| dc.description.abstract | 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) . | en |
