In this paper, we discuss an accurate and fast software tool (INSPCT-S, Inspection of Nuclear Spent fuel-Pool Calculation Tool, version Spreadsheet) developed for calculation of the response of fission chambers placed in a spent fuel pool, such as Atucha-I. INSPCT-S is developed for identification of suspicious regions of the pool that may have missing or substitute assemblies. INSPCT-S uses a hybrid algorithm based on the adjoint function methodology. The neutron source is comprised of spontaneous fission, (α, n) interactions, and subcritical multiplication. The former is evaluated using the ORIGEN-ARP code, and the latter is obtained with the fission matrix (FM) formulation. The FM coefficients are determined using the MCNP Monte Carlo code, and the importance function is determined using the PENTRAN 3-D parallel Sn code. Three databases for the neutron source, FM elements, and adjoint flux are prepared as functions of different parameters including burnup, cooling time, enrichment, and pool lattice size. INSPCT-S uses the aforementioned databases and systems of equations to calculate detector responses, which are subsequently compared with normalized experimental data.