Microfission chambers (MFCs) are one of the most important diagnostics for measuring neutron source strength in ITER. Using MFCs for high-power operations (fusion power of 100 kW-1 GW) and for low-power operations (<100 kW) in combination is one way to fulfill the target measurement requirements of ITER. The MFCs for high-power operations will be installed behind blanket modules in both the upper and lower outboard regions of the vacuum vessel so as to be insensitive to changes in the position of the plasma. For low-power operations, one possible location of MFCs is inside the equatorial (EQ) port. The effect of streaming neutrons and of changes in the position of the plasma on the responses of MFCs is estimated based on a neutron Monte Carlo calculation using the MCNP Version 5 code. Results suggest that the effect of streaming neutrons should be taken into account if the MFCs for high-power operations are installed closer than 20 cm to the gap between blanket modules. It has also been found for MFCs of low-power operations that the averaged output of the MFCs installed at the top and bottom of the EQ port is sensitive to horizontal plasma shifts but not to vertical shifts. This finding suggests that corrections based on the position of the plasma center will be needed for the absolute measurement of neutron source strength.