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reliability-estimation-in-series-systems-model-selection

Model selection for reliability estimation in series systems with Weibull components: when can engineers safely use simpler models?

Started 2023 HTML

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Model Selection for Reliability Estimation in Series Systems

This repository contains the research paper, simulation code, and supplementary materials for studying model selection in series systems with Weibull-distributed component lifetimes.

Key Findings

When can reliability engineers safely use a simpler model?

  • For well-designed systems (components with similar failure characteristics), a reduced homogeneous-shape Weibull model is statistically indistinguishable from the full heterogeneous model—even with 30,000 observations
  • This means practitioners can confidently use the simpler model, which:
    • Halves the parameter count from 2m to m+1
    • Renders the system itself Weibull-distributed
    • Reduces estimator variance without sacrificing accuracy
  • However, deviations in even a single component’s shape parameter quickly provide evidence against the reduced model

Practical Guidelines

Divergence LevelCV of Shape ParametersRecommendation
Low< 10%Use reduced model confidently
Moderate10-20%Depends on sample size
High> 25%Use full heterogeneous model

Repository Structure

.
├── paper/                  # LaTeX source and figures
│   ├── paper.tex          # Main manuscript
│   ├── refs.bib           # Bibliography
│   └── image/             # Figures (PDF)
├── results/               # Simulation code and data
│   ├── 5_system_scale3/   # Scale parameter sensitivity
│   ├── 5_system_shape3/   # Shape parameter sensitivity
│   ├── lrt/               # Likelihood ratio test simulations
│   │   ├── divergence/    # Type I error and power analysis
│   │   ├── vary_m/        # Effect of system complexity
│   │   ├── vary_p/        # Effect of masking probability
│   │   └── vary_q/        # Effect of censoring level
│   └── ...
├── docs/                  # GitHub Pages site
└── CLAUDE.md              # Development guidance

Building the Paper

cd paper
pdflatex paper.tex
bibtex paper
pdflatex paper.tex
pdflatex paper.tex

Or using latexmk:

cd paper
latexmk -pdf paper.tex

Dependencies

R Packages

  • wei.series.md.c1.c2.c3 - Weibull series system with masked data
  • algebraic.mle - Maximum likelihood estimation utilities
  • tidyverse, ggplot2, parallel, boot

Python Packages

  • matplotlib, seaborn, pandas, numpy

LaTeX

Standard distribution with amsmath, amsthm, graphicx, natbib, hyperref

Citation

@article{towell2024modelselection,
  title={Model Selection for Reliability Estimation in Series Systems},
  author={Towell, Alex},
  year={2024},
  note={Preprint}
}

This paper builds on Towell (2023), which developed the likelihood model for masked and censored series system data.

License

This project is licensed under the MIT License - see the LICENSE file for details.

Author

Alex Towell lex@metafunctor.com

Discussion