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.

Indirect measurement of soil electrical conductivity (EC) has become a major data source in spatial/temporal monitoring of soil salinity. However, in many cases, the weak correlation between direct and indirect measurement of EC has reduced the accuracy and performance of the predicted maps. The objective of this research was to estimate soil EC based on a general linear model via using several soil properties. Through calibration equations, the error involved in such model-based data was calculated and employed in mapping soil EC using kriging with measurement errors (KME) method. The results were then compared with those of ordinary kriging (OK) and co-kriging (CK). Soil samples were taken from the depth of 0-20 cm in 78 points with spatial intervals of 500 m from an area of 40 km2, and they were analyzed for their electrical conductivity (EC) and certain other soil properties. Measured soil EC data (hard data) and auxiliary soil data were further used to develop the semi-variance and cross-semi-variance functions,moreover, soil salinity prediction was done on a grid of 100 m with OK and CK methods. Afterwards, the most optimal EC estimation model was developed using auxiliary soil data and GLM. As predicted values always involve uncertainty, the error involved with the predicted values was calculated and then the calibration equations were adjusted. Lastly, soil salinity was predicted using KME method. Results showed that the OK method had the lowest MSE and RMSE values, 0. 65 and 0. 8 dS m-1, respectively. Furthermore, among the auxiliary data, pH and silt content resulted in some of the best cross-semi-variance functions, among which, silt had a better performance regarding the spatial prediction of soil EC. The GLM model developed with the calculated error and KME resulted in predictions close to those of OK method (with MSE and RMSE of 0. 74 and 0. 86 dS m-1, respectively). KME method provided the possibility of merging error resulting from the use of soft data, derived from prediction equations,therefore, it successfully improved the spatial prediction of soil electrical conductivity

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.

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.

Risk assessment processes refer to a set of actions aimed at identifying, analyzing, and managing risks in various workplaces. These processes are a proactive approach to controlling workplace hazards. In fact, risk assessment forms the basis for decision-making in developing occupational safety and health strategies. This can lead to the promotion of a safety culture, employee participation in safety and health programs, and ultimately, the prevention and reduction of occupational accidents (1, 2). Hospitals are among the most challenging work environments, exposing employees to a wide range of hazards that can lead to numerous occupational accidents. Particularly notable are accidents resulting from human error in these dynamic settings (2). Risk assessment in hospitals is critically important and plays a key role in improving the quality of healthcare services, ensuring the safety of patients and staff, and managing resources. This process helps to identify and analyze potential hazards that may expose patients to harm. By identifying these risks, hospitals can implement preventive measures to mitigate them. Additionally, hospital staff are exposed to various hazards. Risk assessment helps identify these hazards and can lead to the design of a safe working environment and improved working conditions for employees. Moreover, by identifying and managing risks, hospitals can enhance the quality of services provided to patients. Risk assessment also assists in identifying weaknesses in compliance with regulations and can help hospitals maintain necessary licenses and accreditation (3).