EFFICIENCY OF SPLIT-PLOT RESPONSE SURFACE DESIGNS IN THE PRESENCE OF MISSING OBSERVATIONS

Abstract

In most experimental designs, situations often arise where some observations are missing due to some unforeseen factors. In such situations, some properties like optimality, orthogonality, and rotatability, which are performance criteria of a design, are destroyed. In the presence of missing observations, efficiency of completely randomized response surface designs has been extensively studied. However, completely randomized response surface designs become inadequate, especially in most industrial experiments, where some factors consist of levels that are difficult and/or expensive to change, which are termed hard-to-change (HTC) factors, and some with levels that are easy to change, termed easy-to-change (ETC) factors. An appropriate approach to such experiments restricts the randomization of the HTC factor levels and this leads to a split-plot structure, for which the designs depend on relative magnitude (d) of model’s variance components. Relatively little or no work has been done on investigating the impact of missing observations on efficiency of response surface designs conducted with a split-plot structure. Therefore, this study examines the impact of pairs of missing observations of factorial point (f), whole-plot axial point(α),subplot axial point(β), and center point(c), on efficiency of split-plot response surface designs in terms of trace(A), maximum (G), integrated average(V) prediction variances optimality criteria under different values of d. At d=0.5, maximum A-efficiency losses of 19.1,10.6,15.7% were observed, due to missing pairs: ff, ββ, fβ, respectively; maximum G- and V-efficiency losses of 10.1,0.1,16.1,0.1% and 0.1,0.1,1.1,0.2% were also observed, due, respectively, to missing pairs ff,αα,ββ,cc. A-efficiency was robust to missing cc,αα,αc,fc,fα while G and V-efficiencies were robust to missing αα. As d increases, the efficiency losses became insignificant.