Binary sensor systems are analog sensors of various types (optical, MEMS – Msicro-Electro-Mechanical Systems, X-ray, gamma-ray, acoustic, electronic, etc.), based on the binary decision process. Typical examples of such «binary sensors» are X-ray luggage inspection systems, product quality control systems, automatic target recognition systems, numerous medical diagnostic systems, and many others. In all these systems, the binary decision process provides only two mutually exclusive responses. There are also two types of key parameters that characterize either a system or external conditions in relation to the system which are determined by their prior probabilities. In this paper, by using a formal neuron model, we analyze the problem of threshold redundancy of binary sensors of a critical state. Three major tasks are solved, videlicet: implementation of the algorithm of error probability calculation for threshold redundancy of a group of sensors; computation of the minimal upper bound for the probability in a closed analytical form and determination of its link with Claude Shannon's theorem; derivation of the expression (estimate) for sensor «weights» when the probability of the binary system error does not exceed the specified minimal upper bound.