Design of Experiments for Estimating Differences Between Responses and Slopes of the Response

A measure of robust slope-rotatability for second-order response surface experimental designs

“…where A k , B k and C k as in Equation (16), and T k as in Equation (14). Note that this quantity in Equation (17) itself is a measure of how much the given design differs from a robust sloperotatable design and hence could be used as a measure of robust slope-rotatability.…”

“…Very recently Huda [14] and Park [25] reviewed the literature on experimental designs for the estimation of the differences among responses, and most of the relevant references are cited there. Some authors, however, have focused attention on the estimation of partial derivatives of the response function with respect to the independent variables.…”

Rotatability is a Sufficient Condition for A- and D-Rotatability

“…Sometimes, the differences between responses at various points may be of greater interest (Box and Draper, 1980;Herzberg, 1967;Huda andMukerjee, 1984, 2010). If interest is in difference between responses at points close together in the factor space, the estimation of local slopes of the response surface becomes important.…”

“…Subsequently, many researchers have dealt with the problems of finding optimal designs for estimating slopes; cf. Huda (2006) and the references therein.…”

“…If there are k factors then at any point in the factor space there are k axial slopes thereby allowing one to define slope-rotatabilty in many different ways and for designs of any order. Various possible concepts of slope-rotatability for a design of order d (≥1) are discussed (Huda, 2006). Among these the ones likely to be most useful are the A-(slope)-rotatability and D-(slope)-rotatability.…”