Abstract
It becomes very difficult to collect reliable data related to some social problem, which are sensitive in nature. When resistance is encountered, the usual modification of the survey method is simply an added effort on the part of the interviewer to gain the confidence of the interviewee. Singh and Joarder [14] propose an Optional Randomized Response Technique (ORRT) in SRSWR, which is always efficient than Eichhorn and Hayre [5] multiplicative scrambled response method. Keeping this in view, we propose a set of alternative estimators in multi-character surveys using ORRT to estimate the population total corresponding to usual estimators in probability proportional to size without replacement sampling design. and derived the expressions for MSE under the model. An empirical study has also been carried out to examine their performance.