MV-OPTIMAL AND OTHER OPTIMAL n-ARY DESIGNS

Abstract

An MV-optimal design minimizes 
  ) R/1 R/1( max di 0d V i 1
+
≤≤
       
Subject to the restriction Rd0+Rd1+…+RdV = n. It is easily seen that an MV-optimal design d* has 
  Rd*i = R for I = 1…V   and 
  Rd*0=n-V R, 
Where  
  
 
 

+
= ∧
∧ ∧
, otherwise ,1 ]R[
, eger int an is R if ,R R ^
  
  )1 V(V2
)Vn4 V2 V V( V V n2 R 2/1 2 3 2 4 2 ^
−
+ − + − − + = 
 We note that for a fixed value of n, the A- and MV-optimality criteria may select substantially different 
optimal n-ary design from those available. For example, when n=30 and V= 15, an A-optimal design d will have 
0d
R = 5 and id
R = 1 or 2 for i = 1,…,15 whereas the MV-optimal design d* will have Rd*0 = 15 and R d*i = 1 for  i = 
1,…,15 and MV- Optimal N-Ary Designs For The One-Way Elimination of Heterogeneity and two way and 
Robust obtimal designs with examples and theorems are given.