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 test, failure times and fitted parameters are illustrative teaching values and belong to no source.

Standards and handbooks

1. MIL-HDBK-189C, Reliability Growth Management, US Department of Defense, 14 June 2011, superseding MIL-HDBK-00189A of 10 September 2009 and the original MIL-HDBK-189 of 13 February 1981. Guidance rather than requirement, and still the current revision. It is the reference for the whole activity: planning, tracking and projection as three distinct exercises, the idealised growth curve, management strategy, A-modes and B-modes, the fix effectiveness factor and growth potential, and it carries the Duane postulate and the power-law model with its estimators and the Cramér-von Mises goodness-of-fit test.
2. MIL-HDBK-781A, Handbook for Reliability Test Methods, Plans, and Environments for Engineering Development, Qualification, and Production, US Department of Defense (test-analyse-and-fix as a programme activity, the test environments, and the distinction between a growth test and a demonstration).
3. IEC 61164:2004, Edition 2.0, Reliability growth, Statistical test and estimation methods (the international treatment of the models and their estimators).
4. IEC 61014:2003, Edition 2.0, Programmes for reliability growth (growth as a management activity rather than as a statistical one, and the complement to 61164).
5. IEC 60300-3-5:2001, Edition 1.0, Dependability management, Part 3-5: Application guide, Reliability test conditions and statistical test principles (the statistical framework around any reliability test).

The models

6. J. T. Duane, Learning Curve Approach to Reliability Monitoring, 1964 (the original observation that cumulative MTBF plots as a straight line on log-log axes during a programme with active corrective action).
7. L. H. Crow, Reliability Analysis for Complex, Repairable Systems, US Army Materiel Systems Analysis Activity (the power law non-homogeneous Poisson process that put the Duane observation on a statistical footing, with maximum likelihood estimators and goodness-of-fit tests; widely called the Crow or AMSAA model, and the basis of the reliability growth analysis in most commercial tools).
8. NIST/SEMATECH e-Handbook of Statistical Methods, chapter 8, Assessing Product Reliability (freely available treatment of repairable system models, the power law process and its estimators).

Related material in this knowledgebase

9. MIL-STD-2155 and MIL-HDBK-2155, the failure reporting, analysis and corrective action lineage (a growth test is a FRACAS with a short loop; see the FRACAS module).
10. IEC 61649, Weibull analysis (the analysis to reach for once the design stops changing; see the life data module).

What this list does not assert. The internal content of the two IEC documents is behind a paywall and is not reproduced here; entries 3 and 4 are cited by edition, title and role. The relationship between cumulative and instantaneous MTBF stated in the foundations is derived on the page from the power-law model rather than quoted from a handbook, so a reader can check it in two lines instead of taking it on trust.

On the estimator results. The bias factors n⁄(n−1) and n⁄(n−2), and the chi-square bounds on β, are standard results carried in the handbooks above, and they are also short derivations rather than tabulated constants: conditional on n failures the times are order statistics of n draws with CDF (t⁄T)^β, which makes Σ ln(T⁄tᵢ) a gamma variable and everything else follows. They are stated here in that derivable form so that a reader can confirm them without a table. Three of the numbers on these pages come from simulation rather than from a source, and are labelled here so that nobody looks for them in a handbook: the Cramér-von Mises critical value of about 0.17 for eighteen failures; the powers against a step change quoted in the goodness-of-fit figure, all four computed against that same 10 per cent value; and the 75 per cent coverage of the naive MTBF interval in the worked example. Each was obtained by simulating the null or the alternative from the formulae given on the pages rather than read off a chart.

For the reporting discipline that makes a growth curve believable, see the FRACAS module; for what to do with failure times once the configuration is frozen, the life data module; for the rates a growth test eventually corrects, the prediction references.