Browsing by Author "Seema Jaggi"

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On the construction of mixed-level rotatable response surface designs when experimental unit experiences overlap effects
(Taylor and Francis Ltd., 2023) Ankita Verma; Seema Jaggi; Eldho Varghese; Cini Varghese; Arpan Bhowmik; Anindita Datta; M. Hemavathi
This paper describes the response surface model for mixed-level factors of the form 2n×3 where experimental units/plots experience the overlap effects from immediate left and right neighboring units. Conditions have been derived for the orthogonal estimation of the parameters of the model. A method of constructing mixed-level response surface designs of the form 2n×3 has been proposed. The designs developed satisfy the derived conditions of rotatability. Further, the method has been extended to the case of mixed-level rotatable designs of the form 2n×3n. An algorithm for the estimation of overlap effects has also been discussed, along with an illustration. © 2021 Taylor & Francis Group, LLC.
Robustness of sequential third-order response surface design to missing observations
(Taylor and Francis Ltd., 2022) M. Hemavathi; Eldho Varghese; Shashi Shekhar; C.K. Athulya; Sanal Ebeneezar; Reshma Gills; Seema Jaggi
Response surface designs are generally used in process/product optimization studies. Sequential third-order response surface designs are advantageous when the experimenter encounters the significance of lack of fit of a fitted second-order model while establishing the relationship between the input and response variables. In some experimental situations, responses pertaining to certain design points may be destroyed or unobtainable or inaccessible. The unavailability of the observations pertaining to certain experimental run(s) affects the design property and affects the analysis of variance. In this paper, we have examined the robustness of sequential third-order rotatable design and investigated the loss of information when one or two observations pertaining to experimental run(s) is (are) missing, which are at different radii from the design centre. It has been found that the maximum loss of information occurs when the observation at the design points which are at higher radii from the design centre is lost and the design has the minimum efficiency. © 2022 The Author(s). Published by Informa UK Limited, trading as Taylor & Francis Group.
Run order consideration for sequential third order rotatable designs
(Taylor and Francis Ltd., 2024) Hemavathi M; Eldho Varghese; Shashi Shekhar; Seema Jaggi; Arpan Bhowmik; T.V. Sathianandan
Random execution of run sequences is employed in response surface designs to avoid bias in the response. Since the randomization of run sequences may induce frequent changes in the factor levels, which makes it difficult or expensive for the experimenter, especially when hard-to-change factors are involved in the experiment. Mostly, second order response surface designs (SORDs) are being used to explore the functional relationship between the response and the input variables. But when the lack of fit of the model becomes significant, it is desirable to explore the relationship with a polynomial model of order three. This requires third order rotatable designs (TORDs), which can be sequentially implemented by adding few more runs to the SORDs. In this paper, the construction of sequential TORDs with minimum level changes in the run sequences has been discussed. © 2022 Taylor & Francis Group, LLC.
Sequential asymmetric third order rotatable designs (SATORDs)
(Taylor and Francis Ltd., 2022) M. Hemavathi; Eldho Varghese; Shashi Shekhar; Seema Jaggi
Rotatable designs that are available for process/ product optimization trials are mostly symmetric in nature. In many practical situations, response surface designs (RSDs) with mixed factor (unequal) levels are more suitable as these designs explore more regions in the design space but it is hard to get rotatable designs with a given level of asymmetry. When experimenting with unequal factor levels via asymmetric second order rotatable design (ASORDs), the lack of fit of the model may become significant which ultimately leads to the estimation of parameters based on a higher (or third) order model. Experimenting with a new third order rotatable design (TORD) in such a situation would be expensive as the responses observed from the first stage runs would be kept underutilized. In this paper, we propose a method of constructing asymmetric TORD by sequentially augmenting some additional points to the ASORDs without discarding the runs in the first stage. The proposed designs will be more economical to obtain the optimum response as the design in the first stage can be used to fit the second order model and with some additional runs, third order model can be fitted without discarding the initial design. © 2020 Informa UK Limited, trading as Taylor & Francis Group.
Theoretical developments in response surface designs: an informative review and further thoughts
(Taylor and Francis Ltd., 2022) M. Hemavathi; Shashi Shekhar; Eldho Varghese; Seema Jaggi; Bikas Sinha; Nripes Kumar Mandal
Response Surface Designs (RSDs) are widely used in process or product optimization studies to explore the input-response relationship. This paper is an attempt to provide a compilation of theoretical developments in the RSDs, since its inception in early 1950s to 2020. Part I (1951–1999) consists of important reviews on basic concepts and its development, which fueled further development during the period 2000 to 2020, included in Part II and concluded with future scope of research. We hope this compilation will be a one-stop platform for researchers to know about the advancements in this field. © 2021 Taylor & Francis Group, LLC.