Presence Of Measurement Errors Research Articles

Process Capability Cp Assessment for Auto-Correlated Data in the Presence of Measurement Errors

In this paper, we shall discuss some statistical properties of the estimator of [Formula: see text] when sample observations are autocorrelated and affected by measurement errors. The presence of autocorrelation in production units is very common in many industries like chemical, food processing, pharmaceutical, paper, and mineral. At the same time some amount of measurement error is invariably present in the sample observations due to inaccurate measurement process. In this paper, we discuss the case of a first-order stationary autoregressive process where measurement error follows a Gaussian distribution. The comparison of the statistical properties of the estimator in this case with the error-free case is the subject matter of this paper.

Maximum likelihood estimation of spatial lag models in the presence of the error-prone variables

ABSTRACT– The literature has recently devoted close attention to error-prone variables. Nevertheless, only a small number of research have considered measurement error in spatial econometric models. The presence of measurement error in the spatial econometric models needs to be considered as a result of the rise in spatial data analysis, as the relationship between the spatial correlation and measurement error influences parameter estimation. Therefore, in this study, the impacts of classical measurement error on the parameter estimation of the spatial lag model are theoretically examined for both response and explanatory variables. Then, using simulation studies, finite sample properties are investigated for various situations. The major findings indicate that although error-prone response variable has an opposing bias effect on parameter estimations, error-prone explanatory variables have a significant influence effect on the bias of parameter estimations. As a result, it is occasionally possible to obtain unbiased estimates only in certain circumstances.

Density estimation for mixed Euclidean and non-Euclidean data in the presence of measurement error

In this paper, we study density estimation for mixed Euclidean and non-Euclidean variables that are subject to measurement errors. This problem is largely unexplored in statistics. We develop a new deconvolution density estimator and derive its finite-sample properties. We also derive its asymptotic properties including the rate of convergence in various modes and the asymptotic distribution. For the derivation, we apply Fourier analysis on topological groups, which has not been well used in statistics. We provide full practical details on the implementation of the estimator as well as several simulation studies and real data analysis.

Novel cooperative localization method of over-the-horizon shortwave emitters based on direction-of-arrival and time-difference-of-arrival measurements

The location of long-distance shortwave radiation sources is practically significant in national defense security. Shortwave multistation-positioning systems mainly include direction-of-arrival (DOA) and time-difference-of-arrival (TDOA) intersection locations. These two systems have their advantages and disadvantages in terms of performance. To combine the advantages of these two positioning technologies, this study focuses on the cooperative positioning problem based on DOA and TDOA measurements. First, the two-dimensional DOA and TDOA observation models are established for the over-the-horizon propagation scenario. Subsequently, the Cramér-Rao lower bound (CRLB) of positioning accuracy is derived in the presence of measurement errors in virtual ionosphere height. Aiming at the strong nonlinear characteristics of the observation equations, a new DOA/TDOA cooperative localization method is proposed. Finally, the asymptotic efficiency of the new estimator is proved using the first-order error analysis theory. The new method comprises two stages. In the first stage, the shortwave DOA observation equation is transformed into a pseudo-linear observation equation by introducing an auxiliary variable, as well as solving a quadratic equation with one unknown. Next, an optimization model with two quadratic equality constraints is constructed, and an iterative optimization algorithm based on matrix $~\bf{QR}$ decomposition is proposed to obtain an intermediate estimate of the emitter position. The second stage transforms the shortwave TDOA observation equation into a pseudo-linear observation equation by combining the intermediate estimates given in the first phase. Also, an iterative-constrained weighted-least-squares estimator based on the matrix decomposition is proposed again to localize the emitter. Simulation results show that the new cooperative localization method has good global convergence, the localization performance can reach the CRLB, and the obtained cooperative gain is quite high.

Single-shot quantum error correction with the three-dimensional subsystem toric code

Fault-tolerant protocols and quantum error correction (QEC) are essential to building reliable quantum computers from imperfect components that are vulnerable to errors. Optimizing the resource and time overheads needed to implement QEC is one of the most pressing challenges. Here, we introduce a new topological quantum error-correcting code, the three-dimensional subsystem toric code (3D STC). The 3D STC can be realized with geometrically-local parity checks of weight at most three on the cubic lattice with open boundary conditions. We prove that one round of parity-check measurements suffices to perform reliable QEC with the 3D STC even in the presence of measurement errors. We also propose an efficient single-shot QEC decoding strategy for the 3D STC and numerically estimate the resulting storage threshold against independent bit-flip, phase-flip and measurement errors to be pSTC ≈ 1.045%. Such a high threshold together with local parity-check measurements make the 3D STC particularly appealing for realizing fault-tolerant quantum computing.

Estimating the AUC of the MROC curve in the presence of measurement errors

Estimating the AUC of the MROC curve in the presence of measurement errors

The effects of measurement errors on estimating and assessing the multivariate process capability with imprecise characteristic

In industrial environments, process capability indices are daily employed as numerical metrics to summarize the performance of a process according to a predefined set of specification limits. Neglecting gauge measurement errors is a common phenomenon in process capability evaluations by researchers in laboratory investigations and by practitioners in daily operations. However, this common negligence is far from reality regardless of the employment of highly modern measuring tools, and may notably influence the efficiency of the measuring method for assessing the performance of a manufacturing process. In this paper, a linear covariate error model is applied to investigate the effects of gauge measurement errors on the classical and fuzzy estimation approaches of the multivariate process capability index SpkT for univariate and multivariate normally distributed quality characteristics with precise specification limits. Moreover, lower confidence bounds are also derived for the yield index SpkT in the presence of measurement errors and based on a fuzzy approach. In addition to the theoretical results, extensive simulations have been conducted to analyze how the behavior of the test statistic and lower confidence bound (LCB) for assessing the performance of the process is affected by different sources of the measurement errors. The obtained results indicate that a serious underestimation of the process capability occurs when the data is contaminated with measurement errors. It is also shown that the underestimation problem is somewhat solved by taking multiple measurements from the identical item. Moreover, comparative analyses show that the proposed method is superior to Scagliarini’s method and Wang’s way such that the negative effects of errors on underestimating the LCB are reduced in the proposed plan. This paper also extends the application of the introduced method to correlated variables. Finally, three practical examples are discussed to demonstrate the use of the proposed method in industrial applications.

The Performance of Max-GWMA Control Chart in the Presence of Measurement Errors

The Performance of Max-GWMA Control Chart in the Presence of Measurement Errors

Partially Linear Single-Index Model in the Presence of Measurement Error

Partially Linear Single-Index Model in the Presence of Measurement Error

The joint influence of estimation of sensitive variable under measurement error and non-response using ORRT models

This paper addresses three important issues of survey sampling: social desirability bias, measurement error and non-response simultaneously. We suggested a combined family of regression-cum-exponential estimators for estimating the population mean of sensitive variable in the presence of measurement error and non-response simultaneously using optional randomized response technique models. The properties of the suggested estimator(s) have been studied and efficiency conditions have been derived. A simulation study is carried out to support the theoretical findings and shows significant improvement in terms of percent relative efficiency (PRE).

Estimation of sparse functional quantile regression with measurement error: a SIMEX approach.

Quantile regression is a semiparametric method for modeling associations between variables. It is most helpful when the covariates have complex relationships with the location, scale, and shape of the outcome distribution. Despite the method's robustness to distributional assumptions and outliers in the outcome, regression quantiles may be biased in the presence of measurement error in the covariates. The impact of function-valued covariates contaminated with heteroscedastic error has not yet been examined previously; although, studies have investigated the case of scalar-valued covariates. We present a two-stage strategy to consistently fit linear quantile regression models with a function-valued covariate that may be measured with error. In the first stage, an instrumental variable is used to estimate the covariance matrix associated with the measurement error. In the second stage, simulation extrapolation (SIMEX) is used to correct for measurement error in the function-valued covariate. Point-wise standard errors are estimated by means of nonparametric bootstrap. We present simulation studies to assess the robustness of the measurement error corrected for functional quantile regression. Our methods are applied to National Health and Examination Survey data to assess the relationship between physical activity and body mass index among adults in the United States.

Coverage-based cooperative guidance law for intercepting hypersonic vehicles with overload constraint

This paper studies the problem of multiple interceptors with low velocity, weak maneuverability, and limited overload constraint to cooperatively intercept hypersonic vehicles under a nonlinear interception model. First, a coverage-based cooperative guidance (CBCG) law is proposed based on three concepts, i.e., interceptor reachable area, interceptor feasible area, and hypersonic vehicle escape area. Then, the relationship among the initial location of the interceptors, the parameters of the CBCG law, and the coverage area of the interceptor for intercepting the hypersonic vehicle is analyzed. Next, an allocation algorithm is designed to assign the coverage area and the initial locations of multiple interceptors. Finally, simulations are performed for intercepting the hypersonic vehicle with different maneuverabilities and maneuvering modes, and the proposed CBCG law is compared with the proportional navigation guidance (PNG) and sliding mode control guidance (SMCG) laws. The simulation results show that the proposed CBCG law can ensure that at least one interceptor can accurately intercept the hypersonic vehicle, giving full play of the scale advantage of low-cost interceptors. And the guidance robustness can be guaranteed in the presence of measurement errors.

Constrained Bayesian optimization and spatio-temporal surveillance for sensor network design in the presence of measurement errors

ABSTRACT The optimal placement of sensors is studied to construct a surveillance sensor network for a complicated stochastic system with random measurement errors. The problem is formulated as a joint problem of constrained black-box optimization for the fast detection of an anomaly event and spatio-temporal change-point detection for a low false alarm rate. An algorithm is proposed called Confidence-Set based Constrained Bayesian Optimization (CSCBO) that models performance measures as Gaussian Processes (GPs) and provides a flexible and easy-to-implement framework for handling noisy black-box constraints. As the decision variables of this problem are high-dimensional binary variables, the Wasserstein similarity metric is introduced as a distance measure among different solutions to capture the similarity among solutions properly. Finally, a newly proposed detection statistic for spatio-temporal surveillance is combined with CSCBO to identify the optimal sensor placement while controlling the false alarm rate. The combined procedure is applied to the Altamaha River.

Mean estimation using scrambled responses with the impact of measurement errors in two-phase sampling

Khalil et al. (2018, 2019a) presented mean estimators of a sensitive study variable in the presence of measurement errors (ME) in single-phase sampling. We extend that work forward in two-phase sampling under both simple and stratified random sampling and present generalized mean estimators. Efficiency of the proposed estimators is validated through a simulation study.

Shape reconstruction in transient heat conduction problems based on radial integration boundary element method

In order to accurately identify the geometric boundary, the radial integration boundary element method (RIBEM) combined with the modified Levenberg-Marquardt (LM) algorithm is proposed for shape reconstruction in transient heat conduction problems. Compared with the finite element method (FEM), the boundary element method (BEM) only discretizes the boundary rather than the whole domain, so it has incomparable advantages in the shape reconstruction. Especially, the radial integration method still maintains the superiority of boundary discretization in transient heat conduction problems. For the iterative scheme of LM algorithm, the shape reconstruction greatly depends on whether the sensitivity matrix can be obtained accurately. Therefore, complex variable derivation method (CVDM) is firstly introduced to carry out shape reconstruction in the transient heat conduction problems, which accurately solves the sensitivity coefficients of node temperature to the reconstructed boundary, and the RIBEM is transformed from the real domain to the complex domain to solve the transient heat conduction problems. The modified LM algorithm effectively overcomes the shortcoming of the excessive dependence on the step size of finite difference scheme. It should be noted that compared with the finite difference scheme, the proposed method can greatly reduce the computational cost of the direct problem in the multi-variate optimization process, thereby greatly improving the efficiency of identifying the boundary shape. Finally, different reconstruction strategies are applied in numerical models with three types of variable boundary, and reconstruction results demonstrate the great accuracy and efficiency of the proposed method in 2D and 3D shape reconstruction, and it also shows good robustness in the presence of measurement errors.

The Performance of Triple Sampling x̄ Control Chart with Measurement Errors

ABSTRACT The presence of measurement errors can seriously alter the statistical performance of Phase II control charts. Up today, no research on designing the triple sampling control charts taking into account the gauge measurement errors is reported in the existing literature. In this paper, we study the adverse effect of measurement errors on detecting performance of triple sampling (TS)- control chart based on an additive covariate model. Three multiple measurement based triple sampling (MMBTS) schemes are developed to reduce the undesired impact of gauge inability on detecting performance of TS- chart. Through simulation studies in terms of average run length (ARL) and standard deviation of run length (SDRL), it is indicated that the run length characteristics of the TS- is significantly affected by the measurement errors. The results also confirm that all proposed remedial approaches can effectively reduce the undesired impact of imprecise measurements on performance of TS- chart. A sensitivity analysis is also carried out to evaluate how the covariate model parameters affect the detection performance of the TS- chart. Finally, using a real industrial data obtained from the spring production system, we demonstrate the performance of TS- chart when the measurement errors exist.

Zero-inflated Poisson models with measurement error in the response.

Zero-inflated count data arise frequently from genomics studies. Analysis of such data is often based on a mixture model which facilitates excess zeros in combination with a Poisson distribution, and various inference methods have been proposed under such a model. Those analysis procedures, however, are challenged by the presence of measurement error in count responses. In this article, we propose a new measurement error model to describe error-contaminated count data. We show that ignoring the measurement error effects in the analysis may generally lead to invalid inference results, and meanwhile, we identify situations where ignoring measurement error can still yield consistent estimators. Furthermore, we propose a Bayesian method to address the effects of measurement error under the zero-inflated Poisson model and discuss the identifiability issues. We develop a data-augmentation algorithm that is easy to implement. Simulation studies are conducted to evaluate the performance of the proposed method. We apply our method to analyze the data arising from a prostate adenocarcinoma genomic study.

Performance of Multivariate Homogeneously Weighted Moving Average Chart for Monitoring the Process Mean in the Presence of Measurement Errors

Multivariate control charts are useful tools for monitoring the product quality in which the process outcome is expressed by several correlated variables. The multivariate homogeneously weighted moving average (MHWMA) control chart is one of the most efficient extensions of the multivariate exponentially weighted moving average (MEWMA) procedure. However, this control chart has been proposed under the assumption of precise measurements. This paper explores the impact of the measurement system inability on sensitivity of MHWMA control chart in Phase II monitoring of the mean vector of multivariate normally distributed quality characteristics. Through simulation studies, the run length (RL) properties of MHWMA chart in the presence of measurement errors are investigated and compared to without-error scenario. The results indicate that the imprecise measurements degrade the detection ability of MHWMA control chart in detecting different process disturbances. The undesired impact of gauge measurement errors increases as the error variance increases. Moreover, multiple measurements on each sampled item are utilized to compensate for the undesired effect of the measurement errors on run length characteristics of the MHWMA control chart. It is also concluded that, as the number of measurements on each sampled point increases, the detection capability of MHWMA chart reduces and approaches the without-error case. Finally, a realistic illustrative example from a healthcare system is utilized to elaborate on the impact of imprecise measurements on chart performance.

Scalable Neural Decoder for Topological Surface Codes.

With the advent of noisy intermediate-scale quantum (NISQ) devices, practical quantum computing has seemingly come into reach. However, to go beyond proof-of-principle calculations, the current processing architectures will need to scale up to larger quantum circuits which will require fast and scalable algorithms for quantum error correction. Here, we present a neural network based decoder that, for a family of stabilizer codes subject to depolarizing noise and syndrome measurement errors, is scalable to tens of thousands of qubits (in contrast to other recent machine learning inspired decoders) and exhibits faster decoding times than the state-of-the-art union find decoder for a wide range of error rates (down to 1%). The key innovation is to autodecode error syndromes on small scales by shifting a preprocessing window over the underlying code, akin to a convolutional neural network in pattern recognition approaches. We show that such a preprocessing step allows to effectively reduce the error rate by up to 2 orders of magnitude in practical applications and, by detecting correlation effects, shifts the actual error threshold up to fifteen percent higher than the threshold of conventional error correction algorithms such as union find or minimum weight perfect matching, even in the presence of measurement errors. An insitu implementation of such a machine learning-assisted quantum error correction will be a decisive step to push the entanglement frontier beyond the NISQ horizon.

Sensitivity analysis of error-contaminated time series data under autoregressive models with the application of COVID-19 data

Autoregressive (AR) models are useful in time series analysis. Inferences under such models are distorted in the presence of measurement error, a common feature in applications. In this article, we establish analytical results for quantifying the biases of the parameter estimation in AR models if the measurement error effects are neglected. We consider two measurement error models to describe different data contamination scenarios. We propose an estimating equation approach to estimate the AR model parameters with measurement error effects accounted for. We further discuss forecasting using the proposed method. Our work is inspired by COVID-19 data, which are error-contaminated due to multiple reasons including those related to asymptomatic cases and varying incubation periods. We implement the proposed method by conducting sensitivity analyses and forecasting the fatality rate of COVID-19 over time for the four most populated provinces in Canada. The results suggest that incorporating or not incorporating measurement error effects may yield rather different results for parameter estimation and forecasting.