  In this paper we define the shifted Schur process as a measure on sequences
of strict partitions. This process is a generalization of the shifted Schur
measure introduced in [TW] and [Mat] and is a shifted version of the Schur
process introduced in [OR]. We prove that the shifted Schur process defines a
Pfaffian point process. We further apply this fact to compute the bulk scaling
limit of the correlation functions for a measure on strict plane partitions
which is an analog of the uniform measure on ordinary plane partitions. As a
byproduct, we obtain a shifted analog of the famous MacMahon's formula.
