A new data analysis method is developed for the angle resolving silicon telescope introduced at the neutron time of flight facility n_TOF at CERN. The telescope has already been used in measurements of several neutron induced reactions with charged particles in the exit channel. The development of a highly detailed method is necessitated by the latest joint measurement of the $^{12}$C($n,p$) and $^{12}$C($n,d$) reactions from n_TOF. The reliable analysis of these data must account for the challenging nature of the involved reactions, as they are affected by the multiple excited states in the daughter nuclei and characterized by the anisotropic angular distributions of the reaction products. The unabridged analysis procedure aims at the separate reconstruction of all relevant reaction parameters - the absolute cross section, the branching ratios and the angular distributions - from the integral number of the coincidental counts detected by the separate pairs of silicon strips. This procedure is tested under the specific conditions relevant for the $^{12}$C($n,p$) and $^{12}$C($n,d$) measurements from n_TOF, in order to assess its direct applicability to these experimental data. Based on the reached conclusions, the original method is adapted to a particular level of uncertainties in the input data.
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