In this work, we study the joint distribution function as well as the copula of (X-Z; Y ) where the random vector (X; Y; Z) is characterized by a copula CX; Y; Z. We use this copula to analyze a measurement error model. Some theoretical results, several examples as well as a simulation study are proposed for illustration.

In this work, we consider the joint distribution function as well as the copula of $(X+Z,Y)$ where the random vector $(X, Y, Z)$  is characterized by a copula $C_{X,Y,Z}$. We use this copula to analyze a Berkson measurement error model. By presenting a general form of a Berkson measurement error model with copula-dependent random variables, we investigate some of its special cases. Some theoretical results, several examples as well as a simulation study, are proposed for illustration.

Annual estimation of average household incomes is one of the main goals of the household income and expenditure survey in Iran. So, regarding importance of accuracy of gathered data and reasons that lead to error in measuring household income, in this paper, model-based methods are used for estimating income measurement error and adjusting sample households declared income for 2011 household income and expenditure survey.

Functional MRI is a noninvasive method in brain imaging. Localization, classification, prediction and connectivity are the most common issues. Functional connectivity is a branch of fMRI that focuses on connectivity between voxels and ROIs. There are several methods for investigating functional connectivity such as correlation analysis. In any field, it is very important that results of any research have reliability according to the experiment. Any methods and measurement instruments need to be reliable. Without reliability, results are meaningless and our research is not trustworthy. Brain imaging can be used as a valuable tool for pre-surgical planning, so the results should be highly reproducible. Test-retest reliability can be explored using the intra-class correlation coefficient (ICC). I2C2 is an extent of ICC to verify the reliability in high-dimensional data as imaging studies. 13 subjects of testretest resting-state fMRI are used to investigate reliability. I2C2 of four ROIs are also computed (Caudate, Cingulate, Cuneus and Precentral regions). Functional connectivity is found to have moderate reliability ranging 0. 6244 to 0. 6941. 95% confidence interval of I2C2 is calculated by nonparametric bootstrap in which CI of Caudate region I2C2 has the shortest length.

In statistical process control, measurement error plays a key role that is usually ignored. measurement error can yield incorrect conclusions about the performance of the process. This study examined the e, ect of measurement error on the shift detection ability of the mixed Exponentially Weighted Moving Average-Cumulative Sum (EWMA-CUSUM) control chart. Then, it investigated the performance of the mixed EWMA-CUSUM chart in case of mean shift through (i) covariate method, (ii) multiple measurement method, and (iii) linearly increasing variance method. The performance measurement tools such as Average Run Length (ARL) and Standard Deviation of Run Length (SDRL) were estimated using the Monte-Carlo simulation method. It was concluded that the performance of the mixed EWMA-CUSUM control chart was adversely a, ected by considering the measurement error. It was revealed from the comparative study that the mixed EWMA-CUSUM control chart outperformed the EWMA and CUSUM control charts in the presence of measurement error. An illustrative example was presented to demonstrate the performance of control charts in case of measurement error.

Uncertainty is an inherent characteristic of biological and geospatial data which is almost made by measurement error in the observed values of the quantity of interest. Ignoring measurement error can lead to biased estimates and inflated variances and so an inappropriate inference. In this paper, the Gaussian spatial model is fitted based on covariate measurement error. For this purpose, we adopt the Bayesian approach and utilize the Markov chain Monte Carlo algorithms and data augmentations to carry out calculations. The methodology is illustrated using simulated data.

Semiparametric linear mixed measurement error models are extensions of linear mixed measurement error models to include a nonparametric function of some covariate. They have been found to be useful in both cross-sectional and longitudinal studies. In this paper first we propose a penalized corrected likelihood approach to estimate the parametric component in semiparametric linear mixed measurement error model and then using the case deletion and subject deletion analysis we survey the influence diagnostics in such models. Finally, the performance of our influence diagnostics methods are illustrated through a simulated example and a real data set.

Process Capability Indices (PCI) show that the process conforms to the specification limits,when the product quality depends on more than one characteristic, Multivariate Process Capability Indices (MCPI) are used. By modifying the process capability indices, the process incapability indices are created,these indices then provide information about the accuracy and precision of the process separately. In the real world, in most cases, the parameters cannot be specified precisely,therefore, the use of fuzzy sets can solve this problem in statistical quality control. The purpose of this paper is to present, for the first time, a Multivariate Process Incapability Index by considering the measurement error in a fuzzy environment. The presented index is shown for practical examples solved by considering Triangular Fuzzy Numbers,then the capability of the model is compared to the time when fuzzy logic is not used. The obtained results emphasize that ignoring the measurement error also leads to the incorrect calculation of process capability, causing a lot of damage to manufacturing industries, especially high-tech ones.