This comprehensive research delves into the mathematical modeling of diagnostic signals in electrical equipment diagnostics using linear random processes (LRPs) and their properties. Beginning with an exploration of stochastic processes with independent increments, the chapter establishes foundational concepts crucial for understanding LRPs. These processes, characterized by their reliance on past and present values, are further examined for their applicability in both continuous and discrete-time scenarios. Special attention is given to the properties of LRPs, including their closure under linear transformations and the simplification of probabilistic analysis through characteristic functions. The chapter extends the discussion to multidimensional random fields, showcasing the versatility of LRPs in modeling complex phenomena across various fields like radiophysics, radio engineering, and optics. Additionally, the exploration of stationarity and homogeneity within random fields elucidates the conditions under which these models can be simplified, further contributing to their practical utility in diagnostics. By providing a fundamental understanding of these processes and demonstrating their applicability through examples, this chapter aims to equip researchers and practitioners in the field of electrical equipment diagnostics with robust mathematical models for diagnostic signals.