- This thesis is a study on the Dorfman-Sterrett group-screening designs assuming equal a-prior probabilities of items being defective. Based on a clear theoretical framework, we have studied both restricted and unrestricted Dorfman-Sterrett procedure without and without errors in decision, deriving expressions for expected number of tests (and cost functions), which are used to compare the performance of this procedures with the Dorfman procedure. \lVehave give an alternative approach to determining the expected number of tests in an unrestricted Dorfman-Sterrett design. The restricted Dorfman-Sterrett procedure without errors in decision has also be examined, giving conditions under which the restricted procedure converges to the unrestricted procedure. vVe have shown that for most prevalence rates, the two-stage Dorfman-Sterrett procedure performs just as well as the unrestricted procedure. We have in this thesis also examined the Restricted Dorfman-Sterrett procedure with error in decision. Expressions for the expected number of runs and cost functions have been derived. The results, based on the expected proportional red uct.ion in testing over individual testing, indicate that the single-step Dorfman-Sterrett procedure performs better than the Dorfman procedure for all the prevalence rates less than 30%. The result.s also indicate the t.here is little. if any, difference in performance between the single-step and the two-step Dorfman-Sterrett procedures. For the multi-step Modified Dorfman-Sterrett procedures without errors in decision we have derived the expected number. of runs and compared this results with the expected number of runs for the Dorfman procedure and the multi-step DorfmanSterrett procedure. In. addition, cost functions and expected number of tests for the multi-step Modified Dorfman-Sterrett procedures with errors in decision have also been derived. The results indicate that the modified procedure perform slightly better than Dorfman procedure fer most prevalence rates but is less efficient than the Dorfman-Sterrett procedure. The expressions for expected number of runs and the expected number of incorrect decisions in screening with errors are derived using vVatsons testing of hypothesis approach. Under the testing of hypothesis approach group factors are tested using orthogonal fractional factorial designs of the type giveil in Plackett and Burman (1946). We have also derived expressions for expected number of runs for both the restricted and the unrestricted Modified Dorfman-Sterrett procedures. The results indicate that the Modified Dorfman-Sterrett procedure performs better than the Dorfman procedure for prevalence rates less than 30%. There is also a greater saving for larger prevalence rates. There is a saving of 3~2%in using the Modified procedure instead of the Dorfman procedure when p = 0.29 compared with a s~,ving of 0.18% for p = 0.001. The results however indicate that Sterrett's procedure is more efficient than t.he Modified procedures for prevalence rates less than 30%. These figures seem to disprove the a.ssertion by Huang et al (1089) that a modified Dorfman-Sterrett procedure is more efficient than Sterrett's procedure when the a-priori probability of an item being defective, P. is somewha.t higher (though still quite low) .