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1.
We analyze the reliability of NASA composite pressure vessels by using a new Bayesian semiparametric model. The data set consists of lifetimes of pressure vessels, wrapped with a Kevlar fiber, grouped by spool, subject to different stress levels; 10% of the data are right censored. The model that we consider is a regression on the log‐scale for the lifetimes, with fixed (stress) and random (spool) effects. The prior of the spool parameters is nonparametric, namely they are a sample from a normalized generalized gamma process, which encompasses the well‐known Dirichlet process. The nonparametric prior is assumed to robustify inferences to misspecification of the parametric prior. Here, this choice of likelihood and prior yields a new Bayesian model in reliability analysis. Via a Bayesian hierarchical approach, it is easy to analyze the reliability of the Kevlar fiber by predicting quantiles of the failure time when a new spool is selected at random from the population of spools. Moreover, for comparative purposes, we review the most interesting frequentist and Bayesian models analyzing this data set. Our credibility intervals of the quantiles of interest for a new random spool are narrower than those derived by previous Bayesian parametric literature, although the predictive goodness‐of‐fit performances are similar. Finally, as an original feature of our model, by means of the discreteness of the random‐effects distribution, we are able to cluster the spools into three different groups. Copyright © 2012 John Wiley & Sons, Ltd. 相似文献
2.
许多研究领域中都会涉及到纵向资料的分析处理.在纵向资料的分析中,常常遇到带有时变协变量的情况.传统的方差分析难以处理具有时变协变量的纵向资料.对线性混合效应模型应用于分析这类资料进行了方法学的探讨,并编制了模型拟合的SAS程序.通过实例应用,对线性混合效应模型分析纵向资料的方法和过程给出详细的介绍. 相似文献
3.
本文证明了三个定理，得到串联、并联、ｋ／ｍ（Ｇ）系统可靠度和平均寿命的Ｂａｙｅｓ点估计表达式（ｔ）和．有助于“经济系统可靠性”的研究． 相似文献
4.
Sheldon M Ross 《Stochastic Processes and their Applications》1976,4(2):167-173
Consider an n-component reliability system having the property that at any time each of its components is either up (i.e., working) or down (i.e., being repaired). Each component acts independently and we suppose that each time the ith component goes up it remains up for an exponentially distributed time having mean μi, and each time it goes down it remains down for an exponentially distributed time having mean υi. We further suppose that whether or not the system itself is up at any time depends only on which components are up at that time. We are interested in the distribution of the time of first system failure when all components are initially up at time zero. In section 2 we show that this distribution has the NBU (i.e., new better than used) property, and in Section 3 we make use of this and other results to obtain a lower bound to the mean time until first system failure. 相似文献
5.
在许多实际研究中, 由于预算限制, 主协变量值只能对某一个有效集进行准确测量, 但同时对应此主协变量的辅助信息则对全部个体均可以观测. 利用这些辅助协变量的信息有助于提高统计研究的效率. 本文在基于共同基准危险率的边际模型框架下, 我们提出了一些统计推断方法来分析多元失效时间数据. 对于回归参数, 我们提出标准的估计部分似然方程来估计它, 同时也给出了累积基准危险率函数的Breslow 型估计. 得到的估计可以证明是相合的和渐近正态的. 利用模拟分析结果来表明了提出的方法在有限样本下的可行性. 相似文献
6.
为了解决开关寿命为连续随机变量且部件工作故障的修理时间与贮备故障后的修理时间各不相同的问题,利用Markov过程理论和Laplace变换方法,研究了有优先权的两不同型部件和两不同修理工组成的温贮备可修系统.假定部件的工作寿命、贮备寿命、工作故障的修理时间和贮备故障的修理时间均服从不同的指数分布,得到了该系统的可靠度Laplace变换和系统的首次故障前平均时间的解析表达式. 相似文献
7.
Anum Shafiq;Andaç Batur Çolak;Showkat Ahmad Lone;Tabassum Naz Sindhu;Taseer Muhammad; 《Mathematical Methods in the Applied Sciences》2024,47(5):3308-3328
In recent years, statisticians have become more and more interested in the study of mixture models, especially in the last decade, without adequately considering the difficulty of modeling the reliability measures of mixture models using artificial neural networks. In this study, in which artificial neural networks and mixed model reliability criteria are analyzed, various reliability parameters are calculated considering different scenarios. In order to estimate the obtained numerical reliability parameters, a multilayer artificial neural network model has been developed. Seven different reliability parameter values have been obtained from the artificial neural network model designed with four input parameters. The prediction values obtained from the artificial neural network model developed with five neurons in the hidden layer have been compared with numerical data, and the performance of the model has been analyzed comprehensively. The mean squared error (MSE) value for the network model has been calculated as 1.98E-08 and the R value as 0.99991. The results clearly revealed that the artificial neural network model developed using data from the appropriate statistical model is an excellent tool that can be used to estimate reliability measures. 相似文献
8.
Phase‐type distribution closure properties are utilized to devise algorithms for generating reliability functions of systems with basic structures. These structures include series, parallel, K‐out‐of‐N, and standby structures with perfect/imperfect switch. The algorithms form a method for system reliability modeling and analysis based on the relationship between the system lifetime and component lifetimes for general structures. The proposed method is suitable for functional system reliability analysis, which can produce reliability functions of systems with independent components instead of only system reliability values. Once the system reliability function is obtained, other reliability measures such as the system's hazard function and mean time to failure can be obtained efficiently using only matrix algebra. Dimensional and numerical comparisons with computerized symbolic processing are also presented to show the superiority of the proposed method. 相似文献
9.
陈胜军 《数学的实践与认识》2005,35(1):126-130
在综合考虑系统功能函数变量不同属性的基础上 ,建立了单一失效模式下复杂系统模糊随机可靠性的广义模型 ,并讨论了广义模型与各个单一模型之间的关系 ,为产品在复杂状态下的可靠性求解提供了统一的数学模型 .分析讨论表明 :所建立的模糊随机可靠性广义模型更具有一般性 . 相似文献
10.
Dynamic response systems are often found in science, engineering, and medical applications, but the discussion on experimental design for such a system is relatively rare in literature. For an experimenter, designing such experiments requires making decisions on (1) when or where to take response measurements along the dynamic variable and (2) how to choose the combination of experimental factors and their levels. The first consideration is unique for such experiments, especially when the measurement cost is high. In this paper, we present a design approach through the mixed‐effect linear model, which is based on a hierarchical B‐spline function for the dynamic response. We develop several theorems that can assist in finding a statistically efficient sampling plan and propose an algorithm for searching the D‐optimal design of a dynamic response system. 相似文献
11.
This work is motivated by a particular software reliability problem in a unit of flight control software developed by the Indian Space Research Organization (ISRO), in which the testing of the software is carried out in multiple batches, each consisting of several runs. As the errors are found during the runs within a batch, they are noted, but not debugged immediately; they are debugged only at the end of that particular batch of runs. In this work, we introduce a discrete time model suitable for this type of periodic debugging schedule and describe maximum likelihood estimation for the model parameters. This model is used to estimate the reliability of the software. We also develop a method to determine the additional number of error‐free test runs required for the estimated reliability to achieve a specific target with some high probability. We analyze the test data on the flight control software of ISRO. Copyright © 2011 John Wiley & Sons, Ltd. 相似文献
12.
Devendra Kumar 《Numerical Methods for Partial Differential Equations》2021,37(1):626-642
In this paper, a parameter‐uniform numerical scheme for the solution of singularly perturbed parabolic convection–diffusion problems with a delay in time defined on a rectangular domain is suggested. The presence of the small diffusion parameter ? leads to a parabolic right boundary layer. A collocation method consisting of cubic B ‐spline basis functions on an appropriate piecewise‐uniform mesh is used to discretize the system of ordinary differential equations obtained by using Rothe's method on an equidistant mesh in the temporal direction. The parameter‐uniform convergence of the method is shown by establishing the theoretical error bounds. The numerical results of the test problems validate the theoretical error bounds. 相似文献
13.
Laurent Pierre-Jean Mazure Marie-Laurence Maxim Voichiţa Teodora 《Numerical Algorithms》1997,15(3-4):373-383
A parametric spline curve is defined whose restriction to each sub-interval belongs to a 4-dimensional piecewise Chebyshev
subspace depending on coefficients which play the role of shape parameters.
This revised version was published online in August 2006 with corrections to the Cover Date. 相似文献
14.
《Random Structures and Algorithms》2018,52(4):576-596
The application of simple random walks on graphs is a powerful tool that is useful in many algorithmic settings such as network exploration, sampling, information spreading, and distributed computing. This is due to the reliance of a simple random walk on only local data, its negligible memory requirements, and its distributed nature. It is well known that for static graphs the cover time, that is, the expected time to visit every node of the graph, and the mixing time, that is, the time to sample a node according to the stationary distribution, are at most polynomial relative to the size of the graph. Motivated by real world networks, such as peer‐to‐peer and wireless networks, the conference version of this paper was the first to study random walks on arbitrary dynamic networks. We study the most general model in which an oblivious adversary is permitted to change the graph after every step of the random walk. In contrast to static graphs, and somewhat counter‐intuitively, we show that there are adversary strategies that force the expected cover time and the mixing time of the simple random walk on dynamic graphs to be exponentially long, even when at each time step the network is well connected and rapidly mixing. To resolve this, we propose a simple strategy, the lazy random walk, which guarantees, under minor conditions, polynomial cover time and polynomial mixing time regardless of the changes made by the adversary. 相似文献
15.
This paper deals with the analysis of accelerated failure time model when the primary covariate is subject to missing. We assume that the true covariate is measured precisely on a randomly chosen validation set, whereas auxiliary information for primary covariate is available to all study subjects. The asymptotic properties for the proposed estimator are developed and the simulation studies show that the efficiency gain is remarkable compared to the method using only the validation sample. A real example is also provided as an illustration. 相似文献
16.
Let be a connected graph with vertices. A simple random walk on the vertex set of G is a process, which at each step moves from its current vertex position to a neighbouring vertex chosen uniformly at random. We consider a modified walk which, whenever possible, chooses an unvisited edge for the next transition; and makes a simple random walk otherwise. We call such a walk an edge‐process (or E‐process). The rule used to choose among unvisited edges at any step has no effect on our analysis. One possible method is to choose an unvisited edge uniformly at random, but we impose no such restriction. For the class of connected even degree graphs of constant maximum degree, we bound the vertex cover time of the E‐process in terms of the edge expansion rate of the graph G, as measured by eigenvalue gap of the transition matrix of a simple random walk on G. A vertex v is ?‐good, if any even degree subgraph containing all edges incident with v contains at least ? vertices. A graph G is ?‐good, if every vertex has the ?‐good property. Let G be an even degree ?‐good expander of bounded maximum degree. Any E‐process on G has vertex cover time This is to be compared with the lower bound on the cover time of any connected graph by a weighted random walk. Our result is independent of the rule used to select the order of the unvisited edges, which could, for example, be chosen on‐line by an adversary. As no walk based process can cover an n vertex graph in less than n – 1 steps, the cover time of the E‐process is of optimal order when . With high probability random r‐regular graphs, even, have . Thus the vertex cover time of the E‐process on such graphs is . © 2013 Wiley Periodicals, Inc. Random Struct. Alg., 46, 36–54, 2015 相似文献
17.
We study the cover time of random geometric graphs. Let $I(d)=[0,1]^{d}$ denote the unit torus in d dimensions. Let $D(x,r)$ denote the ball (disc) of radius r. Let $Upsilon_d$ be the volume of the unit ball $D(0,1)$ in d dimensions. A random geometric graph $G=G(d,r,n)$ in d dimensions is defined as follows: Sample n points V independently and uniformly at random from $I(d)$ . For each point x draw a ball $D(x,r)$ of radius r about x. The vertex set $V(G)=V$ and the edge set $E(G)={{v,w}: wne v,,win D(v,r)}$ . Let $G(d,r,n),,dgeq 3$ be a random geometric graph. Let $C_G$ denote the cover time of a simple random walk on G. Let $c>1$ be constant, and let $r=(clog n/(Upsilon_dn))^{1/d}$ . Then whp the cover time satisfies © 2010 Wiley Periodicals, Inc. Random Struct. Alg., 38, 324–349, 2011 相似文献
18.
The U.S. Air Force is developing an Integrated Communications, Navigation, and Identification Avionics (aviation electronics) system with the acronym ICNIA for use in tactical aircraft. Designers of ICNIA as well as the Air Force need to be informed of the reliability of proposed designs. Hence, the Air Force contracted The Analytic Sciences Corporation (TASC) to develop a model of the ICNIA system and to develop algorithms for determining various system performance measures such as the system reliability. TASC developed the ICNIA model and developed a software package called MIREM to analyze ICNIA systems. Unfortunately, due to the complexity of ICNIA, the developers of MIREM were forced to incorporate several approximations in MIREM. In the report by Foley [2], we showed that these approximations can perform poorly in some artificially constructed examples. Their accuracy on realistic examples is unknown. We have developed and implemented two algorithms for analyzing ICNIA. The algorithms do not use any approximations and are computationally feasible on realistic sized examples. It is recommended that MIREM be modified to use the algorithms described in this paper. 相似文献
19.
修理有延迟且修理设备可更换的多状态可修系统的可靠性分析 总被引：2，自引：0，他引：2
本文研究修理有延迟且修理设备可更换的单部件多状态可修系统.利用更新过程理论,得到了系统的可靠性指标.通过引入修理设备的"广义忙期",简洁地讨论了修理设备感兴趣的许多可靠性指标,得到一系列重要结果. 相似文献
20.
Asymptotic Properties of a Class of Mixture Models for Failure Data: The Interior and Boundary Cases
H. T. V. Vu R. A. Maller X. Zhou 《Annals of the Institute of Statistical Mathematics》1998,50(4):627-653
We analyse an exponential family of distributions which generalises the exponential distribution for censored failure time data, analogous to the way in which the class of generalised linear models generalises the normal distribution. The parameter of the distribution depends on a linear combination of covariates via a possibly nonlinear link function, and we allow another level of heterogeneity: the data may contain "immune" individuals who are not subject to failure. Thus the data is modelled by a mixture of a distribution from the exponential family and a "mass at infinity" representing individuals who never fail. Our results include large sample distributions for parameter estimators and for hypothesis test statistics obtained by maximising the likelihood of a sample. The asymptotic distribution of the likelihood ratio test statistic for the hypothesis that there are no immunes present in the population is shown to be "non-standard"; it is a 50-50 mixture of a chi-squared distribution on 1 degree of freedom and a point mass at 0. Our analysis clearly shows how "negligibility" of individual covariate values and "sufficient followup" conditions are required for the asymptotic properties. 相似文献