A-Optimal Spring Balance Weighing Designs Under Some Conditions

Abstract

In this article, the estimation problem of individual weights of objects in spring balance weighing design using the criterion of A-optimality is discussed. It is assumed that the measurement errors have different variances. The lowest bound of the trace of the dispersion matrix is obtained and the conditions when this lowest bound is achieved are given. A new construction method of an A-optimal design is presented.

Keywords:

• A-optimal design
• Balanced incomplete block design
• Spring balance weighing design

Mathematics Subject Classification:

• 62K05
• 62K10

Acknowledgment

The author wishes to express sincere thanks to the referees for many valuable comments and suggestions about the original manuscript.