Nonintrusive load monitoring (NILM) algorithms may suggest different approaches for solving the NILM problem: The disintegrating of total power consumption to the discrete appliances comprising it. All of these algorithms incorporate some cost function to discriminate between the possible options at each sample time. For the estimation process of such algorithms, and the selection of the most likely possibility, we propose a new formulation of a family of cost functions, on the set of the possible assertions per each appliance. The proposed design, abbreviated ARPM (Additive, Retentive Penalty Method), emphasizes two major properties that were discovered to be significant when performing real-Time estimation in a NILM system. The first is a granular calculation of Hamming distances between possibilities, and the second is the processing of the changes in the measured power consumption, rather than the consumption value itself. This design consists of a low number of free parameters, and can be integrated additively and seamlessly with existing cost functions already embedded in NILM systems. It had been evaluated with a series of experiments and proven to enhance the success rate by all measured criteria and on various datasets, with no parameter adjustments.