Development of Efficient Transformed Ratio-Type Estimators for Finite Population Mean with Engineering Applications

The efficient estimation of a finite-population mean can be materially improved when reliable auxiliary information is available and appropriately incorporated into the estimator. This study develops two flexible families of estimators under simple random sampling without replacement. Each family combines ratio- and exponential-type structures with optimized linear correction terms and one of seven parameterized transformations of the auxiliary mean. Unlike conventional approaches that introduce individual transformations separately, the proposed framework unifies the influence of different auxiliary transformations through a common transformation-error factor gm, allowing the effect of each transformation on auxiliary variability and covariance structure to be systematically evaluated. First-order Taylor linearization is used to derive the bias and mean squared error (MSE) of every family member, closed-form expressions for the MSE-minimizing constants, and general dominance conditions relative to the sample mean, ratio, product, regression, exponential, and recent hybrid estimators. The numerical assessment has two components. First, a Monte Carlo experiment evaluates empirical MSE and percent relative efficiency (PRE), defined from the average squared difference between each estimate and the true finite-population mean, for small, medium, and large samples under low, moderate, and high correlations. A feasible plug-in implementation is used when an optimal constant contains the unknown population mean. The simulation analysis further demonstrates that estimator performance is not universally determined by a single transformation; rather, efficiency depends jointly on the correlation structure, sample size, and appropriate selection of the transformation factor. Second, five engineering-domain populations are examined using the population summaries and PRE values reported in the source study; corresponding MSE values are recovered from the variance of the sample mean. The simulations show that efficiency gains depend jointly on the correlation strength, sample size, and transformation choice. Proposed estimators are competitive across all scenarios and are particularly effective under moderate-to-high correlation, although the regression estimator remains difficult to improve upon in some settings. The engineering applications indicate larger gains for selected transformed estimators, but these results should be interpreted as first-order, population-summary-based comparisons. The proposed methodology therefore provides a unified and analytically tractable extension of transformed ratio-exponential estimation, while highlighting the importance of data-informed transformation selection in practical applications.