Generalized Linear mixed models (GLMMs) are common methods for the analysis of clustered data. In many longitudinal and hierarchical epidemiological frameworks, accurate measurements of variables are invalid or expensive to be obtained and there might be situations that both the response and covariate variables are likely to be mismeasured. Insensitivity of errors in either covariate or response variable is, not always plausible. With nonLinear regression models for the outcome process, classification errors for binary responses and measurement error in covariates basically needs to be accounted for in order to make conclusive inferences. In this article, we provide an approach to simultaneously adjust for non-differential misclassification in the correlated binary response and classical measurement error in the covariates, using the multivariate Gauss-Hermite quadrature technique for the approximation of the likelihood function. Simulation studies are then conducted to inform the effects of correcting for measurement error and misclassification on the estimation of regression parameters. The application of the multivariate Gauss-Hermite quadrature method in the conjunction of measurement error and misclassification problems is further highlighted with real-world data based on a multilevel study of contraceptive methods used by women in Bangladesh.

In recent years, some researches have been done on simultaneous monitoring of multivariate process mean vector and covariance matrix. However, the effect of measurement error, which exists in many practical applications, on the performance of these control charts is not well studied. In this paper, the effect of measurement error with Linearly increasing variance on the performance of ELR control chart for simultaneous monitoring of multivariate process mean vector and covariance matrix is investigated. The multiple measurement approach is also extended to reduce this effect. Also, the performance of the proposed multiple measurement approach is evaluated in terms of average run length (ARL) and standard deviation run length (SDRL). Finally, the application of the proposed monitoring method is illustrated by a real data in manufacturing industry.

This paper introduces a model to make decision on the maintenance of a mechanical component subject to condition monitoring. A stochastic model is used to determine what maintenance action should be taken at a monitoring check and the follow up inspection times. The condition of component has a stochastic relation with measurements. A new state space model is developed and used, to predict the hazard rate and condition monitoring measurements, to indirectly asses the hazard rate of the system. The Proportional covariate model (PCM) which was proposed by Yong Sun (2004) was also used to develop the model. The known Kalman Filter was employed to derive the probability of the conditional hazard rate, which is predicted and updated for condition monitoring. The maintenance is being performed based on the estimated hazard rate so that the desired level of reliability is achieved, in a cost effective approach. This approach is validated by using the experimental data obtained from gearboxes which ran and failed on the Mechanical Diagnostic Test Bed (MDTB) at the Penn State University Applied Research Laboratory.