SS Error = 0.000.
- **Exception Handling:** The tool displayed the warning *“ANOVA could not be fully calculated… (Saturated)”*, avoiding erroneous calculation of infinite F‑values.
- **Sum of Squares (SS) – Pressure:**  
  Calculated: 8.216  
  Expected: ≈8.21  
  Status: VALIDATED

#### 4.3 Prediction and Optimal Levels

**Optimal Configuration Detected:**

- Temperature: 250 (Level 3)
- Pressure: 30 (Level 3)
- Time: 5 (Level 1)
- Voltage: 2 (Level 2)

**Match with Reference:** 100% (Identical Match)

**Predicted Value:**

- SigmaExacta: **19.633**
- Corrected Manual Calculation:

\[
\begin{aligned}
\text{Overall Mean} &= \frac{15.0+17.2+16.5+14.8+15.5+18.1+16.2+19.0+17.8}{9} = \frac{150.1}{9} = 16.678 \\[4pt]
\text{Prediction} &= 16.678 \;+\; (17.667 - 16.678) \;+\; (17.467 - 16.678) \;+\; (17.367 - 16.678) \;+\; (17.167 - 16.678) \\
&= 16.678 + 0.989 + 0.789 + 0.689 + 0.489 = 19.634 \approx 19.63
\end{aligned}
\]

**Validation:** The predicted value (19.63) correctly exceeds the maximum observed value (19.0), consistent with Taguchi theory.

> **Correction note:** In the original version of this report, 16.93 was mistakenly used as the overall mean. The correct value is 16.678, and the resulting prediction is 19.63, which exactly matches SigmaExacta’s output (19.633 after internal rounding).

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### 5. VISUALIZATION & OUTPUT

The tool successfully generated:

- **Pareto Chart:** Correctly ranked Pressure as the most influential factor (Range 2.133), followed by Temperature.
- **Main Effects Plots:** The visualized slopes correspond exactly to the calculated numerical deltas.

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### 6. CONCLUSIONS

The SigmaExacta Taguchi DOE tool has been tested and validated as **OPERATIONAL and ACCURATE**.

**Strengths Identified:**

- **Mathematical Precision:** Means and SS calculations match academic references.
- **Robustness:** Correct handling of statistical exceptions (saturated ANOVA).
- **Sensitivity:** Ability to adjust optimal recommendations based on minor input data changes (verified during data‑correction phase).

**Usage Recommendation:**  
The tool is suitable for quality engineering analysis, robust design of experiments, and industrial process optimization.

**Validation Status:** APPROVED

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