<p>Missing data poses a critical challenge in survey-based research, particularly in time scaled surveys where incomplete observations can compromise both inference and efficiency. While ranked set sampling is known to improve estimator precision relative to simple random sampling, its benefits are diminished when data are missing. To address this issue, we introduce a new class of memory-based logarithmic imputation techniques designed specifically for handling missing values within the ranked set sampling framework. These imputation methods leverage exponentially weighted moving average statistic to recover missing responses, thereby enhancing estimator reliability. We develop the corresponding estimators and derive their theoretical properties, including bias and mean square error to the first order of approximation. The practical performance of the proposed methods is demonstrated through real-data applications and comprehensive simulation studies across varied missingness scenarios. The results clearly indicate that memory-type logarithmic imputation substantially improves data completeness and estimation accuracy, reinforcing its value for time-scaled surveys conducted using ranked set sampling.</p>