active library

expo-masked-fim

Closed-form MLE and Fisher information for exponential series systems with masked failure data. Includes theoretical results, proofs, and numerical validation.

Started 2019 TeX

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Statistical Inference for Series Systems from Masked Failure Time Data

License: MIT GitHub release

Abstract

We consider the problem of estimating component failure rates in series systems when observations consist of system failure times paired with partial information about the failed component. For the case where component lifetimes follow exponential distributions, we derive closed-form expressions for the maximum likelihood estimator, the Fisher information matrix, and establish sufficient statistics. The asymptotic sampling distribution of the estimator is characterized and confidence intervals are provided. A detailed analysis of a three-component system demonstrates the theoretical results.

Key Results

  • Theorem 5.1: Closed-form MLE for mm-component systems with masking cardinality w=m−1w = m-1
  • Proposition 4.2: Independence of failed component KK and system lifetime SS for exponential distributions
  • Explicit Fisher Information: Direct computation without numerical differentiation
  • Sufficient Statistics: Mean system lifetime and candidate set frequencies

Paper

The full paper is available at paper/main.pdf (29 pages).

Building from Source

cd paper
latexmk -pdf main.tex

Repository Structure

paper/              # LaTeX source and PDF
├── main.tex        # Paper source
├── main.pdf        # Compiled PDF
└── references.bib  # Bibliography
docs/               # Documentation site (MkDocs)
research/           # Numerical validation code (C++)
archive/            # Historical versions

Citation

If you use this work, please cite:

@article{towell2026masked,
  title={Statistical Inference for Series Systems from Masked Failure Time Data: The Exponential Case},
  author={Towell, Alexander},
  year={2026},
  url={https://github.com/queelius/expo-masked-fim}
}

Or use the CITATION.cff file for automatic citation in GitHub.

License

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

Author

Alexander Towell Southern Illinois University Edwardsville atowell@siue.edu ORCID: 0000-0001-6443-9897

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