Bivariate distribution models are veritable tools for improving forest stand volume estimations.Their accuracy depends on the method of construction.To-date,most bivariate distributions in forestry have been construct...Bivariate distribution models are veritable tools for improving forest stand volume estimations.Their accuracy depends on the method of construction.To-date,most bivariate distributions in forestry have been constructed either with normal or Plackett copulas.In this study,the accuracy of the Frank copula for constructing bivariate distributions was assessed.The effectiveness of Frank and Plackett copulas were evaluated on seven distribution models using data from temperate and tropical forests.The bivariate distributions include:Burr III,Burr XII,Logit-Logistic,Log-Logistic,generalized Weibull,Weibull and Kumaraswamy.Maximum likelihood was used to fit the models to the joint distribution of diameter and height data of Pinus pinaster(184 plots),Pinus radiata(96 plots),Eucalyptus camaldulensis(85 plots)and Gmelina arborea(60 plots).Models were evaluated based on negative log-likelihood(-ΛΛ).The result show that Frank-based models were more suitable in describing the joint distribution of diameter and height than most of their Plackett-based counterparts.The bivariate Burr III distributions had the overall best performance.The Frank copula is therefore recommended for the construction of more useful bivariate distributions in forestry.展开更多
An adaptive method of residual life estimation for deteriorated products with two performance characteristics (PCs) was proposed, which was sharply different from existing work that only utilized one-dimensional degra...An adaptive method of residual life estimation for deteriorated products with two performance characteristics (PCs) was proposed, which was sharply different from existing work that only utilized one-dimensional degradation data. Once new degradation information was available, the residual life of the product being monitored could be estimated in an adaptive manner. Here, it was assumed that the degradation of each PC over time was governed by a Wiener degradation process and the dependency between them was characterized by the Frank copula function. A bivariate Wiener process model with measurement errors was used to model the degradation measurements. A two-stage method and the Markov chain Monte Carlo (MCMC) method were combined to estimate the unknown parameters in sequence. Results from a numerical example about fatigue cracks show that the proposed method is valid as the relative error is small.展开更多
Modern highly reliable products may have two or more quality characteristics(QCs) because of their complex structures and abundant functions. Relations between the QCs should be considered when assessing the reliabili...Modern highly reliable products may have two or more quality characteristics(QCs) because of their complex structures and abundant functions. Relations between the QCs should be considered when assessing the reliability of these products. This paper conducts a Bayesian analysis for a bivariate constant-stress accelerated degradation model based on the inverse Gaussian(IG) process. We assume that the product considered has two QCs and each of the QCs is governed by an IG process. The relationship between the QCs is described by a Frank copula function. We also assume that the stress on the products affects not only the parameters of the IG processes, but also the parameter of the Frank copula function. The Bayesian MCMC method is developed to calculate the maximum likelihood estimators(MLE) of the model parameters. The reliability function and the mean-time-to-failure(MTTF) are estimated through the calculation of the posterior samples. Finally, a simulation example is presented to illustrate the proposed bivariate constant-stress accelerated degradation model.展开更多
基金supported by the Government of Spain,Department of Economy,Industry and Competitiveness under the Torres Quevedo Contract PTQ-16-08445financially supported by the Gobierno del Principado de Asturias through the project entitled“Estudio del crecimiento y produccion de Pinus pinaster Ait.en Asturias”(CN-07-094)by the Ministerio de Ciencia e Innovacio through the project entitled“Influencia de los tratamientos selvicolas de claras en la produccion,estabilidad mecanica y riesgo de incendios forestales en masas de Pinus radiata D.Don y Pinus pinaster Ait.en el Noroeste de Espana”(AGL2008-02259)。
文摘Bivariate distribution models are veritable tools for improving forest stand volume estimations.Their accuracy depends on the method of construction.To-date,most bivariate distributions in forestry have been constructed either with normal or Plackett copulas.In this study,the accuracy of the Frank copula for constructing bivariate distributions was assessed.The effectiveness of Frank and Plackett copulas were evaluated on seven distribution models using data from temperate and tropical forests.The bivariate distributions include:Burr III,Burr XII,Logit-Logistic,Log-Logistic,generalized Weibull,Weibull and Kumaraswamy.Maximum likelihood was used to fit the models to the joint distribution of diameter and height data of Pinus pinaster(184 plots),Pinus radiata(96 plots),Eucalyptus camaldulensis(85 plots)and Gmelina arborea(60 plots).Models were evaluated based on negative log-likelihood(-ΛΛ).The result show that Frank-based models were more suitable in describing the joint distribution of diameter and height than most of their Plackett-based counterparts.The bivariate Burr III distributions had the overall best performance.The Frank copula is therefore recommended for the construction of more useful bivariate distributions in forestry.
基金Project(60904002)supported by the National Natural Science Foundation of China
文摘An adaptive method of residual life estimation for deteriorated products with two performance characteristics (PCs) was proposed, which was sharply different from existing work that only utilized one-dimensional degradation data. Once new degradation information was available, the residual life of the product being monitored could be estimated in an adaptive manner. Here, it was assumed that the degradation of each PC over time was governed by a Wiener degradation process and the dependency between them was characterized by the Frank copula function. A bivariate Wiener process model with measurement errors was used to model the degradation measurements. A two-stage method and the Markov chain Monte Carlo (MCMC) method were combined to estimate the unknown parameters in sequence. Results from a numerical example about fatigue cracks show that the proposed method is valid as the relative error is small.
基金the National Natural Science Foundation of China(No.11671080)the Jiangsu Provincial Key Laboratory of Networked Collective Intelligence(No.BM2017002)
文摘Modern highly reliable products may have two or more quality characteristics(QCs) because of their complex structures and abundant functions. Relations between the QCs should be considered when assessing the reliability of these products. This paper conducts a Bayesian analysis for a bivariate constant-stress accelerated degradation model based on the inverse Gaussian(IG) process. We assume that the product considered has two QCs and each of the QCs is governed by an IG process. The relationship between the QCs is described by a Frank copula function. We also assume that the stress on the products affects not only the parameters of the IG processes, but also the parameter of the Frank copula function. The Bayesian MCMC method is developed to calculate the maximum likelihood estimators(MLE) of the model parameters. The reliability function and the mean-time-to-failure(MTTF) are estimated through the calculation of the posterior samples. Finally, a simulation example is presented to illustrate the proposed bivariate constant-stress accelerated degradation model.
