Two-type step-wise group screening designs with errors in observations

Abstract

In part one of this project, we discuss the problem of two-type step-wise group screening designs with errors in observations and equal prior probability of factor being defective; wherein ffactors are subdivided into groups of kl factors each, forming gl group-factors called first order group-factors. The first order group-factors are then studied using fractional factorial designs of type given by Placket and Burman (1946) in gl+h runs. The two versions of the first order group-factors are formed by maintaining all component factors at their upper and lower levels respectively. All the first order group-factors found to be defective are subdivided into g2 second order group-factors of sizes k2 factors each. In type-one search steps of the experiments, the second order group-factors are tested for their effects using fractional factorial designs. Then the effects of individual factors from the second order group-factors declared defective are studied in type-two search steps of the experiments using nonorthogonal fractional factorial designs. The expression for the expected number of runs for two-type step-wise group screening designs is obtained and used to generate tables by numerical approximation. In part two of this project, we discuss the problem of two-type stepwise group screening designs with errors in observations and unequal prior probability of a factor being defective, wherein f factors are subdivided into gl first order group-factors of sizes kli factors each. Then the group-factors and individual factors are tested for their effects as in part one, the expression for expected number of runs is obtained for two-type step-wise group screening designs with errors in observations and unequal prior probability of factor being defective.