Construction of repeated measurements designs strongly balanced for residual effects

Abstract

Repeated Measurements Designs have been widely used in agriculture, animal husbandry, education, biology, botany and engineering. Balanced or strongly balanced repeated measurements designs are useful to balance out the residual effects. In this article, some new generators and construction procedures are proposed to obtain circular strongly balanced repeated measurements designs in periods of (a) equal sizes, (b) two different sizes, and (c) three different sizes.

Keywords:

• Repeated measurements designs
• balanced repeated measurements designs
• circular strongly balanced repeated measurements designs
• cyclic shifts
• residual effects

MATHEMATICS SUBJECT CLASSIFICATION (2010):

• 05B05
• 62K10
• 62K05

Acknowledgments

Authors are thankful to the Reviewers for their valuable suggestions and comments which improved the readability of the manuscript. Rashid Ahmed and Farrukh Shehzad are also grateful 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.