Design of Experiments for Extreme Value Distributions Patrick J Laycock 1 and J. L´ opez-Fidalgo 2 1 Mathematics Dept, University of Manchester Institute of Science and Technology, Sackville St, Manchester M60 1QD, UK, pjlaycock@umist.ac.uk 2 Department of Mathematics, University of Castilla la Mancha Avda. Camilo Jos´ e Cela 3, 13071–Ciudad Real, Spain jesus.lopezfidalgo@uclm.es Summary. In this paper experimental designs are considered for classic extreme value distribution models. A careful review of the literature provides some informa- tion matrices in order to study experimental designs. Regression models and their design implications are discussed for some situations involving extreme values. These include a constant variance and a constant coefficient of variation model plus an ap- plication in the strength of materials. Relative efficiencies calculated with respect to D–optimality are used to compare the designs given in this example. Key words: Generalised extreme value distribution, D–optimality, Regres- sion, Weibull distribution 1 Introduction There are many situations where extreme values or extreme objectives might affect the design of experiments. In this paper we consider regression models where the dependent variable is an extreme value or has an implied extreme value distribution. Classic experimental designs, such as factorial designs, fractional and block designs, or response surface designs are typ- ically constructed on the assumption of a linear regression model for the response variate with additive, finite variance, errors. More specifically, the usual model assumes that the data vector y is N (Xθ, σ 2 I) and we choose X = {x 1 , x 2 , ..., x n } T so as to optimise the estimation of θ in some straightfor- ward way. Such designs are typically optimised for conditions where ANOVA techniques are used, implying linearity, additivity and finite variance. Fortu- nately, many designs are known to be useful and relevant under wide variations on this model. See for example Silvey (1980), Atkinson and Donev (1992) or Fedorov and P. (1997). Our examples will concentrate on the strength or en- durance of materials, where max-stable extreme value distributions form a