## On The Construction Of Deletion Designs

##### Abstract

In many exper iment.al si t.uat.ions t.he response var La b.Le may depend on t.he irif'1uence of sever al fact-ors. These fact.ors may be applied at. t.wo or more levels,t-hus giving rise t.o t.reat-ment-combinat.ions. Experiment-s of t-his t-ype are known as fact-orial experiment-s and have been t-he subject. of t.heoret.ical and pract.ical st.udy for many decades.
When all fact-ors are t.ried at- t.he same number of levels we have t.he so called symmet.rical fact.orial experiment.s.On t.he ot.her hand if t.he fact.ors are t.ried at- unequal number of
levels for each fact.or,t.he result. is an asymmet.r i cal
fact-orial experiment-.
The present. t-hesis is concerned wit-h t.he const-ruct.ion of efficient- asymmet.rical single replicat-e fac t.or- ial designs.
Chapt-er I gives a general int.roduct.ion t.o t.he t.hesis. In sect.ion 1.1 an int-J-oduct-ory.•~descript.ion of fact.orial experiment.s is given. In sect-ion 1.2 some preliminary concept.s and not-at.ions are int.roduced. In t-his sect.ion a brief descript-ion of t-he delet-ion t.echnique is also given. A
brief review of t.he relevant- lit.erat.ure is present-ed in sect-ion 1.3. Sect-ions 1.4 and 1.5 deal wit-h t.he st-at-ement.of t.he problem and st.udy t.oget.her wit.h t-he specific object.ives.In t.he last. sect.ion of t.his chapt.er t.he import-ance of t.his st.udy is briefly ment.ioned.
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Chapter II discusses the construction of some deletion designs. After introducing the prime objectives of this chapter in section 2.1 ,we proceed to outline the construction of generalized cyclic designs in section 2.2. These designs will serve as the preliminary designs in the construction of deletion designs. In section 2.3 conditions are given which guarantee the existence of proper or improper deletion designs. A few examples are also given.
Chapter I I I outlines some properties of deletion
designs. The objectives of the chapter are set out in section 3.1. After obtaining some preliminary results useful in developing simple formulas for computing loss of information,due to confounding with blocks in section 3.2, we proceed to derive simple formulas for computing loss of information, due to confounding with blocks, on main effects
in the following section. This is followed with the
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derivation of
simple formulas ~or computing loss of
information, due to confounding with•blocks, on two factor interactions in section 3.4.
In chapter IV we consider the efficiency of the deletion designs. In sectioh 4.1 we point out the objectives of the chapter. The confounding patterns in the generalized cyclic designs are discussed in section 4.2. The efficiency of these designs is studied in section 4.3. Section 4.4 discusses the confounding patterns in the deletion designs
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based on the information available on the estimability of the preliminary cyclic design while in section 4.5 -the efficiency of a class of deletion designs is studied.
Chapter V gives a class of efficient low order
interactions designs. In section 5.2 the efficiency of a class of generalized cyclic designs on low order interactions is given while in section 5.3 efficient low order interactions deletion designs are given.
In chapter VI some comments regarding the significance of the results achieved in this thesis are made. Some areas which need further investigation are also pointed out.

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