Presence Of Random Measurement Errors Research Articles

Estimation of Cpm for autocorrelated data in the presence of random measurement errors

Process capability analysis is a widely used process improvement metric. There are several capability indices used in industries to assess the performance of production process. is one of the most important capability index which is often used in many industries for assessing the performance of the production process by taking into consideration the target value. Although capability indices are estimated under the assumption that the data are independent but in many industries, process outputs are often autocorrelated. At the same time, no measuring device gives accurate results. In this paper, we discuss the statistical properties of the estimator of for autocorrelated data and in the presence of random measurement errors. Here, we show that under the combined effect of autocorrelation and measurement errors, the estimator of behaves differently depending upon the variability of the measurement errors.

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.

A note on statistical analysis of C pk for autocorrelated data in the presence of random measurement errors

Process capability indices (PCIs) have been widely used for process performance assessment. It provides a quantitative measure of performance of an industrial production process. Several PCIs have been proposed in the literature. C p k is one of the most useful capability index. Statistical properties of the estimator of C p k have been discussed by many researches under the assumption of identically and independently normal distribution. Some statistical properties of the estimator of C p k for autocorrelated data in presence of gauge measurement errors have studied by Scagliarini (2010). However, we found some critical error in the expression of expectation and variance of the estimator when process is autocorrelated as well as measurement error is present. Through this article, we present a corrected version of expectation and variance of the estimator.

Evaluation and improvement of residence time distribution analysis methods

Although residence time distributions (RTDs) are frequently used in wetland studies, there is no consensus about the analysis method. Generally, two types of methods can be used to analyze RTD data: the method of moments and the RTD modeling method. RTD curves are obtained by tracer tests. The real RTD curves are usually imperfect due to the presence of random measurement errors, the unreasonable sampling intervals, and the premature termination of the tracer test. This study aims to find a better RTD analysis method providing robust results under these unfavorable factors, which includes: (i) evaluating the existing RTD analysis methods; (ii) improving the existing RTD analysis method using the Rational model. The influence of measurement error, sampling interval, and ending time in tracer tests on RTD analysis methods was first simulated. The results showed that effective volume ratio was a preferable indicator compared with the variance of RTD. The stability of the moment method decreased with the increase of the measurement error and sampling interval, and the accuracy of the moment method decreased with the decrease of the test time. Although the RTD modeling method showed better stability and accuracy, the implicit premise is that the RTD model adequately describes the observed data. Further, 36 observed RTD data sets were used to test the Tanks in Series (TIS) model and the empirical Rational model. The results showed that the widely used TIS model was only effective in partial cases, while the newly proposed Rational model showed broader applicability. Both the moment method and the TIS modeling method were proven to be inadequate. Finally, the moment method was improved by using Rational models to pre-process RTD data. Although the improved method is still affected by random measurement errors, it can significantly increase the accuracy of the moment method when sampling points are small or the test ends prematurely.

Real-time algorithm for self-reflective model predictive control

This paper is about a real-time model predictive control (MPC) algorithm for a particular class of model based controllers, whose objective consists of a nominal tracking objective and an additional learning objective. Here, the construction of the learning term is based on an economic optimal experiment design criterion. It is added to the MPC objective in order to excite the system on purpose thereby improving the accuracy of the state and parameter estimates in the presence of incomplete or noise affected measurements. The focus of this paper is on so-called self-reflective model predictive control schemes, which have the property that the additional learning term can be interpreted as the expected loss of optimality of the controller in the presence of random measurement errors. The main contribution is a formulation-tailored algorithm, which exploits the particular structure of self-reflective MPC problems in order to speed-up the online computation. It is shown that the proposed algorithm can solve the self-reflective optimization problems with reasonable additional computational effort and in real-time.

Interpretation of Falling-Head Tests in Presence of Random Measurement Error

Field data are tainted by random and several types of systematic errors. The paper presents a review of interpretation methods for falling-head tests. The statistical robustness of each method is then evaluated through the use of synthetic data tainted by random error. Six synthetic datasets are used for this evaluation. Each dataset has an average relative error for water elevationZ, respectively, of 0.04%, 0.11%, 0.22%, 0.34%, 0.45%, and 0.90% (absolute errors on elevation are, respectively, 0.10, 0.25, 0.50, 1.0, and 2.0 mm for a range of water elevation change of 150 mm during test). Each synthetic dataset is composed of 40 synthetic tests (each test consisting of 18 data couples of synthetic falling-head measurements). Results show that theZ-tmethod is the most accurate and precise, followed by the Hvorslev method when a correction is applied and the velocity method when appropriately interpreted. Advice on how to interpret falling-head tests tainted by random error concludes the study.

Inference on C pk for autocorrelated data in the presence of random measurement errors

The present paper examines the properties of the C pk estimator when observations are autocorrelated and affected by measurement errors. The underlying reason for this choice of subject matter is that in industrial applications, process data are often autocorrelated, especially when sampling frequency is not particularly low, and even with the most advanced measuring instruments, gauge imprecision needs to be taken into consideration. In the case of a first-order stationary autoregressive process, we compare the statistical properties of the estimator in the error case with those of the estimator in the error-free case. Results indicate that the presence of gauge measurement errors leads the estimator to behave differently depending on the entity of error variability.

Normalized sensitivities and parameter identifiability of in situ diffusion experiments on Callovo–Oxfordian clay at Bure site

Diffusion of inert and reactive tracers (DIR) is an experimental program performed by ANDRA at Bure underground research laboratory in Meuse/Haute Marne (France) to characterize diffusion and retention of radionuclides in Callovo–Oxfordian (C–Ox) argillite. In situ diffusion experiments were performed in vertical boreholes to determine diffusion and retention parameters of selected radionuclides. C–Ox clay exhibits a mild diffusion anisotropy due to stratification. Interpretation of in situ diffusion experiments is complicated by several non-ideal effects caused by the presence of a sintered filter, a gap between the filter and borehole wall and an excavation disturbed zone (EdZ). The relevance of such non-ideal effects and their impact on estimated clay parameters have been evaluated with numerical sensitivity analyses and synthetic experiments having similar parameters and geometric characteristics as real DIR experiments. Normalized dimensionless sensitivities of tracer concentrations at the test interval have been computed numerically. Tracer concentrations are found to be sensitive to all key parameters. Sensitivities are tracer dependent and vary with time. These sensitivities are useful to identify which are the parameters that can be estimated with less uncertainty and find the times at which tracer concentrations begin to be sensitive to each parameter. Synthetic experiments generated with prescribed known parameters have been interpreted automatically with INVERSE-CORE 2D and used to evaluate the relevance of non-ideal effects and ascertain parameter identifiability in the presence of random measurement errors. Identifiability analysis of synthetic experiments reveals that data noise makes difficult the estimation of clay parameters. Parameters of clay and EdZ cannot be estimated simultaneously from noisy data. Models without an EdZ fail to reproduce synthetic data. Proper interpretation of in situ diffusion experiments requires accounting for filter, gap and EdZ. Estimates of the effective diffusion coefficient and the porosity of clay are highly correlated, indicating that these parameters cannot be estimated simultaneously. Accurate estimation of D e and porosities of clay and EdZ is only possible when the standard deviation of random noise is less than 0.01. Small errors in the volume of the circulation system do not affect clay parameter estimates. Normalized sensitivities as well as the identifiability analysis of synthetic experiments provide additional insight on inverse estimation of in situ diffusion experiments and will be of great benefit for the interpretation of real DIR in situ diffusion experiments.

Testing process capability based on Cpm in the presence of random measurement errors

Process capability indices have been widely used in the manufacturing industry providing numerical measures on process performance. The index Cp provides measures on process precision (or product consistency). The index Cpm, sometimes called the Taguchi index, meditates on process centring ability and process loss. Most research work related to Cp and Cpm assumes no gauge measurement errors. This assumption insufficiently reflects real situations even with highly advanced measuring instruments. Conclusions drawn from process capability analysis are therefore unreliable and misleading. In this paper, we conduct sensitivity investigation on process capability Cp and Cpm in the presence of gauge measurement errors. Due to the randomness of variations in the data, we consider capability testing for Cp and Cpm to obtain lower confidence bounds and critical values for true process capability when gauge measurement errors are unavoidable. The results show that the estimator with sample data contaminated by the measurement errors severely underestimates the true capability, resulting in imperceptible smaller test power. To obtain the true process capability, adjusted confidence bounds and critical values are presented to practitioners for their factory applications.

Rainfall Estimation from Polarimetric Radar Measurements: Composite Algorithms Immune to Variability in Raindrop Shape–Size Relation

Polarization diversity radar measurements such as reflectivity factor, differential reflectivity, and differential propagation phase are extensively used in rainfall estimation. Algorithms to estimate rainfall from polarimetric radar measurements are based on a model for the raindrop shape as a function of drop diameter. Most of the current algorithms use an equilibrium shape–size model for raindrops. Variation of the prevailing mean raindrop shapes from an assumed model has a direct impact on the accuracy of radar rainfall estimates. This paper develops composite algorithms to estimate rainfall from polarimetric radar data without an a priori assumption about the specific form of mean raindrop shape–size model such as equilibrium shape model. The accuracy of rainfall estimates is evaluated in the presence of random measurement errors as well as systematic bias errors. The composite algorithms, independent of a prespecified raindrop shape model, were applied to radar parameters simulated from disdrometer data collected over 3 months, and the corresponding rainfall estimates were found to be in good agreement with disdrometer estimates. The composite algorithms were also tested with Colorado State University CHILL radar observations of the 28 July 1997 Fort Collins (Colorado) flood event. The storm total precipitation estimates based on the composite algorithms developed in this paper were in much better agreement with rain gauge estimates in comparison with conventional algorithms.

Statistical inference for the area under the receiver operating characteristic curve in the presence of random measurement error.

The area under the receiver operating characteristic curve is the most commonly used measure of the ability of a biomarker to distinguish between two populations. Some markers are subject to substantial measurement error. Under normality assumptions, the authors develop a confidence interval procedure for the area under the receiver operating characteristic curve that adjusts for measurement error. This procedure assumes the availability of data from a reliability study of the biomarker. A simulation study was used to check the validity of the proposed confidence interval. Furthermore, it was shown that not adjusting for measurement error could result in a serious understatement of the effectiveness of the biomarker.

Optimal infrastructure management decisions under uncertainty

The planning of maintenance and rehabilitation activities for transportation facilities uses information on facility condition from two sources: measurement and forecasting. Both of these sources are characterized by the presence of significant uncertainties, which have important life-cycle cost implications. State-of-the-art decision-making models ignore the uncertainty either in one or both sources of information. This paper presents a methodology (the Latent Markov Decision Process) that explicitly recognizes the presence of random measurement errors in the measurement of facility condition. The methodology can also be used to quantify the “value of more precise information,” which allows an agency to evaluate measurement technologies of different precisions and costs. A parametric study, which demonstrates such an evaluation in the case of highway pavements, is performed.

Measurement error in causal analysis of panel data: Attenuated versus inflated relationships

The presence of random measurement error is commonly thought to cause attenuation of statistical relationships. While this is an unquestionable truth in bivariate analysis, it cannot be generalized to the multivariate case without qualification. This paper shows that measurement error may give rise to overestimates of parameters in causal analysis whenever there is more than one independent variable and the independent variables are correlated. If the independent variables are not measured with the same amount of reliability, there may also be considerable error in estimates of the relative magnitude of their impact. Both problems are particularly serious when the amount of measurement error is large relative to some of the causal effects such as in panel analysis with lagged dependent variables.

Assessing the validity of the achievement motive in the presence of random measurement error.

The presence of random measurement error in indicators of theoretical constructs biases observed estimates of relations among those constructs. Correcting for this bias is particularly important when random measurement error is substantial, or is substantially different for indicators of distinct constructs included in a theoretical model. Validity assessment in the case of thematic apperceptive measures of the achievement motive (TAT n Achievement) has been vulnerable to interpretive errors because these indicators of the achievement motive are typically much less reliable than indicators of other constructs to which the motive may be related, and no correction has been made for the bias introduced by such differential measurement error. Here we illustrate a causal modeling approach to validity assessment for TAT n Achievement that incorporates explicit true-score measurement models of theoretical constructs. We confirm the hypothesis that the achievement motive construct is positively related to work satisfaction in a representative sample of adult males in the United States, taken in 1976 (N = 413). Evidence for the discriminant validity of story content versus story length, an issue raised in the literature on the TAT, is also presented in this nomological network.

Assessing the validity of the achievement motive in the presence of random measurement error.

Assessing the validity of the achievement motive in the presence of random measurement error.