Last week I announced maskedcauses, the R package for estimating component reliability from masked series system failures. That post covered the three likelihood models and the path to CRAN.

This post is about what happened next: the package now supports four observation types (exact, right-censored, left-censored, and interval-censored) via composable observation functors. Along the way, I wrote four vignettes, removed the md.tools dependency, and developed a verification methodology for keeping prose honest about simulation results.

Maximum likelihood estimation sounds clean on paper: write down the likelihood, take derivatives, set them to zero, solve. In practice, the “solve” step is where things get interesting. Most likelihoods don’t have closed-form solutions, so you need numerical methods, and the choice of method matters more than most textbooks let on.

This write-up covers the numerical side of MLE: the optimization algorithms, convergence issues, and computational tricks that make the difference between getting an answer and getting the right answer. The full treatment is in the PDF.

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Related work

For more on the statistical and mathematical context, see my research page and publications.