Knowing an upper bound on the number of optimal design points greatly simplifies the search for an optimal design. Carathéodory’s Theorem is commonly used to identify an upper bound. However, the upper bound from Carathéodory’s Theorem is relative loose when there are three or more parameters in the model. In this paper, an alternative approach of finding a sharper upper bound for classical opt...

Optimal Design of Acceptance Sampling Plans by Variables for Nonconforming Proportions When the Standard Deviation Is Unknown Belmiro P.M. Duarte a & Pedro M. Saraiva b a Department of Chemical and Biological Engineering, Instituto Superior de Engenharia de Coimbra (ISEC), Polytechnic Institute of Coimbra, Coimbra, Portugal b GEPSI PSE Group, Chemical Process Engineering and Forest Products Res...

In the common trigonometric regression model we investigate the optimal design problem for the estimation of the individual coeecients, where the explanatory variable varies in the interval ?a; a]; 0 < a : It is demonstrated that the structure of the optimal design depends sensitively on the size of the design space. For many cases optimal designs can be found explicitly, where the complexity o...

For the heat equation on a bounded subdomain Ω of R, we investigate the optimal shape and location of the observation domain in observability inequalities. A new decomposition of L(R) into heat packets allows us to remove the randomization procedure and assumptions on the geometry of Ω in previous works. The explicit nature of the heat packets gives new information about the observability const...

Article history: Received 14 August 2009 Received in revised form 9 December 2009 Accepted 18 December 2009 Available online 21 January 2010