The issue of survey nonresponse causes substantial effects on the reliability, together with validity of study findings. This research develops precise estimation methods for two distinct nonresponse situations: when nonresponse happens to primary survey variables like the number of students, and when nonresponse includes survey variables together with the accompanying auxiliary variables. The proposed estimators receive full a performance assessment through derived equations for bias and mean square error (MSE) based on first-order approximation. The accuracy and reliability assessment depends heavily on MSE calculations, since this method effectively merges systematic error measurements with random error measurements. The MSE values of different estimators receive numerical evaluation through a comparative analysis under equivalent operational conditions for assessing proposed estimator performance outcomes. The research seeks to find the estimator with the minimal MSE because this selection results in the most trustworthy estimates under nonresponse conditions. All the findings from this study create important guidelines for building educational survey designs.

This study presents the development of a novel distribution through a transformation involving error functions, namely the error function inverse Weibull model, along with an overview of the fundamental characteristics of the proposed model. The hazard function of the recommended model is very flexible; it fits increasing, decreasing, and unimodal factors. For estimating the unknown parameters, we suggested two estimation methods, including the maximum likelihood estimation and Bayesian techniques. We perform a Monte Carlo simulation analysis to assess the stability of the parameter estimation procedure. The numerical results of these simulations show that the Bayesian technique under the square error loss function performs better than another method to obtain the model parameters. We thoroughly examine the significance of the proposed model and illustrate its application using three real-world data sets from the industrial sector. We compared the suitability and flexibility of the suggested distribution with several others, and the results showed that it fits the real-world data better than the competing models.