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Non-intrusive load monitoring (NILM) systems, employed at the utility-customer interface point, provide real-time power usage data to the grid and present real-time per-appliance price data to consumers. Such information will allow consumers to participate in the electricity market, resulting in energy conservation, demand reduction and other benefits. For these reasons, NILM has become an active area of research. In the current paper, a new algorithm is proposed in which both state-switching event identification and load recognition are included. Furthermore, a statistical variable, i.e. cross correlation coefficient, and a statistical method, i.e. crossed index weight determination method, are employed. The key components of the new algorithm, including basic concepts of signal signatures, structure and methodology of the algorithm, are presented. This algorithm is verified by the experiments to identify hybrid home appliances in the laboratory. The experimental results show that the introduction of cross correlation coefficients reveals more information, and that this new algorithm offers minimal computational burden with similar performance to other NILM algorithms reported as well.