  The homogeneity problem for testing if more than two different samples come
from the same population is considered for the case of functional data. The
methodological results are motivated by the study of homogeneity of electronic
devices fabricated by different materials and active layer thicknesses. In the
case of normality distribution of the stochastic processes associated with each
sample, this problem is known as Functional ANOVA problem and is reduced to
test the equality of the mean group functions (FANOVA). The problem is that the
current/voltage curves associated with Resistive Random Access Memories (RRAM)
are not generated by a Gaussian process so that a different approach is
necessary for testing homogeneity. To solve this problem two different
parametric and nonparametric approaches based on basis expansion of the sample
curves are proposed. The first consists of testing multivariate homogeneity
tests on a vector of basis coefficients of the sample curves. The second is
based on dimension reduction by using functional principal component analysis
of the sample curves (FPCA) and testing multivariate homogeneity on a vector of
principal components scores. Different approximation numerical techniques are
employed to adapt the experimental data for the statistical study. An extensive
simulation study is developed for analyzing the performance of both approaches
in the parametric and non-parametric cases. Finally, the proposed methodologies
are applied on three samples of experimental reset curves measured in three
different RRAM technologies.
