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Statistical Reliability: Recommended Reading

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Recommended Reading

This list extends the Statistical Reliability series with the canonical literature of the field. Entries marked ✦ are the works I would hand someone starting out; the rest is depth.

The list is organized to mirror the series: the foundational survival-analysis canon first, then parametric models, then the specific thread the series develops (competing risks under masking), then the likelihood machinery, then software.

Foundations

The graduate-level canon. If you are going to own two books on survival analysis, these are the two.

  • The Statistical Analysis of Failure Time Data by Kalbfleisch & Prentice (2002, 2nd ed.) [book] ✦. Censoring, likelihood construction, parametric and semiparametric models, competing risks. The reference I reach for first.
  • Survival Analysis: Techniques for Censored and Truncated Data by Klein & Moeschberger (2003, 2nd ed.) [book] ✦. The applied-stats counterpoint to Kalbfleisch-Prentice. Worked examples, cleaner for self-study.
  • Regression Models and Life-Tables by Cox (1972) [paper] ✦. The proportional hazards model. JRSS B.
  • Nonparametric Estimation from Incomplete Observations by Kaplan & Meier (1958) [paper]. The product-limit estimator. Foundational for anything involving right-censored data. JASA.

Parametric Models

The series works almost entirely in parametric land: specifying distribution families for component lifetimes and estimating parameters via MLE. These are the texts that made that setting rigorous.

  • Statistical Methods for Reliability Data by Meeker, Escobar & Pascual (2022, 2nd ed.) [book] ✦. The reliability-engineering companion to Kalbfleisch-Prentice. Strong on parametric likelihood, Fisher information, large-sample theory, accelerated life testing.
  • A Statistical Distribution Function of Wide Applicability by Weibull (1951) [paper]. The original Weibull paper. Short, historically essential. J. Appl. Mech. 18.
  • Statistical Models and Methods for Lifetime Data by Lawless (2003, 2nd ed.) [book]. Encyclopedic parametric reference; covers what the other two skim.
  • Applied Life Data Analysis by Nelson (1982, Wiley reprint 2005) [book]. Older but strong on engineering applications.

Competing Risks and Masked Data

The specific thread the series develops. Classical competing risks assumes the cause of each failure is observed; the series relaxes that assumption. This section traces the prior art that treatment builds on.

  • The Analysis of Failure Times in the Presence of Competing Risks by Prentice, Kalbfleisch, Peterson, Flournoy, Farewell, Breslow (1978) [paper] ✦. Canonical framing of cause-specific hazards and the identifiability issues competing risks creates. Biometrics 34.
  • Estimating Component Reliability from Masked System Life Data by Flehinger, Reiser & Yashchin (1996; extended in 1998, 2001, 2002) [paper] ✦. A decade-long program on inference under masked component causes. Directly in the series’ lineage.
  • Bayesian Estimation of Component Reliability from Masked System Life Data by Reiser, Flehinger & Conn (1996) [paper]. The Bayesian counterpart to the frequentist program above.
  • A Nonparametric Estimation of Component Reliability from Masked System Life Test Data by Guess, Usher & Hodgson (1991) [paper]. Earlier treatment of the masked-cause problem; one of the starting points the foundation paper revisits.
  • Inference Based on the Weibull Model from Masked-Failure Data by Lin, Usher & Guess (1993) [paper]. Classical parametric (Weibull) treatment of masked series systems. Essentially the point of departure for the master’s thesis.

Likelihood Theory

The likelihood-based foundation the whole series rests on. The R-package ecosystem (algebraic.mle, likelihood.model, and friends) is a direct expression of ideas in these works.

  • In All Likelihood by Pawitan (2001) [book] ✦. The best modern text on likelihood-based inference. Pairs almost line-for-line with the semantics of likelihood.model and algebraic.mle.
  • Theory of Statistical Estimation by Fisher (1925) [paper]. Where likelihood inference was born. Worth reading for the framing alone.
  • Note on the Consistency of the Maximum Likelihood Estimate by Wald (1949) [paper]. The consistency theorem; cited in every formal treatment since.
  • Assessing the Accuracy of the Maximum Likelihood Estimator: Observed Versus Expected Fisher Information by Efron & Hinkley (1978) [paper] ✦. Essential for understanding what the MLE’s standard errors really estimate. Relevant whenever the series discusses Fisher information.
  • Asymptotic Properties of Maximum Likelihood Estimators and Likelihood Ratio Tests Under Nonstandard Conditions by Self & Liang (1987) [paper]. When regularity conditions fail, relevant for series-system likelihoods at parameter boundaries.

Software

The R ecosystem the series interoperates with, plus the packages produced by the series itself.

Prior art (use these before rolling your own)

  • survival by Therneau, CRAN [software] ✦. The R standard. Cox PH, parametric AFT, frailty, multistate. If you are going to use one package, use this one.
  • flexsurv by Jackson, CRAN [software]. Flexible parametric survival: AFT/PH, spline hazards, custom families. Major inspiration for flexhaz.
  • icenReg by Anderson-Bergman, CRAN [software]. Interval censoring done right.
  • brms / rstanarm [software]. Bayesian survival via Stan. Natural companion when component parameters warrant priors.

This ecosystem

  • algebraic.dist, GitHub [software]. Distributions as first-class algebraic objects; the base layer.
  • algebraic.mle, GitHub [software]. Algebra over MLEs: asymptotic normality, delta method, composition.
  • likelihood.model, GitHub [software]. Compose likelihood contributions from heterogeneous observations (censored, truncated, masked, …).
  • flexhaz, GitHub [software]. Dynamic failure-rate distributions built hazard-first. Substrate for serieshaz and maskedhaz.
  • serieshaz, GitHub [software]. Series-system distributions derived from DFR components.
  • maskedcauses, GitHub [software]. Closed-form MLE for masked series systems with exponential components.
  • maskedhaz, GitHub [software]. Masked-cause likelihood models for series systems with general DFR components.

How this list is opinionated

The thread: series systems with masked component causes, inferred from censored observations via maximum likelihood. Works that illuminate that thread are in. Works that branch toward counting-process theory (Andersen-Borgan-Gill-Keiding), nonparametric competing risks (Fine-Gray), or Bayesian nonparametrics are out, not because they are bad, but because they belong to a different book.

If you read three things before anything else in the series itself, read Kalbfleisch-Prentice, Meeker-Escobar-Pascual, and Pawitan’s In All Likelihood. Everything else clarifies corners of what those establish.