A common approach to studying $beta$-delayed proton emission is to measure the energy of the emitted proton and corresponding nuclear recoil in a double-sided silicon-strip detector (DSSD) after implanting the $beta$-delayed proton emitting ($beta$p) nucleus. However, in order to extract the proton-decay energy, the measured energy must be corrected for the additional energy implanted in the DSSD by the $beta$-particle emitted from the $beta$p nucleus, an effect referred to here as $beta$-summing. We present an approach to determine an accurate correction for $beta$-summing. Our method relies on the determination of the mean implantation depth of the $beta$p nucleus within the DSSD by analyzing the shape of the total (proton + recoil + $beta$) decay energy distribution shape. We validate this approach with other mean implantation depth measurement techniques that take advantage of energy deposition within DSSDs upstream and downstream of the implantation DSSD.
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