Statistical Analysis of Reliability Data

Crowder, Martin; Kimber, A. C.; Smith, Richard L.; Sweeting, T. J.

doi:10.1007/978-1-4899-2953-2

Cited by 317 publications

(145 citation statements)

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“…There seems to be a missing piece in the theoretical arsenal of evolutionary biologists trying to explain aging, 528 and this missing piece is about the general theory of system failures. This theory, known as the theory of reliability (Lloyd & Lipow, 1962;Barlow et al, 1965;Barlow & Proschan, 1975;Kaufmann et al, 1977;Crowder et al, 1991;Aven & Jensen, 1999;Rigdon & Basu, 2000), allows researchers to understand many puzzling features of mortality and lifespan (Gavrilov, 1978(Gavrilov, , 1987Gavrilov et al, 1978;Abernethy, 1979;D [ oubal, 1982;Gavrilov & Gavrilova, 1991Bains, 2000) not readily explainable otherwise (i.e. the Gompertz law, mortality plateaus, and the compensation law of mortality).…”

Section: Introductionmentioning

confidence: 99%

The Reliability Theory of Aging and Longevity

Gavrilov

Gavrilova

2001

Journal of Theoretical Biology

435

251

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Reliability theory is a general theory about systems failure. It allows researchers to predict the age-related failure kinetics for a system of given architecture (reliability structure) and given reliability of its components. Reliability theory predicts that even those systems that are entirely composed of non-aging elements (with a constant failure rate) will nevertheless deteriorate (fail more often) with age, if these systems are redundant in irreplaceable elements. Aging, therefore, is a direct consequence of systems redundancy. Reliability theory also predicts the late-life mortality deceleration with subsequent leveling-o!, as well as the late-life mortality plateaus, as an inevitable consequence of redundancy exhaustion at extreme old ages. The theory explains why mortality rates increase exponentially with age (the Gompertz law) in many species, by taking into account the initial -aws (defects) in newly formed systems. It also explains why organisms &&prefer'' to die according to the Gompertz law, while technical devices usually fail according to the Weibull (power) law. Theoretical conditions are speci"ed when organisms die according to the Weibull law: organisms should be relatively free of initial #aws and defects. The theory makes it possible to "nd a general failure law applicable to all adult and extreme old ages, where the Gompertz and the Weibull laws are just special cases of this more general failure law. The theory explains why relative di!erences in mortality rates of compared populations (within a given species) vanish with age, and mortality convergence is observed due to the exhaustion of initial di!erences in redundancy levels. Overall, reliability theory has an amazing predictive and explanatory power with a few, very general and realistic assumptions. Therefore, reliability theory seems to be a promising approach for developing a comprehensive theory of aging and longevity integrating mathematical methods with speci"c biological knowledge. Academic Press

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Section: Introductionmentioning

confidence: 99%

The Reliability Theory of Aging and Longevity

Gavrilov

Gavrilova

2001

Journal of Theoretical Biology

435

251

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“…The survival function of U is e −u , with unit mean and variance. Crowder et al (1991) find that the spool effect is very significant in the model and obtain an acceptable fit as far as the plot of residuals are concerned, but with a less satisfactory performance for the lowest stress level. In a recent paper, Leon et al (2007) argue that the fixed-effects model does not allow to make inference on vessels wrapped with fibre taken from a new spool.…”

Section: Introductionmentioning

confidence: 82%

“…Eleven lifetimes with the lowest level of stress are administratively censored at 41000 hours. Crowder et al (1991) present a frequentist analysis of the data and fit an AFT model with both stress and spool as fixed effects, using Weibull distributions to model survival times. Leon et al (2007) take a Bayesian parametric approach to the problem, still using Weibull survival times, however considering a mixed-effects model, where the stress and intercept parameters are a priori independent from each other and from the spool parameters, and the spool parameters are exchangeable.…”

Section: Introductionmentioning

confidence: 99%

“…2 Accelerated life models for Kevlar fibre life data Crowder et al (1991) consider 108 Kevlar fibre lifetimes, coming from the combination of eight different spools and four levels of stress (pressure), and fit an AFT model with both stress and spool as fixed effects. We can describe the model equivalently both in additive and multiplicative form:…”

Section: Introductionmentioning

confidence: 99%

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Estimation, prediction and interpretation of NGG random effects models: an application to Kevlar fibre failure times

2013

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AperTO -Archivio Istituzionale Open Access dell'Università di TorinoEstimation, prediction and interpretation of NGG random effects models: An application to Kevlar fibre failure times / Argiento, R.; Pievatolo, A.. -55(2014), pp. 805-826. Original Citation:Estimation, prediction and interpretation of NGG random effects models: An application to Kevlar fibre failure times Compared to a previous parametric Bayesian analysis, we obtain narrower credibility intervals and a better fit to the data. We also fit a similar semiparametric model, which can be seen a a special case of ours, where the error is a scale mixture of Weibull densities, mixed by a Dirichlet process, whereas the shape parameter has a parametric prior. The adequacy of the two semiparametric models is comparable, but the more general model provides a different evaluation of the posterior variance of the left tail of the lifetime distribution, which is an effect of assuming a nonparametric prior on both parameters of the Weibull density.

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“…[32] which also discusses maximum likelihood estimation of γ and δ. The power law model is often referred to as the Duane-Crow-AMSAA model in the context of reliability growth; cf.…”

Section: Estimation: One Type Of Fm; All Fms Present Initially; Each mentioning

confidence: 99%