A major objective of the Tropical Rainfall Measuring Mission (TRMM) is to produce a multi-year time series of monthly rainfall over 5 degree(s) latitude and 5 degree(s) longitude boxes with an uncertainty of 1mm/day for low rain rates and 10% for high rain rates. Based on some simple assumptions about the error structure, we compute the non-systematic errors of monthly oceanic rainfall over the same space/time domain derived from data taken by the Special Sensor Microwave Imager (SSM/I) on board the Defense Meteorological Satellite Program (DMSP) satellites and TRMM Microwave Imager (TMI). The mean rain rates over a two-year period (1998-1999) are calculated to be 3.0, 2.85, 2.94 mm day-1 for SSM/I onboard the DMSP F-13, F-14 and TMI, respectively. Assuming that the non-systematic errors for each sensor are independent, the errors are calculated to be 22.2%, 22.4%, and 19.7% for F-13, F-14 and TMI, respectively. The non- systematic error for the TMI is smaller than that for either F-13 or F-14 SSM/I at the low rain rates but is comparable at rain rates higher than about 5mm/day. The TRMM objective of 1mm day-1 for non-systematic error is met by TMI for rain rates up to 5-6mm day-1. For higher rain rates, the nonsystematic error is in the 15% range. The goal of a 10% error for high rain rates may be realized by a combination of sensor measurements from multiple satellites, such as that advocated by the Global Precipitation Mission (GPM).