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Parametric and nonparametric inference for the reliability of copula‐based stress‐strength models
Author(s) -
Andrade Bernardo Borba,
Nascimento Alex Rodrigues,
Rathie Pushpa Narayan
Publication year - 2020
Publication title -
quality and reliability engineering international
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 62
eISSN - 1099-1638
pISSN - 0748-8017
DOI - 10.1002/qre.2694
Subject(s) - copula (linguistics) , nonparametric statistics , parametric statistics , inference , bivariate analysis , econometrics , computer science , kernel density estimation , statistical inference , monte carlo method , robustness (evolution) , parametric model , multivariate statistics , statistics , mathematics , machine learning , artificial intelligence , estimator , biochemistry , chemistry , gene
This paper provides a general treatment of statistical inference for the reliability in copula‐based stress‐strength models. Most of the current literature is either focused on specific models that yield clean formulas or restricted to estimation and engineering aspects without addressing statistical inference. We present two general frameworks, one parametric, one nonparametric, for the estimation of the reliability. The parametric methodology is presented under the general framework of estimating equations, mostly as a combination of existing methodologies from the fields of multivariate analysis, reliability, and econometrics, with some new results. The nonparametric methodology is a novel application based on an existing bivariate kernel method combined with Monte Carlo estimation of the reliability without specification of the copula or the margins. We present results from a small simulation study designed to assess the robustness of the methods discussed in terms of model misspecification. We used geotechnical data and data from the Brazilian Household Survey to illustrate the proposed methodologies in the estimation of factors of safety and financial fragility.