  The quantum measurement incompatibility is a distinctive feature of quantum
mechanics. We investigate the incompatibility of a set of general measurements
and classify the incompatibility by the hierarchy of compatibilities of its
subsets. By using the approach of adding noises to measurement operators we
present a complete classification of the incompatibility of a given measurement
assemblage with $n$ members. Detailed examples are given to the incompatibility
for unbiased qubit measurements based on semidefinite programm.
