In a variety of neutron lifetime experiments, in addition to $beta-$decay, neutrons can be lost by other mechanisms including wall losses. Failure to account for these other loss mechanisms produces systematic measurement error and associated systematic uncertainties in neutron lifetime measurements. In this work, we develop a physical model for neutron wall losses and construct a competing risks survival analysis model to account for losses due to the joint effect of $beta-$decay losses, wall losses of marginally trapped neutrons, and an additional absorption mechanism. We determine the survival probability function associated with the wall loss mechanism by a Monte Carlo method. Based on a fit of the competing risks model to a subset of the NIST experimental data, we determine the mean lifetime of trapped neutrons to be approximately 700 s -- considerably less than the current best estimate of (880.1 $pm$ 1.1) s promulgated by the Particle Data Group [1]. Currently, experimental studies are underway to determine if this discrepancy can be explained by neutron capture by ${}^3$He impurities in the trapping volume. Analysis of the full NIST data will be presented in a later publication.
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