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Register a new userAllocations of Cold Standbys to Series and Parallel Systems with Dependent Components
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Added by
Yiying Zhang
Publication date
2018
fields
Mathematical Statistics
and research's language is
English
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In the context of industrial engineering, cold-standby redundancies allocation strategy is usually adopted to improve the reliability of coherent systems. This paper investigates optimal allocation strategies of cold standbys for series and parallel systems comprised of dependent components with left/right tail weakly stochastic arrangement increasing lifetimes. For the case of heterogeneous and independent matched cold standbys, it is proved that better redundancies should be put in the nodes having weaker [better] components for series [parallel] systems. For the case of homogeneous and independent cold standbys, it is shown that more redundancies should be put in standby with weaker [better] components to enhance the reliability of series [parallel] systems. The results developed here generalize and extend those corresponding ones in the literature to the case of series and parallel systems with dependent components. Numerical examples are also presented to provide guidance for the practical use of our theoretical findings.
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In this paper we extend the Weibull power series (WPS) class of distributions and named this new class as extended Weibull power series (EWPS) class of distributions. The EWPS distributions are related to series and parallel systems with a random num- ber of components, whereas the WPS distributions (Morais and Barreto-Souza, 2011) are related to series systems only. Unlike the WPS distributions, for which the Weibull is a limiting special case, the Weibull law is a particular case of the EWPS distributions. We prove that the distributions in this class are identifiable under a simple assumption. We also prove stochastic and hazard rate order results and highlight that the shapes of the EWPS distributions are markedly more flexible than the shapes of the WPS distributions. We define a regression model for the EWPS response random variable to model a scale parameter and its quantiles. We present the maximum likelihood estimator and prove its consistency and normal asymptotic distribution. Although the construction of this class was motivated by series and parallel systems, the EWPS distributions are suitable for modeling a wide range of positive data sets. To illustrate potential uses of this model, we apply it to a real data set on the tensile strength of coconut fibers and present a simple device for diagnostic purposes.
Mean profiles are widely used as indicators of the electricity consumption habits of customers. Currently, in Electricite De France (EDF), class load profiles are estimated using point-wise mean function. Unfortunately, it is well known that the mean is highly sensitive to the presence of outliers, such as one or more consumers with unusually high-levels of consumption. In this paper, we propose an alternative to the mean profile: the $L_1$-median profile which is more robust. When dealing with large datasets of functional data (load curves for example), survey sampling approaches are useful for estimating the median profile avoiding storing the whole data. We propose here estimators of the median trajectory using several sampling strategies and estimators. A comparison between them is illustrated by means of a test population. We develop a stratification based on the linearized variable which substantially improves the accuracy of the estimator compared to simple random sampling without replacement. We suggest also an improved estimator that takes into account auxiliary information. Some potential areas for future research are also highlighted.
In the past years we have witnessed the rise of new data sources for the potential production of official statistics, which, by and large, can be classified as survey, administrative, and digital data. Apart from the differences in their generation and collection, we claim that their lack of statistical metadata, their economic value, and their lack of ownership by data holders pose several entangled challenges lurking the incorporation of new data into the routinely production of official statistics. We argue that every challenge must be duly overcome in the international community to bring new statistical products based on these sources. These challenges can be naturally classified into different entangled issues regarding access to data, statistical methodology, quality, information technologies, and management. We identify the most relevant to be necessarily tackled before new data sources can be definitively considered fully incorporated into the production of official statistics.
We perform experimental and theoretical study of the parallel-series arrays of Cold-Electron Bolometers (CEBs) integrated into a cross-slot antenna and composed with an immersion silicon lens. The purpose is to determine the absorption efficiency, the responsivity and the noise equivalent power (NEP) of the bolometers. The absorbed power has been found in two independent ways. The comparison of two approaches gives better understanding of the system and secures from misinterpretations. The first approach is fitting of the bolometer IV curves with solutions of heat-balance equations. The second approach is modeling of electromagnetic properties of the system, including an antenna, lens, optical can, band-pass filters and black body source. The difference between both methods does not exceed $30%$. The optimization of experimental setup is proposed to approach the photon limited detection mode.
We provide a MATLAB toolbox, BFDA, that implements a Bayesian hierarchical model to smooth multiple functional data with the assumptions of the same underlying Gaussian process distribution, a Gaussian process prior for the mean function, and an Inverse-Wishart process prior for the covariance function. This model-based approach can borrow strength from all functional data to increase the smoothing accuracy, as well as estimate the mean-covariance functions simultaneously. An option of approximating the Bayesian inference process using cubic B-spline basis functions is integrated in BFDA, which allows for efficiently dealing with high-dimensional functional data. Examples of using BFDA in various scenarios and conducting follow-up functional regression are provided. The advantages of BFDA include: (1) Simultaneously smooths multiple functional data and estimates the mean-covariance functions in a nonparametric way; (2) flexibly deals with sparse and high-dimensional functional data with stationary and nonstationary covariance functions, and without the requirement of common observation grids; (3) provides accurately smoothed functional data for follow-up analysis.
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