  This paper deals with the construction of a metamodel (i.e. a simplified
mathematical model) for a stochastic computer code (also called stochastic
numerical model or stochastic simulator), where stochastic means that the code
maps the realization of a random variable. The goal is to get, for a given
model input, the main information about the output probability distribution by
using this metamodel and without running the computer code. In practical
applications, such a metamodel enables one to have estimations of every
possible random variable properties, such as the expectation, the probability
of exceeding a threshold or any quantile. The present work is concentrated on
the emulation of the quantile function of the stochastic simulator by
interpolating well chosen basis function and metamodeling their coefficients
(using the Gaussian process metamodel). This quantile function metamodel is
then used to treat a simple optimization strategy maintenance problem using a
stochastic code, in order to optimize the quantile of an economic indicator.
Using the Gaussian process framework, an adaptive design method (called QFEI)
is defined by extending in our case the well known EGO algorithm. This allows
to obtain an "optimal" solution using a small number of simulator runs.
