MixedLevelRSDs: Mixed Level Response Surface Designs.

Abstract

Response Surface Designs (RSDs) involving factors not all at same levels are called Mixed Level RSDs (or Asymmetric RSDs). In many practical situations, RSDs with asymmetric levels will be more suitable as it explores more regions in the design space. (J.S. Mehta and M.N. Das (1968) <doi:10.2307/1267046>. ("Asymmetric rotatable designs and orthogonal transformations").This package contains function named ATORDs_I() for generating asymmetric third order rotatable designs (ATORDs) based on third order designs given by Das and Narasimham (1962). Function ATORDs_II() generates asymmetric third order rotatable designs developed using t-design of unequal set sizes, which are smaller in size as compared to design generated by function ATORDs_I(). In general, third order rotatable designs can be classified into two classes viz., designs that are suitable for sequential experimentation and designs for non-sequential experimentation. The sequential experimentation approach involves conducting the trials step by step whereas, in the non-sequential experimentation approach, the entire runs are executed in one go (M. N. Das and V. Narasimham (1962) <doi:10.1214/AOMS/1177704374>. "Construction of Rotatable Designs through Balanced Incomplete Block Designs"). ATORDs_I() and ATORDs_II() functions generate non-sequential asymmetric third order designs. Function named SeqTORD() generates symmetric sequential third order design in blocks and also gives G-efficiency of the given design. Function named Asymseq() generates asymmetric sequential third order designs in blocks (M. Hemavathi, Eldho Varghese, Shashi Shekhar and Seema Jaggi (2020) <doi:10.1080/02664763.2020.1864817>. "Sequential asymmetric third order rotatable designs (SATORDs)"). In response surface design, situations may arise in which some of the factors are qualitative in nature Jyoti Divecha and Bharat Tarapara (2017) <doi:10.1080/08982112.2016.1217338>. "Small, balanced, efficient, optimal, and near rotatable response surface designs for factorial experiments asymmetrical in some quantitative, qualitative factors"). The Function named QualRSD() generates second order design with qualitative factors along with their D-efficiency and G-efficiency. The function named RotatabilityQ() calculates a measure of rotatability (measure Q, 0 <= Q <= 1) given by Draper and Pukelshiem(1990) for given a design based on a second order model, (Norman R. Draper and Friedrich Pukelsheim(1990) <doi:10.1080/00401706.1990.10484635>. "Another look at rotatability")