🔧 Reliability Theory — Tool Wear Analysis

A structured Python notebook applying Reliability Theory to real-world predictive maintenance data.
Covers distribution fitting, MLE/UMVUE estimation, KS goodness-of-fit testing, and the four core reliability functions.

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📌 Project Overview

This project analyses the AI4I 2020 Predictive Maintenance Dataset (10,000 machine records) through the lens of Reliability Theory. The Tool wear [min] column is treated as Time-To-Failure (TTF) and used to:

• Understand its statistical distribution
• Fit and compare three lifetime models (Exponential, Lognormal, Weibull)
• Estimate the failure rate λ using MLE and UMVUE
• Compute and visualise the four pillars of reliability

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📁 Repository Structure

reliability-theory/
│
├── reliability_analysis.ipynb   ← Main analysis notebook
├── maintainance dataset_SI.xlsx ← Raw dataset
├── four_pillars.png             ← Auto-generated plot (created on first run)
├── requirements.txt             ← Python dependencies
└── README.md                    ← This file

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📊 Dataset

Field	Detail
Source	AI4I 2020 Predictive Maintenance Dataset
Records	10,000
Key column	Tool wear [min] (used as TTF)
Failure types	No Failure, Heat Dissipation, Power Failure, Overstrain, Tool Wear, Random

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🔬 Analysis Pipeline

Raw Data
   │
   ├─ 1. Load & Overview (failure type breakdown, box plots)
   │
   ├─ 2. EDA  (histogram, KDE, summary statistics)
   │
   ├─ 3. Distribution Fitting
   │       ├─ Exponential
   │       ├─ Lognormal
   │       └─ Weibull
   │
   ├─ 4. Goodness-of-Fit (KS Test)
   │       └─ p-value comparison table + bar chart
   │
   ├─ 5. MLE & UMVUE Estimation
   │       └─ Consistency check (convergence plot)
   │
   ├─ 6. Four Pillars of Reliability (2×2 subplot)
   │       ├─ PDF  — f(t)
   │       ├─ CDF  — F(t)
   │       ├─ Survival Function — S(t)
   │       └─ Hazard Function  — h(t)
   │
   └─ 7. Final Model Selection & Insights

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📐 Key Concepts

Estimators (Exponential Model)

Estimator	Formula	Property
MLE	λ̂ = n / Σt	Biased, consistent
UMVUE	λ̂ = (n−1) / Σt	Uniformly Minimum Variance Unbiased

Four Pillars

Function	Formula	Interpretation
PDF	f(t)	Probability of failing at time t
CDF	F(t)	Probability of failing by time t
Survival	S(t) = 1 − F(t)	Probability of surviving past time t
Hazard	h(t) = f(t) / S(t)	Instantaneous failure rate given survival to t

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🖼️ Sample Output

The notebook auto-generates this 2×2 plot showing all four reliability functions:

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⚙️ Setup & Usage

1. Clone the repository

git clone https://github.com/your-username/reliability-theory.git
cd reliability-theory

2. Install dependencies

pip install -r requirements.txt

3. Run the notebook

jupyter notebook reliability_analysis.ipynb

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📦 Requirements

See requirements.txt. Key libraries:

pandas
numpy
matplotlib
seaborn
scipy
openpyxl
jupyter

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📝 Results Summary

Model	KS p-value	Verdict
Exponential	—	See notebook output
Lognormal	—	See notebook output
Weibull	—	See notebook output

The best-fit model is determined automatically by highest KS p-value.

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🎓 Academic Context

This project is part of a study on Reliability Theory and Statistical Inference, demonstrating:

• Point estimation under exponential lifetime models
• Non-parametric goodness-of-fit testing
• Reliability function derivation from empirical industrial data

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📄 License

MIT License — free to use and adapt with attribution.