On circular designs

Abstract

SummaryA general method of analysis of circular designs (Das [3]) is suggested. Average efficiency factors of these designs have been tabulated. A-optimality of circular designs has been studied in comparison to group divisible incomplete block designs.

Generalized incomplete Trojan-type designs

“…Considering rows as blocks, ignoring column and cell classifications, the design is a PBIB design following a circular association scheme (Das, 1960;Kulshreshtha et al, 1971;Saha et al, 1974) with m 2 + 1 (for m even) associate classes and parameters v, b = m, r = p, k = ps, n 1 = s − 1, n 2 = · · · = n m 2 = 2s, n m 2 +1 = s, λ i = p − (i − 1), i = 1, 2, . .…”

Partially Balanced Incomplete Block Designs

“…These designs are based on circular association scheme defined by Kulshreshtha et al (1971) and given in Section 4.2.1 Let there be n equal arcs on the circumference of a circle denoted in order by a 1 ,a 2, …,a n . If we form bigger arcs say A pi such that it is the sum of p consecutive small arcs starting with a i , we shall have in all n such arcs different values of i.…”