References

The public standards and references this topic draws on. Every factual claim in the preceding chapters traces to one of these or to the mathematics itself; the worked example's fleet, ages and fitted parameters are illustrative teaching values and belong to no source.

The mathematics in this module is standard and checkable: the distribution functions, the plotting positions, the likelihood equations and the B-life definitions are the same in every reference below. Where the sources differ is in the practical guidance, and that is where the edition matters.

Standards

1. IEC 61649:2008, Edition 2.0, Weibull analysis, published 13 August 2008 by IEC Technical Committee 56, Dependability (status current; there is no Edition 3.0). It replaced Edition 1.0 of 1997, which carried the longer title Goodness-of-fit tests, confidence intervals and lower confidence limits for Weibull distributed data. The standard requires independent and identically distributed data and defers to IEC 60300-3-5 for test conditions; it carries the two- and three-parameter forms, a normative clause on Weibayes, Fisher-matrix and rank-regression beta-binomial confidence bounds, sudden-death testing, and an annex on mixtures of failure modes.
2. IEC 60300-3-5:2001, Edition 1.0, Dependability management, Part 3-5: Application guide, Reliability test conditions and statistical test principles (the surrounding statistical framework for life testing, and the distinction between the different censoring schemes).
3. IEC 61810-2:2017, Edition 3.0, Electromechanical elementary relays, Part 2: Reliability (cited here for one reason: it applies the Weibayes approach in a normative context, which confirms that the technique is standards-body practice rather than only a practitioner convention).
4. MIL-HDBK-338B, Electronic Reliability Design Handbook, US Department of Defense (life data analysis alongside the other reliability methods, in an engineering rather than a statistical register).
5. MIL-HDBK-189C, Reliability Growth Management (relevant here for the distinction between a distribution fitted to a fixed design and a process that is changing, which is the reliability growth module).

Freely available references

6. NIST/SEMATECH e-Handbook of Statistical Methods, chapter 8, Assessing Product Reliability (the reference most practitioners actually use: distributions, censoring, plotting positions, maximum likelihood, confidence bounds, worked examples, and free).
7. R. B. Abernethy, The New Weibull Handbook (the standard practitioner text, and the origin of much of the working vocabulary, including B-life notation, Weibayes and the guidance on reading probability plots).

On the surrounding practice

8. SAE JA1011 and JA1012, the RCM criteria standard and its guide (where a fitted β decides whether an age-based task is applicable at all; see the RCM module).
9. MIL-STD-1629A, Procedures for Performing a Failure Mode, Effects and Criticality Analysis (the mode list that decides what each dataset is a fit to; see the FMECA module).

What this list does not assert. The internal content of the IEC documents is behind a paywall and is not reproduced here. The estimation mechanics on these pages, the plotting positions, the likelihood equations, the adjusted-rank treatment of suspensions and the small-sample bias correction, are standard mathematics stated so that a reader can check them, not quotations from any one standard.

On the small-sample numbers. The bias factor of 1.17 and the interval multipliers 0.74 and 1.82, quoted in the foundations and used in the worked example, are for ten complete failures. Unbiasing factors of this kind are tabulated in the practitioner literature, and the values here were generated directly rather than copied, by simulating the distribution of β̂ ⁄ β for samples of ten. That is possible because the distribution depends on the sample size alone, which is the same property the published tables rest on, so anyone can reproduce the three numbers without access to a table.

For where the ages and suspensions come from, see the FRACAS module; for what a fitted β does to a maintenance programme, the RCM module; for the constant rates this analysis replaces, the prediction references.