Monitoring population mean using EEWMA and DEWMA control charts for calibration estimators

Auxiliary information plays a very vital role in estimating parameters within heterogeneous populations. In survey sampling, calibration techniques are widely used to incorporate such information, thereby improving the accuracy of population parameter estimates. In this study, we have utilized the calibration estimators within a stratified sampling framework. Furthermore, the extended exponentially weighted moving average (EEWMA) and double exponentially weighted moving average (DEWMA) statistic are commonly employed to detect shifts in ongoing processes. We utilized both EEWMA and DEWMA statistic to estimate the population mean in the context of calibration estimation. Our simulation study focused on evaluating the performance of calibrated ratio, exponential, and log ratio estimators using EEWMA and DEWMA statistic. Control limits were developed, and the average run length (ARL) and standard deviation of run length (SDRL) were also computed by varying the smoothing parameters ( λ ₁ and λ ₂ ) considering different magnitudes of mean shifts. The EEWMA and DEWMA statistic were found to be effective in assessing the performance of the calibrated estimators. Additionally, a comparative and practical analysis demonstrated that the calibrated exponential ratio estimator under EEWMA and DEWMA statistic outperformed the other estimators in detecting process shifts.