Some new construction of circular weakly balanced repeated measurements designs in periods of two different sizes

Abstract

Balanced repeated measurements designs (RMDs) balance out the residual effects. Williams Latin square designs work as minimal combinatorial balanced as well as variance balanced for RMDs for p (period sizes) = v (number of treatments). If minimal balanced RMDs cannot be constructed for the situations where p must be less than v then weakly balanced RMDs should be preferred. In this article, some generators are developed to generate circular weakly balanced RMDs in periods of two different sizes. To obtain the proposed designs, some construction procedures are also described for some of the cases where we could not develop generators.

Keywords:

• Repeated measurements designs
• balanced repeated measurements designs
• circular weakly balanced repeated measurements designs
• minimal circular weakly balanced repeated measurements designs

Mathematics Subject Classification (2010):

• 05B05
• 62K10
• 62K05

Acknowledgements

Authors are thankful to the Reviewers for their valuable comments and suggestions which made this manuscript worth publishing. Corresponding author and H. M. Kashif Rasheed are highly grateful also to the Higher Education Commission Pakistan Research and Development Division National Research Program for Universities for providing grant for this research. Grant No: 6294/Punjab/NRPU/R&D/HEC/2016.