  Measurement models (MMs) stand at the highest structural level of quantum
measurement theory. MMs can be employed to construct instruments which stand at
the next level. An instrument is thought of as an apparatus that is used to
measure observables and update states. Observables, which are still at the next
level, are used to determine probabilities of quantum events. The main
ingredient of an MM is an interaction channel $\nu$ between the system being
measured and a probe system. For a general $\nu$, the measured observable $A$
need not have an explicit useful form. In this work we introduce a condition
for $\nu$ called separability and in this case $A$ has an explicit form. Under
the assumption that $\nu$ is separable, we study product MMs and conditioned
MMs. We also consider the statistics of MMs and their uncertainty principle.
Various concepts are illustrated using examples of L\"uders and Holevo
instruments.
