  Context. Galaxy clusters are the last and largest objects to form in the
standard hierarchical structure formation scenario through merging of smaller
systems. The substructure frequency in the past and present epoch provides
excellent means for studying the underlying cosmological model. Aims. Using
X-ray observations, we study the substructure frequency as a function of
redshift by quantifying and comparing the fraction of dynamically young
clusters at different redshifts up to z=1.08. We are especially interested in
possible biases due to the inconsistent data quality of the low-z and high-z
samples. Methods. Two well-studied morphology estimators, power ratio P3/P0 and
center shift w, were used to quantify the dynamical state of 129 galaxy
clusters, taking into account the different observational depth and noise
levels of the observations. Results. Owing to the sensitivity of P3/P0 to
Poisson noise, it is essential to use datasets with similar photon statistics
when studying the P3/P0-z relation. We degraded the high-quality data of the
low-redshift sample to the low data quality of the high-z observations and
found a shallow positive slope that is, however, not significant, indicating a
slightly larger fraction of dynamically young objects at higher redshift. The
w-z relation shows no significant dependence on the data quality and gives a
similar result. Conclusions. We find a similar trend for P3/P0 and w, namely a
very mild increase of the disturbed cluster fraction with increasing redshifts.
Within the significance limits, our findings are also consistent with no
evolution.
