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Residual lifetime prediction model of nonlinear accelerated degradation data with measurement error

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Journal of Systems Engineering and Electronics 2017年第5期28卷 1028-1038页

作者： Zhongyi Cai Yunxiang Chen Qiang Zhang Huachun Xiang Equipment Management & Safety Engineering College Air Force Engineering University Defense Technology Research Academy China Aerospace Science & Industry Corporation

For the product degradation process with random effect (RE), measurement error (ME) and nonlinearity in step-stress accelerated degradation test (SSADT), the nonlinear Wiener based degradation model with RE and ME is built. An analytical approximation to the probability density function (PDF) of the product's lifetime is derived in a closed form. The process and data of SSADT are analyzed to obtain the relation model of the observed data under each accelerated stress. The likelihood function for the population-based observed data is constructed. The population-based model parameters and its random coefficient prior values are estimated. According to the newly observed data of the target product in SSADT, an analytical approximation to the PDF of its residual lifetime (RL) is derived in accordance with its individual degradation characteristics. The parameter updating method based on Bayesian inference is applied to obtain the posterior value of random coefficient of the RL model. A numerical example by simulation is analyzed to verify the accuracy and advantage of the proposed model.

关键词： accelerated degradation test residual lifetime (RL) prediction measurement error random effect nonlinearity

Partially Linear Single-Index Model in the Presence of measurement error

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Journal of Systems Science & Complexity 2022年第6期35卷 2361-2380页

作者： LIN Hongmei SHI Jianhong TONG Tiejun ZHANG Riquan School of Statistics and Information Shanghai University of International Business and EconomicsShanghai 201620China Key Laboratory of Advanced Theory and Application in Statistics and Data Science Ministry of EducationEast China Normal UniversityShanghai 200062China School of Mathematics and Computer Science Shanxi Normal UniversityLinfen 041081China Department of Mathematics Hong Kong Baptist UniversityHongKong 519087China School of Statistics East China Normal UniversityShanghai 200062China

The partially linear single-index model(PLSIM) is a flexible and powerful model for analyzing the relationship between the response and the multivariate covariates. This paper considers the PLSIM with measurement error possibly in all the variables. The authors propose a new efficient estimation procedure based on the local linear smoothing and the simulation-extrapolation method,and further establish the asymptotic normality of the proposed estimators for both the index parameter and nonparametric link function. The authors also carry out extensive Monte Carlo simulation studies to evaluate the finite sample performance of the new method, and apply it to analyze the osteoporosis prevention data.

关键词： Local linear regression measurement error partially linear model SIMEX single-index model

measurement error of Refractive Index for Spectacle Lens

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Journal of Donghua University(English Edition) 2017年第4期34卷 613-616页

作者：叶佳意蒋伟忠唐玲玲 Research Institute Donghua UniversityShanghai 201620China College of Materials Science and Engineering Donghua UniversityShanghai 201620China

As an important optical constant of optical properties for spectacle lens,the refractive index measurement is studied using V prism refractometer. In the experiment,according to various factors inducing measurement error,the experimental results are analyzed,which include right angle deviation,contact liquid,curvature,and focusing accuracy. The study results show that focusing accuracy is the most important factor of influence for measurement,consists of contact liquid wettability,sample shape,and effective width of light transmission. In addition,the refractive index measurement is less affected by angle deviation of sample and the refractive index deviation of contact liquid. On the basis of the experimental data analysis,it is possible to relax the deviation of right angle of the sample to 1' or 2'.

关键词： spectacles lens refractive index measurement error V prism refractometer

Corrected empirical likelihood for a class of generalized linear measurement error models

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Science China Mathematics 2015年第7期58卷 1523-1536页

作者： YANG YiPing LI GaoRong TONG TieJun College of Mathematics and Statistics Chongqing Technology and Business University Beijing Center for Scientific and Engineering Computing Beijing University of Technology College of Applied Sciences Beijing University of Technology Department of Mathematics Hong Kong Baptist University

Generalized linear measurement error models, such as Gaussian regression, Poisson regression and logistic regression, are considered. To eliminate the effects of measurement error on parameter estimation, a corrected empirical likelihood method is proposed to make statistical inference for a class of generalized linear measurement error models based on the moment identities of the corrected score function. The asymptotic distribution of the empirical log-likelihood ratio for the regression parameter is proved to be a Chi-squared distribution under some regularity conditions. The corresponding maximum empirical likelihood estimator of the regression parameter π is derived, and the asymptotic normality is shown. Furthermore, we consider the construction of the confidence intervals for one component of the regression parameter by using the partial profile empirical likelihood. Simulation studies are conducted to assess the finite sample performance. A real data set from the ACTG 175 study is used for illustrating the proposed method.

关键词： generalized linear model empirical likelihood measurement error corrected score

The measurement error analysis when a pitot probe is used in supersonic air flow

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Science China(Physics,Mechanics & Astronomy) 2011年第4期54卷 690-696页

作者： ZHANG XiWen HAO PengFei YAO ZhaoHui School of Aerospace Tsinghua University Beijing 100084 China

Pitot probes enable a simple and convenient way of measuring mean velocity in air flow. The contrastive numerical simulation between free supersonic airflow and pitot tube at different positions in supersonic air flow was performed using Navier-Stokes equations, the ENN scheme with time-dependent boundary conditions （TDBC） and the Spalart-Allmaras turbulence model. The physical experimental results including pitot pressure and shadowgraph are also presented. Numerical results coincide with the experimental data. The flow characteristics of the pitot probe on the supersonic flow structure show that the measure- ment gives actually the total pressure behind the detached shock wave by using the pitot probe to measure the total pressure. The measurement result of the distribution of the total pressure can still represent the real free jet flow. The similar features of the intersection and reflection of shock waves can be identified. The difference between the measurement results and the actual ones is smaller than 10%. When the pitot probe is used to measure the region of L=0-4D, the measurement is smaller than the real one due to the increase of the shock wave strength. The difference becomes larger where the waves intersect. If the pitot probe is put at L=SD-10D, where the flow changes from supersonic to subsonic, the addition of the pitot probe turns the original supersonic flow region subsonic and causes bigger measurement errors.

关键词： pitot probe supersonic air flow numerical simulation measurement error

Effect of measurement error on the Multivariate CUSUM Control Chart for Compositional Data

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Computer Modeling in Engineering & Sciences 2023年第8期136卷 1207-1257页

作者： Muhammad Imran Jinsheng Sun Fatima Sehar Zaidi Zameer Abbas Hafiz Zafar Nazir School of Automation Nanjing University of Science and TechnologyNanjing210094China School of Economics and Statistics Guangzhou UniversityGuangzhou510006China Department of Mathematics and Statistics East China Normal UniversityShanghai200062China Department of Statistics Government Ambala Muslim Graduate CollegeSargodha40100Pakistan Department of Statistics University of SargodhaSargodha40100Pakistan

Control charts(CCs)are one of the main tools in Statistical Process Control that have been widely adopted in manufacturing sectors as an effective strategy for malfunction detection throughout the previous *** errors(M.E’s)are involved in the quality characteristic of interest,which can effect the CC’s *** authors explored the impact of a linearmodel with additive covariate M.E on the multivariate cumulative sum(CUSUM)CC for a specific kind of data known as compositional data(CoDa).The average run length(ARL)is used to assess the performance of the proposed *** results indicate that M.E’s significantly affects themultivariate *** authors haveused theMarkov chainmethod to study the impact of different involved parameters using six different cases for the variance-covariance matrix(VCM)(i.e.,uncorrelated with equal variances,uncorrelated with unequal variances,positively correlated with equal variances,positively correlated with unequal variances,negatively correlatedwith equal variances and negatively correlated with unequal variances).The authors concluded that the error VCM has a negative impact on the performance of themultivariate CUSUM-CoDa CC,as the ARL increases with an increase in the value of the error *** subgroup size m and powering operator b positively impact the proposed CC,as the ARL decreases with an increase in m or *** number of variables p also has a negative impact on the performance of the proposed CC,as the values of ARL increase with an increase in *** the implementation of the proposal,two illustrated examples have been reported formultivariate CUSUM-CoDaCCs inthe presence ofM.E’*** themanufacturingprocessof uncoated aspirin tablets,and the other is based on monitoring the machines involved in the muesli manufacturing process.

关键词： MCUSUM chart CoDa measurement error manufacturing process performance

THE ASYMPTOTIC DISTRIBUTIONS OF EMPIRICAL LIKELIHOOD RATIO STATISTICS IN THE PRESENCE OF measurement error

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Acta Mathematica Scientia 2007年第2期27卷 232-242页

作者：伍长春张润楚 School of Mathematics and Information Jiaxing University LPMC and School of Mathematical Sciences Nankai University

Suppose that several different imperfect instruments and one perfect instrument are independently used to measure some characteristics of a population. Thus, measurements of two or more sets of samples with varying accuracies are obtained. Statistical inference should be based on the pooled samples. In this article, the authors also assumes that all the imperfect instruments are unbiased. They consider the problem of combining this information to make statistical tests for parameters more relevant. They define the empirical likelihood ratio functions and obtain their asymptotic distributions in the presence of measurement error.

关键词： Empirical likelihood ratio statistics asymptotic distribution measurement error

Empirical Likelihood Inference Under Stratified Random Sampling in the Presence of measurement error

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Acta Mathematicae Applicatae Sinica 2005年第3期21卷 429-440页

作者： Chang-chun Wu Run-chu Zhang Department of Statistics School of Mathematics Nankai University Tianjin 300071 China Department of Mathematics Xiangnan University Chenzhou 423000 China

Suppose that several different imperfect instruments and one perfect instrument are used independently to measure some characteristic of a population. In order to make full use of the sample information, in this paper the empirical likelihood method is put forward for making inferences on parameters of interest under stratified random sampling in the presence of measurement error, Our results show that it can lead to estimators which are asymptotically normal and utilize all the available sample information. We also obtain the asymptotic distribution of empirical likelihood testing statistics. In particular, we apply the method to obtain estimator and confidence interval of population mean.

关键词： Empirical likelihood stratified random sampling measurement error empirical likelihood testingstatistic asymptotic normal asymptotical distribution

Beam induced vacuum measurement error in BEPC II

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Beam induced vacuum measurement error in BEPC II