Cumulative damage and times of occurrence for a multicomponent system: A discrete time approach

Raúl Fierro, Víctor Leiva, Jean Paul Maidana

Resultado de la investigación: Article

2 Citas (Scopus)

Resumen

A discrete time stochastic model for a multicomponent system is presented, which consists of two random vectors representing a multivariate cumulative damage and their corresponding failure times. The times of occurrence of some events, for the system components, are correlated and their associate cumulative damages are assumed to be additive. Since, in general, it is not possible to obtain a closed form for the distribution of these random vectors, their asymptotic distribution is studied. A central limit theorem and a large deviation principle for the multivariate cumulative damage are derived. An application to neurophysiology is presented. Parameters associated with the mean and covariance matrix of the shocks are assumed known. Otherwise, they can be estimated through well-known methods. However, the critical levels (thresholds) of resistance for the components of the system are assumed to be unknown parameters. One of the objectives of this work is to carry out asymptotic statistical inference on these parameters. To this end, the asymptotic distribution of certain Mahalanobis type distances is studied, which enables us to estimate the parameters of interest and to test hypotheses concerning their values. Numerical results complete the analysis.

Idioma originalEnglish
Páginas (desde-hasta)323-333
Número de páginas11
PublicaciónJournal of Multivariate Analysis
Volumen168
DOI
EstadoPublished - 1 nov 2018
Publicado de forma externa

Huella dactilar

Cumulative Damage
Multicomponent Systems
Discrete-time
Neurophysiology
Random Vector
Asymptotic distribution
Stochastic models
Covariance matrix
Asymptotic Inference
Large Deviation Principle
Discrete-time Model
Hypothesis Test
Failure Time
Statistical Inference
Central limit theorem
Unknown Parameters
Stochastic Model
Shock
Closed-form
Numerical Results

ASJC Scopus subject areas

  • Statistics and Probability
  • Numerical Analysis
  • Statistics, Probability and Uncertainty

Citar esto

Fierro, Raúl ; Leiva, Víctor ; Maidana, Jean Paul. / Cumulative damage and times of occurrence for a multicomponent system : A discrete time approach. En: Journal of Multivariate Analysis. 2018 ; Vol. 168. pp. 323-333.
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Cumulative damage and times of occurrence for a multicomponent system : A discrete time approach. / Fierro, Raúl; Leiva, Víctor; Maidana, Jean Paul.

En: Journal of Multivariate Analysis, Vol. 168, 01.11.2018, p. 323-333.

Resultado de la investigación: Article

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