Statistical Inference for Exponential Series Systems with Masked Failure Data¶

This repository contains the research paper and supporting materials for closed-form statistical inference in series systems when component lifetimes follow exponential distributions and failure data is masked.

Overview¶

In reliability engineering, series systems fail when any single component fails. Often, the exact cause of failure cannot be determined with certainty, but can be narrowed to a subset of components. This partial information is known as masked failure data.

This work provides the first complete analytical treatment of maximum likelihood estimation for such systems, including:

Closed-form MLE for three-component systems with pairwise masking
Explicit Fisher information matrix for arbitrary masking patterns
Sufficient statistics characterization
Asymptotic distribution theory with confidence intervals

Key Results¶

For a system with \(m\) components where each observation identifies a candidate set of size \(w\):

The minimal sufficient statistics are the mean system lifetime \(\bar{t}\) and the candidate set frequency vector \(\mathbf{\omega}\)
The Fisher information matrix has closed-form expression depending only on \(w\), not on the specific masking pattern
For \(m=3\), \(w=2\), the MLE has explicit closed-form solution:

\[\hat{\lambda}_j = \frac{\omega_{jk} + \omega_{j\ell}}{2n\bar{t}}\]

where \(\{j,k,\ell\} = \{1,2,3\}\)

Resources¶

Paper (PDF): Download PDF - Full paper with proofs and numerical validation
Source Code: GitHub Repository - Simulation code and numerical experiments

Citation¶

If you use this work, please cite:

@article{towell2025masked,
  title={Statistical Inference for Series Systems from Masked Failure Time Data: The Exponential Case},
  author={Towell, Alexander},
  year={2025},
  note={Working paper}
}

License¶

This work is available under the MIT License.