The purpose of this work was to test our theoretical model for the interpretation of radiation data measured in space. During the space missions astronauts are exposed to the complex field of radiation type and kinetic energies from galactic cosmic rays (GCRs), trapped protons, and sometimes solar particle events (SPEs). The tissue equivalent proportional counter (TEPC) is a simple, time-dependent approach to radiation monitoring for astronauts on board the International Space Station. Another and a newer approach to microdosimetry is the use of silicon-on-insulator (SOI) technology launched on the MidSTAR-1 mission in low Earth orbit (LEO). In the radiation protection practice, the average quality factor of a radiation field is defined as a function of linear energy transfer (LET), Qavg(LET). However, TEPC measures the average quality factor as a function of the lineal energy y, Qavg(y), defined as the average energy deposition in a volume divided by the average chord length of the volume. Lineal energy, y, deviates from LET due to energy straggling, delta-ray escape or entry, and nuclear fragments produced in the detector volume. Using an integrated space radiation model (which includes the transport codes BRYNTRN and HZETRN, and the quantum nuclear interaction model QMSFRG) and the response distribution functions of the walled-TEPC, we compared model calculations with the walled-TEPC measurements from NASA missions in LEO in order to develop a method of accurate exposure predictions for the lunar and the Mars missions. Good agreement was found for Qavg(y) between the model and measured spectra from past NASA missions. The Qavg(y) values for the trapped or the solar protons over-estimate the Q avg(LET) values, and the quantities increase with shield thickness due to nuclear fragmentation. The Qavg(y) for the complete GCR spectra measured from flight TEPCs under-estimate the Qavg(LET). The values for the GCR decrease with the shield thickness. Our analysis for a proper interpretation of observed data supports the use of TEPCs for monitoring the space radiation environment.