A generalized series-based formulation is developed to determine the hierarchical rank of any given linear permutation selected from a set of all possible linear permutations arranged according to a predefined order of priority of elements like digits, letters, and all other objects. The proposed model applies to permutations of words, numbers, and other discrete objects, enabling systematic identification of their positions in an ordered sequence. The formulation is expressed as a finite series in which each term corresponds to a specific element of the permutation. It applies to sets of distinguishable objects characterized by identifiable properties such as shape, size, colour, or surface pattern, assuming that all elements are equally likely to occupy any position in the arrangement without replacement. The model introduces three parameters, Formerity (F), Permuty (P), and Similarity (S), which collectively define the structure of the series. These parameters depend on the preceding elements, the permutations of successive elements, and the repetition characteristics within the arrangement. Notably, the number of terms in the series is equal to the number of elements in the permutation. This generalized formulation provides a structured and scalable approach for analyzing and ranking linear permutations in a wide range of combinatorial contexts.