Presence Of Measurement Errors Research Articles

Novel combined Shewhart-CUmulative EWMA-SUM mean charts without- and with measurement error

The precision of process monitoring often encounters challenges in determining the exact shift size. Therefore, combined control charts have gained considerable attention because of their excellent speed to detect simultaneously small-to-moderate and large-size shifts. The effectiveness of the applied quality control methods strongly depends on the performance of the measurement system. Measurement error presence contributes significantly negatively toward the performance of the usual control charting schemes. This article proposes novel two-sided combined Shewhart-Cumulative EWMA-sum (Shewhart-CUESUM) control charts designed to efficiently monitor the mean of normally distributed processes. In addition, to address measurement errors, the M-Shewhart-CUESUM chart is proposed, incorporating an additive measurement error model. Evaluation of the charts through Monte-Carlo simulations, considering metrics such as average run length (ARL), extra quadratic loss, relative ARL, and performance comparison index. It is found that the combined Shewhart-CUESUM outperforms than CUESUM chart. The results show that the presence of measurement errors can significantly diminish the charts’ performance, which can be mitigated by utilizing a multiple measurements scheme. Among the different well-established combined charts examined, the M-Shewhart-CUESUM chart shows considerably more sensitive to detecting simultaneously detect small and large size shifts. To employ simulated datasets to illustrate the impact of measurement errors and demonstrate the implications of the proposed charts on process mean shifts.

Calibration estimator for a sensitive variable using dual auxiliary information under measurement errors

In survey research, it is commonly assumed that all the observations are measured accurately. However, in practice, this assumption is not achieved due to many reasons, so it causes measurement errors to be inevitably present in the sample estimation. This article addresses the problem of estimation of finite population mean under stratified random sampling in the presence of measurement errors. A calibration estimator is proposed for the sensitive variable by utilizing suitable calibration techniques, which can be applied to obtain the optimal strata weight. The calibration estimator not only incorporates the auxiliary information but also the ranks of the auxiliary variable. Expressions for bias and mean square error are derived up to first order of approximation. Simulation studies and real-life datasets are used to assess the performances of the proposed estimator by comparing them with the contemporary estimators in the presence and absence of measurement errors. The theoretical and empirical studies demonstrate that the proposed calibration estimator consistently outperforms classical mean, usual ratio, conventional difference, Khail randomized response estimators.

Inspection policy optimization for hierarchical multistate systems under uncertain mission scenarios: A risk-averse perspective

Most engineered systems intend to perform missions with a pre-specified target success probability to reduce undesirable failure risks. Before executing the next mission, inspection activities are conducted across various physical levels for assessing the probability of mission success. However, due to the randomness of a system’s degradation behavior and the presence of measurement errors, inspection results inevitably contain uncertainty. Meanwhile, mission durations and acceptable system states may also be uncertain, due to uncontrollable factors, such as random operating environments and mission demands. In such a circumstance, it is of great significance to identify the optimal multilevel inspection policy to answer, as great confident as possible, the question that the system can complete the next mission with a target mission success probability. This paper develops a novel metric to gauge the effectiveness of a multilevel inspection policy to assess if the system can complete the next mission with a pre-specified target success probability from a risk-averse perspective, based on which an optimization method is proposed to seek an inspection policy under uncertain scenarios with the aim of minimizing the maximum regret of the proposed metric. A stochastic fractal search algorithm, along with two tailored local search rules, is designed to efficiently resolve the resulting optimization problem. Two cases, including a three-component system and a rocket fueling mechanism’s control system, are used to illustrate the efficacy of the proposed approach, which is capable of effectively identifying the risk of mission failures by inspection policies.

Single-Shot Decoding of Good Quantum LDPC Codes

Quantum Tanner codes constitute a family of quantum low-density parity-check codes with good parameters, i.e., constant encoding rate and relative distance. In this article, we prove that quantum Tanner codes also facilitate single-shot quantum error correction (QEC) of adversarial noise, where one measurement round (consisting of constant-weight parity checks) suffices to perform reliable QEC even in the presence of measurement errors. We establish this result for both the sequential and parallel decoding algorithms introduced by Leverrier and Zémor. Furthermore, we show that in order to suppress errors over multiple repeated rounds of QEC, it suffices to run the parallel decoding algorithm for constant time in each round. Combined with good code parameters, the resulting constant-time overhead of QEC and robustness to (possibly time-correlated) adversarial noise make quantum Tanner codes alluring from the perspective of quantum fault-tolerant protocols.

The performance of the one-sided truncated exponentially weighted moving average X ¯ control chart in the presence of measurement errors

When the direction of a potential mean shift can be anticipated, the one-sided exponentially weighted moving average (EWMA) X ¯ control chart using the truncation method (namely, the one-sided TEWMA X ¯ chart) is more efficient than those conventional one- and two-sided EWMA X ¯ schemes for process monitoring. Although attractive, there are no studies on designing the one-sided TEWMA X ¯ chart by taking measurement errors into account. In this context, we investigate the effect of measurement errors on the performance of the one-sided TEWMA X ¯ chart based on the linear covariate error model. Additionally, a Markov chain model is established to evaluate the run length properties of the scheme in the presence of measurement errors. Then, an optimal design procedure is developed for searching the optimal design parameters of the scheme. Based on these mentioned studies, several tables and figures are presented to evaluate the detecting performance of the scheme under different parameters of the linear covariate error model, and then a conventional one-sided EWMA X ¯ chart with reflecting boundary is introduced to further study the effect of the presence and absence of measurement errors on control chart comparison studies. Simulation results show that although the detecting performance of the proposed scheme is significantly affected by measurement errors, its performance is still superior to the classic competing chart under the same comparison conditions. Finally, an illustrative example is given to show the implementation of the recommended scheme.

Generalized Estimator of Population Mean Using Auxiliary Information in Presence of Measurement Errors

It is assumed in survey research that the respondent’s reported response is precise. More often, due to prestige bias, the data provided by respondents frequently include estimates that are significantly different from the genuine values. As a consequence, measurement error is present in the sample estimates that may affect the results. Therefore, this study illustrates an improved generalized estimator that utilizes auxiliary data under measurement error. A numerical study to establish its effectiveness is also conducted.

Spatial classification in the presence of measurement error

In recent decades, spatial classification has received considerable attention in a wide array of disciplines. In practice, binary response variable is often subject to measurement error, misclassification. To account for the misclassified response in spatial classification, we proposed validation data-based adjustment methods that use interval validation data to rectify misclassified responses. Regression calibration and multiple imputation methods are utilized to correct the misclassified outcomes at the locations where the gold-standard device is not available. Generalized linear mixed model and indicator Kriging are applied for spatial classification at unsampled locations. Simulation studies are performed to compare the proposed methods with naive methods that ignore the misclassification. It was found that the proposed models significantly improve prediction accuracy. Additionally, the proposed models are applied for precipitation detection in South Korea.

Testing for Threshold Regulation in Presence of Measurement Error

Testing for Threshold Regulation in Presence of Measurement Error

On the Selection of Item Scores or Composite Scores for Clinical Prediction

Recent shifts to prioritize prediction, rather than explanation, in psychological science have increased applications of predictive modeling methods. However, composite predictors, such as sum scores, are still commonly used in practice. The motivations behind composite test scores are largely intertwined with reducing the influence of measurement error in answering explanatory questions. But this may be detrimental for predictive aims. The present paper examines the impact of utilizing composite or item-level predictors in linear regression. A mathematical examination of the bias-variance decomposition of prediction error in the presence of measurement error is provided. It is shown that prediction bias, which may be exacerbated by composite scoring, drives prediction error for linear regression. This may be particularly salient when composite scores are comprised of heterogeneous items such as in clinical scales where items correspond to symptoms. With sufficiently large training samples, the increased prediction variance associated with item scores becomes negligible even when composite scores are sufficient. Practical implications of predictor scoring are examined in an empirical example predicting suicidal ideation from various depression scales. Results show that item scores can markedly improve prediction particularly for symptom-based scales. Cross-validation methods can be used to empirically justify predictor scoring decisions.

Value‐at‐Risk under Measurement Error

We propose a method for estimating Value‐at‐Risk that corrects for the effect of measurement errors in stock prices. We show that the presence of measurement errors might pose serious problems for estimating risk measures. In particular, when stock prices are contaminated, existing estimators of Value‐at‐Risk are inconsistent and might lead to an underestimation of risk, which can result in extreme leverage ratios within the held portfolios. Using a Fourier transform and a deconvolution kernel estimator of the probability distribution function of actual latent prices, we derive a robust estimator of Value‐at‐Risk in the presence of measurement errors. Monte Carlo simulations and real data analysis illustrate satisfactory performance of the proposed method.

Robo-advising: Optimal investment with mismeasured and unstable risk preferences

We develop a robo-advising framework that incorporates interactions with a client who has time-varying risk preferences that can be mismeasured. In the presence of measurement error, a client’s welfare decreases compared to perfect measurements. The worse the quality of the measurements (higher measurement volatility), the worse this is for the client. When measurements are more volatile, interacting frequently can lead to further losses in a client’s welfare. We include a client’s willingness to interact using a budget constraint. A trade-off arises between interacting frequently to obtain up-to-date information with more volatile measurements versus less up-to-date information with more accuracy. We find that integrating client-initiated interactions and using an average of measured risk aversions both lead to more personalised investment advice. Using an alternative investment strategy rather than a time-consistent strategy can lead to improved welfare for the client.

Monitoring the process mean under the Bayesian approach with application to hard bake process

This study introduces the Bayesian adaptive exponentially weighted moving average (AEWMA) control chart within the framework of measurement error, examining two separate loss functions: the squared error loss function and the linex loss function. We conduct an analysis of the posterior and posterior predictive distributions utilizing a conjugate prior. In the presence of measurement error (ME), we employ a linear covariate model to assess the control chart's effectiveness. Additionally, we explore the impacts of measurement error by investigating multiple measurements and a method involving linearly increasing variance. We conduct a Monte Carlo simulation study to assess the control chart's performance under ME, examining its run length profile. Subsequently, we offer a specific numerical instance related to the hard-bake process in semiconductor manufacturing, serving to verify the functionality and practical application of the suggested Bayesian AEWMA control chart when confronted with ME.

Nonparametric estimation of a survival function in the presence of measurement errors on the failure time of interest

AbstractThis article discusses nonparametric estimation of a survival function in the presence of measurement errors on the observation of the failure time of interest. One situation where such issues arise would be clinical studies of chronic diseases where the observation on the time to the failure event of interest such as the onset of the disease relies on patient recall or chart review of electronic medical records. It is easy to see that both situations can be subject to measurement errors. To resolve this problem, we propose a simulation extrapolation approach to correct the bias induced by the measurement error. To overcome potential computational difficulties, we use spline regression to approximate the unspecified extrapolated coefficient function of time, and establish the asymptotic properties of our proposed estimator. The proposed method is applied to nonparametric estimation based on interval‐censored data. Extensive numerical experiments involving both simulated and actual study datasets demonstrate the feasibility of this proposed estimation procedure.

Memory-type variance estimators using exponentially weighted moving average statistic in presence of measurement error for time-scaled surveys

The present study suggested memory-type ratio and product estimators for variance estimation in the presence of measurement errors. We applied the exponentially weighted moving averages statistic which simultaneously utilizes the current and prior information for better estimation in surveys based on the time-scale. The expressions of approximate mean square errors of memory-type estimators are derived using Taylor series up to first order. Mathematical conditions are also obtained for which the suggested memory-type ratio and product estimators perform better than the conventional ratio and product estimators. The efficiency of the proposed estimators is observed using an extensive simulation study in the presence of measurement errors. A real data application is also carried out to support the mathematical expressions. From the results, it is shown that the use of prior sample information significantly increased the efficiency of the proposed estimators.

Measuring One-Sided Process Capability Index for Autocorrelated Data in the Presence of Random Measurement Errors

Abstract Many quality characteristics in manufacturing industry are of one sided specifications. The well-known process capability indices C P ⁢ U C_{PU} and C P ⁢ L C_{PL} are often used to measure the performance of such type of production process. It is usually assumed that process observations are independent and measurement system is free of errors. But actually in many industry it has been proven that auto-correlation is an inherent nature of the production process, especially for chemical processes. Moreover, even with the use of highly sophisticated advanced measuring instruments some amount of measurement error is always present in the observed data. Hence gauge measurement error also needs to be considered. In this paper we discuss some inferential properties of one-sided process capability indices for a stationary Gaussian process in the presence of measurement errors. As a particular case of a stationary Gaussian process, we discuss the case of a stationary AR ⁡ ( 1 ) \operatorname{AR}(1) process where measurement error follows an independent Gaussian distribution.

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

In a classification scenario, we usually come across data with and without class labels. If the class labels of individuals are unknown or masked by hidden components, the classifier rules must include the identification of the actual number of subcomponents in the data. Also, the presence of measurement errors in the data may influence the measures of the receiver operating characteristic model. In this paper, a mixture of multivariate receiver operating characteristic models is proposed to deal with multi-model patterns in the data, and a bias-corrected estimator is derived for estimating the area under the curve of the proposed model. The proposed methodology is supported by the real dataset and simulation studies.

Vault Height Is a Key Predictive Factor for Anterior Segment Measurement Error by IOLMaster 700 in Eyes With Phakic Intraocular Lens.

To identify risk factors of ocular anterior segment measurement error by the IOLMaster 700 in eyes implanted with an implantable Collamer lens (ICL). In total, 152 patients with clear lens (152 eyes, group 1) and another 32 cataract patients (57 eyes, group 2) who underwent ICL implantation were included, and the presence of measurement error by the IOLMaster 700 was determined based on B-scan images. The risk factors for measurement error were evaluated by logistic regression, and the optimal threshold was determined using receiver operating characteristic analysis. The ICL was misidentified as the anterior surface of the crystalline lens in 51.97% of eyes (79/152) in group 1 and 80.70% of eyes (46/57) in group 2. For every 100-µm decrease in the vault height, a 3.57- and 5.78-fold increase in the risk of measurement error was observed in group 1 and group 2, respectively. We identified an optimal threshold of the vault height at 389.47 µm for predicting biometric measurement error in eyes implanted with ICL, which showed an area under the curve of 0.93 (95% confidence interval, 0.90-0.97), a sensitivity of 0.87, and a specificity of 0.86. Patients with ICL implantation, particularly those with a vault height less than 389.47 µm, are at a greater risk of anterior segment biometric measurement error by the IOLMaster 700. The threshold of vault height can help to identify high-risk patients and further optimize biometric measurement.

Stages and main tasks of the century-long the control theory and system identification development. Part I. State space method in the theory of linear automatic control systems

This article opens a series of publications dedicated to the scientific and technical achievements of the century-long development of control theory and methods. Problems that could not be fully resolved based on one approach or another are also noted. The first of these articles is devoted to the state space method, which began to actively develop somewhere in the 70-80s of the last century within the framework of systems theory and general systems theory. A description of the method is given in relation to linear automatic control systems. A generally accepted description of controlled and observable dynamic processes in such systems is given. The problems of synthesis of stabilizing control in closed loop systems with feedback based on the theory of stability formulated by Lyapunov are mainly considered. In addition to stability, within the framework of the state space method, such important qualitative properties as controllability and observability are formulated. The most developed method is the synthesis of state-based linear controllers. Among them, a special pole placement by method of modal control synthesis occupies a special place which is considered within the framework of the Jordan implementation and various modifications of the method depending on the dimension of the control vector. The synthesis of an optimal controller with a quadratic criterion of a fairly general form is considered. In case of incomplete measurements, when the dimension of the output is less than the dimension of the state vector, in order to implement synthesized control laws based on the state, it becomes necessary to include a state estimator in the control system. In the deterministic case, you can use the Luenberger estimator described in the article, and in the presence of measurement errors in the form of zero-mean white noise, the widely used Kalman filter, also presented in the article. The output control method was not left unattended in the work. The conclusions give the advantages and disadvantages of control methods based on state-space descriptions.

Estimation of Finite Population Variance Under Stratified Sampling in the Presence of Measurement Errors

ABSTRACT Measurement errors may significantly distort the properties of an estimator. In this paper, estimators of the finite population variance using the information on first and second raw moments of the study variable are developed under stratified random sampling that incorporate the variance of a measurement error component. Additionally, combined and separate estimators are also developed for estimating the finite population variance using supplementary information in terms of one or two auxiliary variables. An empirical study is carried out to study the effect of measurement error on the relative efficiencies of the proposed estimators.

Density estimation and regression analysis on hyperspheres in the presence of measurement error

AbstractThis paper studies density estimation and regression analysis with data observed on a general unit hypersphere and contaminated by measurement errors. We establish novel density and regression estimators, and study their asymptotic properties such as the rates of convergence and asymptotic normality. We also provide two types of asymptotic confidence intervals for both density and regression functions. One type is based on the asymptotic normality of their estimators and the other type is based on the empirical likelihood technique. We present practical details on the implementation of our method as well as simulation studies and real data analysis.