The performance of subset response surface designs for estimating third order terms

TY - JOUR

T1 - The performance of subset response surface designs for estimating third order terms

AU - Arshad, Hafiz Muhammad

AU - Gilmour, Steven G.

PY - 2012/1

Y1 - 2012/1

N2 - Response surface designs are widely used in industries like chemicals, foods, pharmaceuticals, bioprocessing, agrochemicals, biology, biomedicine, agriculture and medicine. One of the major objectives of these designs is to study the functional relationship between one or more responses and a number of quantitative input factors. However, biological materials have more run to run variation than in many other experiments, leading to the conclusion that smaller response surface designs are inappropriate. Thus designs to be used in these research areas should have greater replication. Gilmour (2006) introduced a wide class of designs called "subset designs" which are useful in situations in which run to run variation is high. These designs allow the experimenter to fit the second order response surface model. However, there are situations in which the second order model representation proves to be inadequate and unrealistic due to the presence of lack of fit caused by third or higher order terms in the true response surface model. In such situations it becomes necessary for the experimenter to estimate these higher order terms. In this study, the properties of subset designs, in the context of the third order response surface model, are explored.

AB - Response surface designs are widely used in industries like chemicals, foods, pharmaceuticals, bioprocessing, agrochemicals, biology, biomedicine, agriculture and medicine. One of the major objectives of these designs is to study the functional relationship between one or more responses and a number of quantitative input factors. However, biological materials have more run to run variation than in many other experiments, leading to the conclusion that smaller response surface designs are inappropriate. Thus designs to be used in these research areas should have greater replication. Gilmour (2006) introduced a wide class of designs called "subset designs" which are useful in situations in which run to run variation is high. These designs allow the experimenter to fit the second order response surface model. However, there are situations in which the second order model representation proves to be inadequate and unrealistic due to the presence of lack of fit caused by third or higher order terms in the true response surface model. In such situations it becomes necessary for the experimenter to estimate these higher order terms. In this study, the properties of subset designs, in the context of the third order response surface model, are explored.

KW - Alias matrix

KW - Alphabetic optimality

KW - Lack of fit

KW - Response surface models

KW - Second order designs

KW - Subset designs

KW - Third order designs

UR - http://www.scopus.com/inward/record.url?scp=80052294847&partnerID=8YFLogxK

U2 - 10.1016/j.jspi.2011.07.012

DO - 10.1016/j.jspi.2011.07.012

M3 - Article

AN - SCOPUS:80052294847

SN - 0378-3758

VL - 142

SP - 232

EP - 247

JO - JOURNAL OF STATISTICAL PLANNING AND INFERENCE

JF - JOURNAL OF STATISTICAL PLANNING AND INFERENCE

IS - 1

ER -