Year : 2022, Volume : 14, Issue : 2
First page : ( 208) Last page : ( 212)
Print ISSN : 0975-2315. Online ISSN : 2394-4471. Published online : 2022 December 18.
Article DOI : 10.5958/2394-4471.2022.00047.8

Construction of response surface design of the form 2^n×s with border units

Verma Ankita^1,*

¹ICAR-Indian Agricultural Statistics Research Institute, New Delhi-110 022, India

^*Ankita Verma (Corresponding author) ankiverma95@gmail.com

Online Published on 18 March, 2023.

Received:  04  October,  2022; :  19  November,  2022; Accepted:  19  November,  2022.

Abstract

Response surface methodologies are commonly used in industries, electronics, medical departments, and agriculture where product optimization is the focus. The main goal of response surface design (RSD) is to identify the best set of factors at which a product or response is optimised. It explores the relationship between numerous explanatory variables and response variable(s). When units are organized in a linear pattern relatively closely together, experimental plot may encounter neighbour effects from the treatment used in nearby border units. For instance, if a chemical treatment is used on one plot in a field experiment, wind drift may cause the chemical treatment’s spray effect to spread to the adjacent plots, or the preparation of the soil through soil cultivation may result in the mixing of sterilized soil from one plot with non-sterile soil from the next plot. Including neighbour effects in the response surface model will improve the precision of the estimated response. It might not be reasonable to assume the same levels of all factors in RSD.Our work discusses the effects of immediate left and right borders on experimental units/plots using a response surface model that incorporates asymmetrical factors of the form 2ⁿ’s. A method has been suggested for constructing asymmetrical response surface designs of the form 2ⁿ’s based on border units. Designs are developed that satisfy the conditions of near orthogonal estimation of coefficients of response models, with rotatability property.

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Keywords

Asymmetrical Response surface design, Border unit, Orthogonal estimation rotatable design.

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