The Experts below are selected from a list of 3090 Experts worldwide ranked by ideXlab platform
Ross L Prentice - One of the best experts on this subject based on the ideXlab platform.
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Nonparametric estimation of the multivariate Survivor Function: the multivariate Kaplan–Meier estimator
Lifetime Data Analysis, 2018Co-Authors: Ross L Prentice, Shanshan ZhaoAbstract:The Dabrowska (Ann Stat 16:1475–1489, 1988 ) product integral representation of the multivariate Survivor Function is extended, leading to a nonparametric Survivor Function estimator for an arbitrary number of failure time variates that has a simple recursive formula for its calculation. Empirical process methods are used to sketch proofs for this estimator’s strong consistency and weak convergence properties. Summary measures of pairwise and higher-order dependencies are also defined and nonparametrically estimated. Simulation evaluation is given for the special case of three failure time variates.
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Nonparametric estimation of the multivariate Survivor Function: the multivariate Kaplan-Meier estimator.
Lifetime data analysis, 2016Co-Authors: Ross L Prentice, Shanshan ZhaoAbstract:The Dabrowska (Ann Stat 16:1475–1489, 1988) product integral representation of the multivariate Survivor Function is extended, leading to a nonparametric Survivor Function estimator for an arbitrary number of failure time variates that has a simple recursive formula for its calculation. Empirical process methods are used to sketch proofs for this estimator’s strong consistency and weak convergence properties. Summary measures of pairwise and higher-order dependencies are also defined and nonparametrically estimated. Simulation evaluation is given for the special case of three failure time variates.
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self consistent nonparametric maximum likelihood estimator of the bivariate Survivor Function
Biometrika, 2014Co-Authors: Ross L PrenticeAbstract:As usually formulated the nonparametric likelihood for the bivariate Survivor Function is overparameterized, resulting in uniqueness problems for the corresponding nonparametric maximum likelihood estimator. Here the estimation problem is redefined to include parameters for marginal hazard rates, and for double failure hazard rates only at informative uncensored failure time grid points where there is pertinent empirical information. Double failure hazard rates at other grid points in the risk region are specified rather than estimated. With this approach the nonparametric maximum likelihood estimator is unique, and can be calculated using a two-step procedure. The first step involves setting aside all doubly censored observations that are interior to the risk region. The nonparametric maximum likelihood estimator from the remaining data turns out to be the Dabrowska (1988) estimator. The omitted doubly censored observations are included in the procedure in the second stage using self-consistency, resulting in a noniterative nonparametric maximum likelihood estimator for the bivariate Survivor Function. Simulation evaluation and asymptotic distributional results are provided. Moderate sample size efficiency for the Survivor Function nonparametric maximum likelihood estimator is similar to that for the Dabrowska estimator as applied to the entire dataset, while some useful efficiency improvement arises for the corresponding distribution Function estimator, presumably due to the avoidance of negative mass assignments.
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An Adjustment to Improve the Bivariate Survivor Function Repaired NPMLE
Lifetime Data Analysis, 2005Co-Authors: F. Zoe Moodie, Ross L PrenticeAbstract:We recently proposed a representation of the bivariate Survivor Function as a mapping of the hazard Function for truncated failure time variates. The representation led to a class of estimators that includes van der Laan’s repaired nonparametric maximum likelihood estimator (NPMLE) as an important special case. We proposed a Greenwood-like variance estimator for the repaired NPMLE but found somewhat poor agreement between the empirical variance estimates and these analytic estimates for the sample sizes and bandwidths considered in our simulation study. The simulation results also confirmed those of others in showing slightly inferior performance for the repaired NPMLE compared to other competing estimators as well as a sensitivity to bandwidth choice in moderate sized samples. Despite its attractive asymptotic properties, the repaired NPMLE has drawbacks that hinder its practical application. This paper presents a modification of the repaired NPMLE that improves its performance in moderate sized samples and renders it less sensitive to the choice of bandwidth. Along with this modified estimator, more extensive simulation studies of the repaired NPMLE and Greenwood-like variance estimates are presented. The methods are then applied to a real data example.
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hazard based nonparametric Survivor Function estimation
Journal of The Royal Statistical Society Series B-statistical Methodology, 2004Co-Authors: Ross L Prentice, Zoe F Moodie, Jianrong WuAbstract:A representation is developed that expresses the bivariate Survivor Function as a Function of the hazard Function for truncated failure time variables. This leads to a class of nonparametric Survivor Function estimators that avoid negative mass. The transformation from hazard Function to Survivor Function is weakly continuous and compact differentiable, so that such properties as strong consistency, weak convergence to a Gaussian process and bootstrap applicability for a hazard Function estimator are inherited by the corresponding Survivor Function estimator. The set of point mass assignments for a Survivor Function estimator is readily obtained by using a simple matrix calculation on the set of hazard rate estimators. Special cases arise from a simple empirical hazard rate estimator, and from an empirical hazard rate estimator following the redistribution of singly censored observations within strips. The latter is shown to equal van der Laan's repaired nonparametric maximum likelihood estimator, for which a Greenwood-like variance estimator is given. Simulation studies are presented to compare the moderate sample performance of various nonparametric Survivor Function estimators. Copyright 2004 Royal Statistical Society.
Laurence A. Baxter - One of the best experts on this subject based on the ideXlab platform.
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Towards a theory of confidence intervals for system reliability
Statistics & Probability Letters, 1993Co-Authors: Laurence A. BaxterAbstract:Consider a binary coherent system of nonrepairable components, the lifelength distributions of which lie in the single parameter exponential family of distributions. Given observations of the lifelengths of the constituent components, it is shown how inversion of the likelihood ratio test can be used to calculate strongly consistent approximate confidence intervals for the Survivor Function of the system lifelength and for the mean time to system failure.
R.k. Saket - One of the best experts on this subject based on the ideXlab platform.
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reliability evaluation of seig rotor core magnetization with minimum capacitive excitation for unregulated renewable energy applications in remote areas
Ain Shams Engineering Journal, 2014Co-Authors: Lokesh Varshney, R.k. SaketAbstract:Abstract This paper presents reliability evaluation of residual magnetism in rotor core of the induction motor operated as SEIG using probability distribution approach and Monte Carlo simulation for unregulated renewable energy applications in remote areas. Parallel capacitors with calculated minimum capacitive value across the terminals of the induction motor operated as SEIG with unregulated shaft speed are connected during the experimental study. A three phase, 4 poles, 50 Hz, 5.5 hp, 12.3 A, 230 V induction motor coupled with DC Shunt Motor is tested in the electrical machine laboratory with variable reactive loads. Using this experimental study, it is possible to choose a reliable induction machines operated as SEIG for unregulated renewable energy application. Failure density Function, cumulative failure distribution Function, Survivor Function, hazard model, probability of success and probability of failure for reliability evaluation of the three phase induction motor operating as a SEIG have been presented graphically in this paper.
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Reliability evaluation of residual magnetism in rotor of SEIG
2013 Students Conference on Engineering and Systems (SCES), 2013Co-Authors: Lokesh Varshney, R.k. SaketAbstract:Evaluation of the probability of success and probability of failure have been presented in this paper by using Monte Carlo simulation due to loss of residual magnetism in the rotor core of the three phase induction machine operating as a Self Excited Induction Generator (SEIG). Based on this experimental study, it is possible to choose a reliable induction machines operated as a SEIG for unregulated renewable energy application. A three phase delta connected, 4 poles, 50Hz, 5.5 hp, 12.3A, 230V induction motor coupled with 230V, 11.6A DC Shunt Motor was tested in the electrical machine laboratory with variable reactive loads. Failure density Function, cumulative failure distribution Function, Survivor Function, hazard model for reliability evaluation of the three phase induction motor operating as a SEIG have been presented graphically in this paper by using probability distribution approach.
Lev V. Utkin - One of the best experts on this subject based on the ideXlab platform.
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Reliability analysis of load-sharing m-out-of-n systems with arbitrary load and different probability distributions of time to failure
International Journal of Reliability and Safety, 2015Co-Authors: Sergey V. Gurov, Lev V. UtkinAbstract:The reliability analysis of load-sharing m-out-of-n systems where the workload is shared by the remaining working units when a unit fails is proposed in the paper. General expressions are provided for the m-out-of-n system reliability by arbitrary probability distributions of time to failure of units. Simplified methods are given for computing the Survivor Function in cases when the time to unit failure is governed by the Weibull and exponential probability distributions. The system Survivor Function and the mean time to failure in the explicit form are obtained for systems with arbitrary load (decreasing and increasing) by the exponential time to unit failure. Numerical examples illustrate the properties of load-sharing m-out-of-n systems.
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An inverse problem of the load-sharing system reliability analysis: Constructing the load Function
Proceedings of the Institution of Mechanical Engineers Part O: Journal of Risk and Reliability, 2014Co-Authors: Sergey V. Gurov, Lev V. UtkinAbstract:The reliability analysis of the load-sharing systems under different behaviors of the load has been provided in this article. An inverse problem of determining the load Function by having requirements concerning the system Survivor Function is solved. Simple and explicit expressions for computing the load Function are provided under the assumption that the Weibull probability distributions of time to failure are derived. A standby system consisting of two units under the changeable load is studied. The various numerical examples illustrate the proposed models.
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Load-share reliability models with the piecewise constant load
International Journal of Reliability and Safety, 2012Co-Authors: Sergey V. Gurov, Lev V. UtkinAbstract:In this paper, we study methods for reliability analysis of the load-share models. In load-share systems, component or system failure rates depend on the working state of the other components in the system or on changeable conditions of system Functioning. A special type of load, namely the piecewise constant load is investigated. The main assumption used in the paper is the so-called 'condition of the residual lifetime conservation' of the system, which is equivalent to the condition of continuity of the reliability (Survivor) Function. Rather simple recurrent expressions are obtained for computing reliability measures. Various numerical examples illustrate the proposed models.
Maria Luz Gamiz - One of the best experts on this subject based on the ideXlab platform.
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Weighted Estimation of Component Reliability in Series Systems
IEEE Transactions on Reliability, 2012Co-Authors: Maria Luz GamizAbstract:The characteristics of the failure times of components in a series system are estimated from observed system failure times and causes of failure. Usually this situation is also approached from a competing risks model viewpoint where, in case of statistical independence, the lifetime of each component may be estimated by the Kaplan-Meier method (KM) . For simplicity, we consider only two components in the system. If we are interested in estimating the reliability or Survivor Function of each component, we may construct for each case an estimator by conveniently interpreting the data set. In this paper, we suggest a modified version of the KM method for estimating the Survivor Function of a component that uses the information about the lifetime of the other component (which is not being analysed at the moment) to get a better accuracy with heavily censored sampling information, which in fact is the case of the reliability context addressed here.
