Cosmetic Process Optimisation: Dual-Engine Multivariate Analysis (MANOVA)

An industrial data analytics project that evaluates the multi-variable quality profile of a cosmetic emulsion formulation using an interactive Excel process dashboard alongside a Python-driven Multivariate Analysis of Variance (MANOVA) statistical engine.

🧪 Project Overview

In cosmetic manufacturing, altering process parameters typically impacts multiple physical properties simultaneously. This project simulates and analyses 120 production batches of a hair cream formulation to determine how variations in formula ingredients and processing temperatures interact to affect the final product's physical vector space.

Independent Variables (Factors)

• Formula Type: Standard, Organic Polymer, Surfactant Boosted
• Mixing Temperature: Low (35°C) vs. High (60°C)

Dependent Variables (Quality Metrics)

• Viscosity (cP): Emulsion thickness (Target: 2000–3500 cP)
• pH: Skin safety and compatibility (Target: 6.0–7.0)
• Stability (Days): Product shelf life before phase separation (Target: > 10 days)

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📊 Dual-Engine Methodology

1. Excel Interactive Dashboard

• Cross-Tabulation: Built structured Pivot Tables to isolate and compute multivariate averages for every combination of formula and temperature treatment.
• Dynamic Control: Integrated interactive Slicers to allow plant operators and quality control managers to dynamically filter and inspect chemical batch traits on the fly.
• Exploratory Insights: Visually identified a stark, universal drop in product shelf life (Stability_Days) when batches were exposed to high thermal mixing configurations.

2. Python Statistical Engine (statsmodels & seaborn)

• Type I Error Protection: Utilizing a multivariate approach (MANOVA) instead of running isolated ANOVAs protected the experiment against alpha inflation ($1 - 0.95^3 \approx 14.3%$ false-positive risk).
• Data Visualization: Generated paired subplots featuring 95% Confidence Interval error bars to visually map data distribution variance and overlap metrics.
• Mathematical Validation: Executed a two-way MANOVA to mathematically prove the standalone significance of process factors and map interaction boundaries.

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📈 Key Statistical Findings

The Python MANOVA script generated the following multivariate outputs based on Wilks' Lambda ($\Lambda$):

Process Factor	Wilks' Lambda ($\Lambda$)	P-Value (Pr > F)	Industrial Significance
Formula Type	0.0896	< 0.001	🔴 Highly Significant standalone effect
Mixing Temperature	0.5768	< 0.001	🔴 Highly Significant standalone effect
Formula × Temperature	0.9498	0.4432	🟢 Non-Significant Interaction

Operational Conclusions:

1. The Interaction is Not Significant ($P = 0.443$): This mathematically confirms that temperature variations affect all three formulation matrices uniformly. There are no volatile, specific chemical interactions unique to a single pairing.
2. Thermal Degradation: Combining the non-significant interaction with the visual confidence intervals proves that high heat consistently degrades emulsion stability across the board.
3. Actionable Recommendation: To maximize shelf life without sacrificing viscosity metrics, the production line should prioritize Low-Temperature (35°C) mixing profiles, specifically utilizing the Organic Polymer baseline for optimal long-term batch stability.

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💻 Tech Stack & Libraries Used

• Spreadsheet Architecture: Microsoft Excel (Pivot Tables, Advanced Filtering, Slicers, Custom Layouts)
• Language Engine: Python 3.x
• Data Manipulation: pandas
• Statistical Modeling: statsmodels.multivariate.manova
• Data Visualization: seaborn, matplotlib

📂 Repository Structure

├── cosmetic_process_optimisation.csv    # Raw experimental dataset (120 batches)
├── cosmetics_process_optimisation.csv.xlsx               # Excel file with Pivot Tables and Slicers
├── manova_engine.py                     # Python statistical testing pipeline
├── process_optimization_plots.png       # Generated interaction bar charts
└── README.md                            # Project documentation