Multi-Type Step-Wise Group Screening Designs

Abstract

The inspection of individual members of a

large population is an expensive and tedious process. In many inspections, the objective is to eliminate all the defective members of the population. This

situation arises in manufacturing processes where the defective being tested for can result in disastrous failures. It also arises in certain inspections of human population with say infectious diseases. Where the objective is to weed out individual

defective units, a sample inspection will not suffice. In this case we need designs which will classify all the items in the population as defective Qr non- defective. Such designs are called screening designs. Earlier work iw this area was done by

Dorfman [lJ and Sterret [10J. Watson [llJ and Patel [6J have approached the problem from the point of view of designs of experiments and called this designs "group screening designs". Patel and Manene [7J have also approached the problem from the point of view of designs of experiments and called the designs "Step-wise group screening designs". This project is along the lines o£ Patel and Manene's paper [7J.. The problem has been approached from the point of view of designs of experiments.

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Chapter 1 defines the concept of group screening designs and describes briefly the work done in this and other related areas by several authors in the past. The chapter also lays down the assumptions which are used in this project.

In chapter II, multi-type step-wise group screening designs have been introduced and are studied assuming that all factors have the same a-priori probability of being defective. A compari-

son of two-type and three-type step-wise designs

with one type step-wise designs have been presented.

Chapter III extends the results of chapter II to the case where factors are defective with unequal a-priori probabilities.

Throughout this pro jec t , it lS assumed that " the value of 'p~, the a-pri~ri probability of a factor to be defective is known. Thus no attempt is made to estimate it.