Browsing by Author "ASHUTOSH DALAL"
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ThesisItem Open Access CONSTRUCTION OF RESPONSE SURFACE DESIGNS WITH MIXED LEVELS OF FACTORS INCORPORATING NEIGHBOUR EFFECTS(ICAR-Indian Agricultural Statistics Research Institute Indian Agricultural Research Institute New Delhi- 110012 2021, 2021) ASHUTOSH DALAL; Dr. Seema Jaggi,; T-10734The relationship between numerous explanatory variables and one or more response variable(s) is determined and quantified using response surface methodology (RSM), which is then utilized to optimize an underlying process. In agriculture and allied subjects, the treatment combination administered to one experimental plot may affect the response on neighboring plots as well as the response on the plot to which it is applied. These effects are known as neighbour effects and integrating them in the response surface model improves the experiment's precision. A response surface with n1 factors at s1 levels each, n2 factors at s2 levels each and n3 factors at s3 levels each resulting in 1 2 n3 3 n2 n 1 s s s combinations has been considered here. The methodology for response surface with mixed levels of factors incorporating neighbour effects has been described for particular cases. The model considered is a (si-1)th order model without interaction terms, where si is the level of the ith highest factor. The conditions required for the near orthogonal estimation of coefficients of response model and also for the constancy of variances have been obtained. Further, conditions for rotatability under these models have also been obtained. The design satisfying these properties are called as Mixed Level Response Surface Design with Neighbour Effects (MLRDNE). Method of constructing MLRDNE for 1 2 n3 3 n2 n 1 s s s has been developed. Particular cases of the type n1 n2 1 2 s ×s , n1 n2 1 2 3 s ×s ×s , n1 1 2 3 s ×s ×s , n1 1 2 s ×s , n1 1 s , 1 2 3 s ×s ×s and 1 2 s ×s have been discussed. The developed designs are either rotatable or partially rotatable depending on the model considered. A list of the designs developed has been prepared along with the variance of the estimated response. It is seen that in the presence of neighbour effects, variance of estimated parameters and variance of estimated response reduces as the value of neighbour coefficient increases. R codes have been developed to generate the designs along with the variance of parameter estimates and estimated response under second and higher order models incorporating neighbour effect.