ENBIS: European Network for Business and Industrial Statistics

Robustness of 3-level Response Surface Design against missing Data

22 September 2009, 14:45 – 15:05

Abstract

Submitted by

Martin Tanco

Authors

Martín Tanco(1), Enrique Del Castillo (2), Elisabeth Viles (1)

Affiliation

(1) TECNUN, University of Navarra; (2) Pennsylvania State University

Abstract

The problem of missing observations in a well-designed experiment has attracted much attention in recent years, because it happens often in practice. Practical experimenters must always be aware of the possibility that some of their observations could become unavailable for analysis. Therefore, the design chosen must be “robust” to the situation when some information is missing. Several authors have investigated the robustness of designed experiments against missing data. However, most of the research has focus on factorial designs and complete and incomplete block designs.

The aim of this article is to study the impact (robustness) of missing data in the analysis of three level designs useful to estimate all parameters of a general second-order model. The designs studied are classified in three groups: classical (Box-Behnken and Face Centred Composite Design), intermediate design (Morris, Mee, Block-Mee) and smaller designs (Draper-Lin, Hoke, Katasaounis and Notz). All these designs are compared against others in their group for 3 to 7 factors.

Each of the designs are analysed with three criterions for robustness. The first criterion calls a design matrix (X) robust against the loss of (t  1) observations if the remaining design matrix (X*) is able to estimate all the parameters under an assumed model. Even if a design is robust according to this first criterion, the remaining designs may have poor efficiency relative to the original design. Therefore, the D-efficiency criteria can be used to compare the remaining design with respect to the original design given. Finally a new criterion is considered, related to the first one, which measures the maximum amount of observation that can be missing to still be able to estimate all the parameters with a certain probability.

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