Modern Semiconductors must operate reliably for years powering everything from cars to smartphones, but testing engineers can’t wait years to validate reliability. Instead, they run accelerated stress tests such as:
- HTOL (High-Temperature Operating Life)
- THB (Temperature Humidity Bias)
- TC (Temperature Cycling)
These tests simulate years of aging in weeks or months. The challenge is to extract meaningful reliability insights from limited, noisy, and often censored lifetime data.
This project demonstrates such an analysis pipeline using synthetic accelerated life test data, combining survival statistics, Weibull reliability modeling, and Arrhenius temperature acceleration.
- Generate realistic synthetic semiconductor reliability data with multiple stress conditions (HTOL, THB, TC) and censoring.
- Apply Kaplan–Meier survival analysis (with censoring).
- Perform Weibull-2P modeling per stress condition.
- Use Arrhenius acceleration modeling to relate temperature and lifetime for HTOL.
- Showcasing-quality visualizations publication-style plots and reproducible CSV summaries.
File: data/reliability_synthetic.csv
560 synthetic devices tested under multiple stress conditions.
| Column | Description |
|---|---|
Device_ID |
Unique identifier for each device |
Test_Type |
HTOL, THB, or TC |
Stress_Temperature_C |
Applied stress temperature (°C) |
Stress_Voltage_V |
Operating voltage under stress |
Failure_Time_Hours |
Time-to-failure or censoring point (hours) |
Censored |
0 = failure observed, 1 = still alive at test end |
Batch_ID |
Manufacturing lot ID (captures lot-to-lot variation) |
Note: Censoring is common in real semiconductor tests, not all parts fail within the test window. For further analysis, we could think of more features such as, Measurement_No, Parameter_Value, Test_Date and so on.
Median Survival Times
File: results/km_medians_by_group.csv
- Median device lifetimes per stress group (Test_Type × Temperature).
- Derived from Kaplan–Meier survival curves.
- Useful for quick comparison across conditions.
Weibull Fit Parameters
File: results/weibull_group_fits.csv
- Fitted Weibull-2P parameters for each group.
- β (shape): indicates failure mode (β>1 -> wear-out).
- η (scale): characteristic life (hours).
- Includes MTTF (mean time to failure) and hazard interpretation.
Arrhenius Regression Coefficients (HTOL only)
File: results/arrhenius_fit_coeffs_HTOL.csv
- Linear regression of ln(η) vs 1/T.
- Provides activation energy for temperature-driven aging.
- Used to extrapolate field lifetimes from high-temperature stress tests.
- HTOL @ 150 °C fails fastest (median ≈ 270 h).
- HTOL @ 125 °C lasts longer (median ≈ 704 h).
- THB (85 °C) and TC (-40 °C, 125 °C) show minimal degradation within test duration.
HTOL at higher temperature accelerates electromigration and oxide breakdown, while humidity bias (THB) and thermal cycling (TC) induce failures much more slowly, so survival remains high in this test window.
- HTOL shows a broad failure distribution due to combined temperature + voltage acceleration.
- TC and THB distributions are much narrower, with failures concentrated around stress thresholds.
The wider HTOL spread reflects device-to-device variability in degradation rates (e.g., electromigration onset). By contrast, TC and THB failures occur more uniformly, triggered by package cracking or moisture ingress once specific stress limits are reached.
- β > 1 : wear-out dominated failures.
- η decreases with temperature (HTOL), confirming stress acceleration.
- TC/THB have higher η (longer lifetimes).
The upward trend in β at higher HTOL stress means devices fail more progressively once wear-out mechanisms (like electromigration or oxide breakdown) start. The drop in η at 150 °C clearly reflects temperature-activated aging, may reducing lifetime. HTOL shows decreasing η with temperature, confirms acceleration. TC has higher η, consistent with its slower degradation.
- HTOL @ 125 °C, 4.5 V: η ≈ 916 h and β ≈ 2.05, here devices show wear-out failures at a moderate pace.
- HTOL @ 150 °C, 5.0 V: η ≈ 313 h and β ≈ 2.10, visibly much shorter lifetimes due to higher stress, but similar failure mode.
- When stress ↑ -> η ↓, β stable -> same failure mode.
- In both plots, points align closely with the fitted Weibull CDF, and confidence intervals are narrow, confirming stable parameter estimates.
Its evident that increasing temperature accelerates degradation (lower η), while the failure mechanism remains the same (β ~ 2). No evidence of early-life (“infant mortality”) failures is seen, may consistent with controlled semiconductor reliability testing using this sample dataset.
- Positive slope in ln(η) vs 1/T, shorter lifetimes at higher T supports Arrhenius acceleration.
- Extracted slope corresponds to realistic activation energy (~0.6–0.8 eV), typical for diffusion-driven mechanisms like electromigration or oxide wear-out.
This means our synthetic data reproduces the kind of temperature dependence expected in real semiconductor qualification. Such fits are used to extrapolate device lifetimes from accelerated stress (125–150 °C) down to normal operating conditions (e.g., 55–85 °C).
| File | Description |
|---|---|
data/reliability_synthetic.csv |
Synthetic dataset with Test_Type, Temp, Voltage, Failures, and Censoring |
results/km_medians_by_group.csv |
Median survival times by stress group |
results/weibull_group_fits.csv |
Weibull fit parameters per group |
results/arrhenius_fit_coeffs_HTOL.csv |
Arrhenius regression coefficients for HTOL |
notebooks/reliability_analysis.ipynb |
Full analysis workflow |
reliability_demo/ # Python package (data, Weibull fits, plotting, CLI)
notebooks/ # Clean showcase notebook
data/ # Synthetic dataset
results/ # Output plots + CSV summaries
requirements.txt # Dependencies
README.md # Project overview
# better to have venv & install deps
python3 -m venv venv
source venv/bin/activate # for Windows: venv\Scripts\activate
# install dependencies
pip install -r requirements.txt
# run pipeline
python -m reliability_demo.cli --seed 2025
# explore notebook
jupyter notebook notebooks/reliability_pipeline.ipynb- Here Dataset is synthetic; real semiconductor data would show mixed failure modes and noisier censoring.
- Only temperature acceleration (Arrhenius) was modeled; real devices require multi-stress models (Eyring).
- Did not include degradation parameters (e.g., leakage, ΔVth).
- Extend to multi-stress acceleration models (temperature + voltage + humidity).
- Incorporate degradation measurements alongside failure times.
- Apply Bayesian or hierarchical models for lot-to-lot variation.
- Project field lifetime estimates under normal operating conditions.
- Apply Machine Learning models training and predict.