To apply reliability theory and statistical inference on real industrial failure data — studying failure lifetime distributions, empirical survival functions, and hypothesis testing on machine sensor data.
This project is motivated by research on Statistical Inference for Lifetime Distributions (Kayal et al., 2019–2025), with the goal of empirically validating theoretical reliability concepts on a publicly available industrial dataset.
AI4I 2020 Predictive Maintenance Dataset — sourced from Kaggle
- 10,000 machine observations with 14 features
- Records sensor readings: Air Temperature, Process Temperature, Rotational Speed, Torque, and Tool Wear
- Labels 5 failure modes: TWF, HDF, PWF, OSF, RNF
- Binary target:
Machine failure(0 = working, 1 = failed)
| Tool | Purpose |
|---|---|
| Python | Core language |
| Pandas | Data loading and manipulation |
| NumPy | Numerical computations |
| Matplotlib & Seaborn | Visualizations |
| Scipy (stats) | Distribution fitting, KS test, T-test, Chi-square |
Predictive_Maintenance_Project.ipynb ← Main analysis notebook
datasets/
ai4i2020.csv ← Dataset (from Kaggle)
README.md ← This file
- Total machines observed: 10,000
- Total failures: 339
- Overall failure rate: 3.39% — highly imbalanced, realistic of real industry
- Mean tool wear: 107.95 min | Max tool wear: 253 min
| Failure Type | Count | % of All Failures |
|---|---|---|
| Heat Dissipation Failure (HDF) | 115 | 33.9% |
| Overstrain Failure (OSF) | 98 | 28.9% |
| Power Failure (PWF) | 95 | 28.0% |
| Tool Wear Failure (TWF) | 46 | 13.6% |
| Random Failure (RNF) | 19 | 5.6% |
HDF dominates, while RNF is extremely rare — consistent with the bathtub curve in reliability engineering, where random failures occur only during the useful life phase.
Three classical reliability distributions were fitted to the failure lifetime data (tool wear at failure):
| Distribution | KS Statistic |
|---|---|
| Exponential | 0.2087 |
| Weibull | 0.1813 ✅ Best Fit |
| Log-Normal | 0.1918 |
Best fitting distribution: Weibull (lowest KS statistic = 0.1813)
- Weibull shape parameter β = 1.95 > 1 → confirms wear-out failure behaviour
- This means failure risk increases with time — machines become more likely to fail as tool wear accumulates
- Consistent with reliability theory: β > 1 indicates the wear-out phase of the bathtub curve
R(t) = Probability that a machine survives beyond tool wear time t
| Reliability Metric | Tool Wear Time |
|---|---|
| B10 Life (10% failure point) | 195 minutes |
| Median Life (50% failure point) | 108 minutes |
| B90 Life (90% failure point) | 20 minutes |
Practical Interpretation: Maintenance should be scheduled before 195 minutes of tool wear accumulation to keep failure probability below 10%. By 108 minutes, half of all machines have failed.
Test 1 — Chi-Square: Does failure rate differ by machine type (L/M/H)?
- Chi-square statistic: 13.7517
- P-value: 0.001032
- Degrees of freedom: 2
- ✅ Result: Failure rate SIGNIFICANTLY differs by machine type (p < 0.05)
Test 2 — Independent T-Test: Is tool wear higher in failed machines?
- Mean tool wear (Failed machines): 143.78 min
- Mean tool wear (Working machines): 106.69 min
- T-statistic: 10.6029
- P-value: < 0.000001
- ✅ Result: Failed machines have significantly higher tool wear (p < 0.05)
Key findings from the correlation heatmap:
- Air Temperature ↔ Process Temperature: 0.88 — strong positive correlation (they move together)
- Rotational Speed ↔ Torque: −0.88 — strong negative correlation (higher speed = lower torque, consistent with physics)
- Torque ↔ Machine Failure: 0.19 — highest individual correlation with failure
- Tool Wear ↔ Machine Failure: 0.11 — moderate positive correlation
-
Weibull distribution best describes the failure lifetime data (KS = 0.1813), with shape parameter β = 1.95 confirming wear-out failure behaviour — failure risk increases over time.
-
B10 life = 195 minutes — maintenance should be scheduled before this threshold to keep failure probability under 10%.
-
Median machine lifetime = 108 minutes of tool wear — 50% of machines fail by this point.
-
Failure rate significantly differs by machine type (Chi-square, p = 0.001032) — machine quality variants (L/M/H) have different failure sensitivities.
-
Failed machines have statistically higher tool wear (T-test, p < 0.05) — tool wear is a significant predictor of failure, though not sufficient alone.
-
Torque shows the strongest individual correlation (0.19) with machine failure — mechanical overload is a key failure driver alongside tool wear.
This analysis empirically demonstrates:
- Lifetime distribution fitting (Weibull, Log-Normal, Exponential) using MLE + KS test
- Survival/Reliability function R(t) and its industrial interpretation (B10, B50 life)
- Statistical inference on failure data as studied theoretically in Kayal et al. (2019–2025)
- MLE estimation for Chen/Burr XII distributions on this dataset
- Progressive censoring simulation (right-censored lifetime data)
- Stress-Strength reliability modelling: P(X < Y) estimation
- Bayesian reliability estimation with prior distributions
- Hazard function h(t) estimation and plotting
Matzka, S. (2020). AI4I 2020 Predictive Maintenance Dataset. UCI Machine Learning Repository / Kaggle.
Link: https://www.kaggle.com/datasets/stephanmatzka/predictive-maintenance-dataset-ai4i-2020