Robustness of Augmented Box-Behnken Designs to Two and Three Missing Observations

Document Type : Original Article

Authors
Oluchukwu Chukwuemeka Asogwa 1
Oluwaseun Aramide Otekunrin 2
1 Department of Mathematics and Statistics, Faculty of Physical Sciences, Alex Ekwueme Federal University Ndufu-Alike, Ebonyi State, Nigeria
2 Statistical Design of Investigations Unit, Department of Statistics, Faculty of Science, University of Ibadan, Nigeria
10.22034/jirss.2024.1999151.1015
Abstract
In real experimentation, second order response surface models may in some cases be inadequate and unrealistic due to lack of fit introduced by the presence of third-order terms in the response surface model. This willingly opens the door for augmentation of a second order response surface model to a third order model. The third--order design that takes care of the estimates of the model in this work is augmented Box Behnken Design (ABBD), which has always been confronted with missing observation scenario. This scenario that has affected the power of its test and desirable fundamental properties of this design, often surfaces when an observation is lost, ignored, miss-collected, etc. Therefore, this work constructed a minimaxloss design for ABBD that is robust to two and three missing observations under minimaxloss criterion.
Keywords
Box-Behnken Design
Lack of Fit
Response Surface Model
Second-order Designs
Third-order Design
Robustness of Design
Missing Observations
Subjects

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Journal of the Iranian Statistical Society
Volume 22, Issue 2
December 2023
Pages 59-75

  • Receive Date 28 March 2023
  • Revise Date 01 April 2024
  • Accept Date 03 July 2024