Construction of second and third order calculus optimum/unit value specific and sequential rotatable designs in both order and dimension from the six second order design classes comprising letter parameter second order rotatable designs in three dimensions postulated in a paper by Draper, N. R. (1960b). Third order rotatable designs in three dimensions, Annals of Mathematical Statistics 31, 865-874 see pages 871-874 in particular for which alphabetic optimality criteria are also being determined evidence being that in:-
2002 introduced A-, E-, D-, T- optimality criteria into these designs in a landmark M.Sc. thesis by Dr. Mathew Kipchumba Kosgei the current Associate Dean of the school.
2016 introduced calculus and unit value designs and expanded the optimality criteria to I-, G- in the M.Sc. thesis of Nicholas Kipkosgei Kiplagat.
2017 added the efficiency perspective to the calculus and unit value designs in the M.Sc. thesis of Franklin Koech Kiplagat.
2018 carried out optimum production of rose coco beans at Kesese area just outside Moi University gate using the second order calculus optimum A- optimality criterion twenty four points rotatable design in a landmark Ph.D. thesis by Dr. Isaac Kipkosgei Tum.
Currently Jepleting Julieth Bitok is working on combination of two second order rotatable designs to get a third order rotatable design then evaluate its alphabetic optimality criteria so that in production process if the response curve becomes cubic there will be a third order rotatable design to cater for that change.
We also want to explore what happens if we add a factor which we also call dimension and/or combine second order rotatable designs to get third order rotatable designs to the alphabetic optimality criteria do these alphabetic optimality criteria change or do they remain constant. Another student is investigating this already. Now , in practice, the nature of the variables whose levels are represented by actual values will change from one application of a design to another. In one case, for example, the actual values may refer to a temperature reading and in another to the dosage of a drug. Therefore, it is useful to define the general design in terms of standardized variables, which in any particular application are related linearly to the actual values by a transformation. The question is do actual values and standardized values have the same alphabetic optimality criteria? This student is also considering this aspect.
The research thrust going forward is then to produce goods and services from these designs.