We present a method to estimate an upper limit of the mission integrated fluence of hard X-rays
(HXRs) produced by solar flares for a probe traveling at heliocentric distances R<1 AU. By using (1) the number and peak of both soft X-ray
(SXR) flares and microwave (MW) solar bursts observed during the last three solar cycles, (2) either frequency distributions of HXR flare parameters, or correlations between the HXR fluence and the SXR flare class or the MW burst flux intensity, and (3) virtual launches of the probe at different times throughout the last three solar cycles, we accumulate statistics of the mission-integrated HXR fluences and provide values at the 95% confidence level. We apply this method to the Solar Probe Plus mission.