International Journal of Advances in Scientific Research and Engineering (ijasre) E-ISSN : 2454-8006 DOI: 10.31695/IJASRE.2021.34003 Volume 7, Issue 4 April - 2021 www.ijasre.net Page 80 Licensed Under Creative Commons Attribution CC BY-NC Robustness of Higher Levels Rotatable Designs for Two Factors against Missing Data Nyakundi Omwando Cornelious 1 & Evans Mbuthi Kilonzo 2 1, 2 Department of Mathematics, Physics, and Computing Moi University, Eldoret Kenya _______________________________________________________________________________________ ABSTRACT Experimenters should be aware of the possibility that some of their observations may be unavailable for analysis. This paper considers a criterion which assesses the robustness for missing data when running four and five levels designs in estimating a full second order polynomial model. The criterion gives the maximum number of runs that can be missing and still allow the remaining runs to estimate a second order model for four and five levels. Key words: Robustness Criterion, Missing Data, Four and Five Level Designs, Second Order Rotatability. ____________________________________________________________________________________________________ 1.0 INTRODUCTION Response surface methodology (RSM) is a collection of statistical and mathematical techniques used for the purpose of setting up a series of experiments for adequate predictions of responses. In a majority of experiments which utilize response surface methodology, there is a possibility that some observations may be unavailable or missing for analysis. Missing data is a problem that occurs in many experiments and can have substantial consequences on study quality [1]. Strategies to limit the impact of missing data on the analysis and interpretation of experiments are supported by the natural academy of sciences report [2]. The report recommends that a more principled approach to design and analysis in the presence of missing data is both needed and that careful design and conduct limit the amount and impact of missing data [1]. Experiments which utilize higher level models can become lengthy and as such missing data is commonly seen through subject dropout [2]. First introduced by [6], and also defined on page 32 of [5], data are said to be missing at random, conditional on the observed data. The problem of missing observations has been common lately in most experiments due to its existence in practice [8]. The causes of missing data include; loss of experimental units, miscoded data, and the use of experiments that take too long to complete, resulting in the cancellation of runs [7]. Therefore, the designs chosen must be robust in situations where some information is missing. The inclusion of sensitivity to outliers as one important property of an experimental design was done by [3]. Several other authors have investigated the robustness of designed experiments against missing data [4]. However, most of this research has focused on factorial designs and complete and incomplete block designs. The aim of this article is to study the robustness for missing data for different two factor designs in four and five dimensions for estimating a full second order polynomial model. 2.0 METHODS Response surface methodology explores the relationships between several explanatory variables and one or more response variables with the aim of optimizing the response variables. It is assumed that the form of the functional relationship is unknown but that within the range of interest, the function could be represented by a Taylor series expansion of moderately low order. For example in two independent variables and to terms of second order model, the series has the form                         (1) Where; y is the expected value of the dependent variable,   and   are the independent variables and B’s are unknown co- efficient in the series. Normally, the specific problem considered is that of the choice of the combinations of the independent variables so as to achieve certain desirable properties in the final estimates.