This thesis addresses the challenges of collecting accurate information on sensitive variables by employing randomized response technique (RRT).Conventional survey methods often suffer from non-response and misreporting, while RRT protect respondent privacy and reduce bias. In Chapter 1, the background, motivation and objectives of the study are outlined, emphasizing the need for more efficient estimators in sensitive surveys. In Chapter 2, a scrambled randomized response model is proposed by introducing correlated scrambling variables. Theoretical derivations and numerical illustration confirm that the estimator is unbiased and its variance is shown to be lower than competitor estimator. In Chapter 3, the methodology is extended to simultaneous estimation of means of two sensitive variables case. The proposed estimators are unbiased and efficiency comparisons highlight their superiority over earlier models. In Chapter 4, contains the conclusion and future recommendations. Overall, the research contributes novel uni-variate and bivariate scrambled response models that enhance respondent confidentiality while improving efficiency of the estimators in survey methodology.