This paper evaluates the remaining useful life (RUL) of the product when its degradation path follows the Wiener process with mixed random effects. In the discussed model, the random effects are included into drift an...
详细信息
ISBN:
(纸本)9781728171029
This paper evaluates the remaining useful life (RUL) of the product when its degradation path follows the Wiener process with mixed random effects. In the discussed model, the random effects are included into drift and diffusion parameters of Wiener process to describe the heterogeneity among different products. The expectation maximization (em) algorithm is adopted to estimate the model parameters. The exact expressions of the probability density functions (PDFs) and cumulative distribution functions (CDFs) of the lifetime and the RUL distributions of products are derived. Finally, an illustrative example is provided to show the effectiveness of the mixed random effect model. The results show that the mixed random effect model has a better performance than that of the fixed effect, random volatility and random drift models.
In degradation analysis, there exist two natural features for the degradation data. The first is the dependence of degradation rate and degradation volatility, and the other is the time-varying mean-to-variance ratio....
详细信息
In degradation analysis, there exist two natural features for the degradation data. The first is the dependence of degradation rate and degradation volatility, and the other is the time-varying mean-to-variance ratio. Ignoring them may lead to a significant bias in assessing lifetime information of materials. This paper proposes a generalized Wiener degradation model, which puts these two characteristics and unit-to-unit variation into consideration simultaneously. The proposed model includes many existing Wiener degradation models as special cases. Then, a generalized closed-form approximated residual lifetime distribution is given for the proposed model. Statistical inference for the model parameters is conducted based on the expectation maximizing (em) method, and two simple auxiliary frameworks are developed for the determination of initial values and the forms of the time-scaled functions. The developed methodologies are then illustrated and verified in a simulation study and two real data analysis.
Often in longitudinal studies, some subjects complete their follow-up visits, but others miss their visits due to various reasons. For those who miss follow-up visits, some of them might learn that the event of intere...
详细信息
Often in longitudinal studies, some subjects complete their follow-up visits, but others miss their visits due to various reasons. For those who miss follow-up visits, some of them might learn that the event of interest has already happened when they come back. In this case, not only are their event times interval-censored, but also their time-dependent measurements are incomplete. This problem was motivated by a national longitudinal survey of youth data. Maximum likelihood estimation (MLE) method based on expectation-maximization (em) algorithm is used for parameter estimation. Then missing information principle is applied to estimate the variance-covariance matrix of the MLEs. Simulation studies demonstrate that the proposed method works well in terms of bias, standard error, and power for samples of moderate size. The national longitudinal survey of youth 1997 (NLSY97) data is analyzed for illustration.
As an extension of the Birnbaum-Saunders distribution, the class of generalized crack (life-time) distributions has gained popularity in various applications including reliability theory and loss severity modeling. In...
详细信息
As an extension of the Birnbaum-Saunders distribution, the class of generalized crack (life-time) distributions has gained popularity in various applications including reliability theory and loss severity modeling. In particular for fat-tailed or heavy-tailed data sets, the generalized crack distribution family built on an appropriate base density functions, such as Student's t or generalized Gaussian densities, provides a sufficient level of flexibility to fit the empirical distribution effectively. In this paper, we introduce a further extension of the generalized crack distribution by including an additional shape parameter. We study some theoretical properties of the novel distribution family with a focus on its tail behavior. We further describe an application of the em algorithm for model estimation with application to a real catastrophic loss data.
Superimposed renewal processes arise when the events from multiple renewal processes and all labels, which allow us to identify where they have come from, are missing. In reliability engineering, individual renewal pr...
详细信息
ISBN:
(纸本)9781728171029
Superimposed renewal processes arise when the events from multiple renewal processes and all labels, which allow us to identify where they have come from, are missing. In reliability engineering, individual renewal processes are stochastic failure time models for components, and the superimposed renewal process from them is the model for the system failure times. Labels are the identity information of individual failures, such as the serial number of the failed component, or the most recent failure time. When these labels are missing, it is challenging to conduct statistical inference on renewal processes because of the loss of information on identities. Recently a likelihood-based method is proposed under the assumption that all renewal processes under a superimposed process are homogeneous. This paper discusses the argument used in the method and tries to extend it for heterogeneous cases.
Sum-Product Networks (SPNs) can be seen as deep mixture models that have demonstrated efficient and tractable inference properties. In this context, graph and parameters learning have been deeply studied but the stand...
详细信息
Sum-Product Networks (SPNs) can be seen as deep mixture models that have demonstrated efficient and tractable inference properties. In this context, graph and parameters learning have been deeply studied but the standard approaches do not apply to interval censored data. In this paper, we derive an approach for learning SPN parameters based on maximum likelihood using Expectation-Maximization (em) in the context of interval censored data. Assuming the graph structure known, our algorithm makes possible to learn Gaussian leaves parameters of SPNs with right, left or interval censored data. We show that our em algorithm for incomplete data outperforms other strategies such as the midpoint for censored intervals or dropping incomplete values.
作者：
Saadaoui, FouedKing Abdulaziz Univ
Fac Sci Dept Stat POB 80203 Jeddah 21589 Saudi Arabia Univ Monastir
Fac Sci Lab Algebre Theorie Nombres & Anal Nonlineaire Monastir 5019 Tunisia Univ Sousse
Inst Hautes Etud Commerciales Sahloul 3 Dist Sousse 4054 Tunisia
Various extrapolation methods have been applied to accelerate convergence of the em algorithm. These methods are easy to implement, since they work only with em basic iterations. In other words, auxiliary quantities, ...
详细信息
Various extrapolation methods have been applied to accelerate convergence of the em algorithm. These methods are easy to implement, since they work only with em basic iterations. In other words, auxiliary quantities, such as gradient and hessian, are not needed. In this paper, we define a new family of iterative schemes based on nonlinear extrapolation methods. It is shown that these strategies can accelerate convergence of the em algorithm much more stably than competing methods. They are extremely general in the sense that they can accelerate any linearly convergent fixed point iterative method, and hence, any em-type algorithm. A randomly relaxed version is also deduced and numerically tested. (C) 2019 Elsevier B.V. All rights reserved.
We consider the problem of determining Granger causal influences among sources that are indirectly observed through low-dimensional and noisy linear projections. Commonly used methods proceed in a two-stage fashion, b...
详细信息
ISBN:
(纸本)9781728140841
We consider the problem of determining Granger causal influences among sources that are indirectly observed through low-dimensional and noisy linear projections. Commonly used methods proceed in a two-stage fashion, by first solving an inverse problem to localize the sources, and then inferring the Granger causal influences from the estimated sources. The inferred Granger causal links thus inherit the various biases that are used in source localization techniques, in the form of spatiotemporal priors designed in favor of spatial localization. In addition, this approach does not account for the structural properties of the underlying functional networks such as sparsity of the links. We address these issues by modeling the source dynamics as sparse vector autoregressive processes and estimate the model parameters directly from the observations, with no recourse to intermediate source localization. We evaluate the performance of the proposed methodology using both simulated and experimentally-recorded MEG data.
Synthetic Reduced Nearest Neighbor (SRNN) is a Nearest Neighbor model which is constrained to have K synthetic samples (prototypes/centroids). There has been little attempt toward direct optimization and interpretabil...
详细信息
ISBN:
(纸本)9781728163956
Synthetic Reduced Nearest Neighbor (SRNN) is a Nearest Neighbor model which is constrained to have K synthetic samples (prototypes/centroids). There has been little attempt toward direct optimization and interpretability of SRNN with proper guarantees like convergence. To tackle these issues, this paper, inspired by K-means algorithm, provides a novel optimization of Synthetic Reduced Nearest Neighbor based on Expectation Maximization (em-SRNN) that always converges while also monotonically decreases the objective function. The optimization consists of iterating over the centroids of the model and assignment of training samples to centroids. The em-SRNN is interpretable since the centroids represent sub-clusters of the classes. Such type of interpretability is suitable for various studies such as image processing and epidemiological studies. In this paper, analytical aspects of problem are explored and linear complexity of optimization over the trainset is shown. Finally, em-SRNN is shown to have superior or similar performance when compared with several other interpretable and similar state-of-the-art models such trees and kernel SVMs.
The traditional estimation of Mixture regression models is based on the normal assumption of component errors and thus is sensitive to outliers and heavy-tailed errors. In this paper, we propose a robust Mixture regre...
详细信息
The traditional estimation of Mixture regression models is based on the normal assumption of component errors and thus is sensitive to outliers and heavy-tailed errors. In this paper, we propose a robust Mixture regression models in which a mixture of slash distributions is assumed for the errors. Using the fact that the slash distribution can be written as a scale mixture of a normal and a latent distribution, we also estimate model parameters an expectation-maximization (em) algorithm. The results of our simulation show that based on AIC and BIC criterion, the proposed robust regression model mixture on slash distribution dominates the robust regression based the normal and the t distribution. Finally, the proposed model is compared with other procedures, based on a real data set. (C) 2020 The Authors. Published by Atlantis Press SARL.
暂无评论