The independent support motion (ISM) response spectrum method is currently used in seismic analysis to calculate the response of piping systems subjected to independent excitations at several points of a supporting structure. This approach leads to considerable overestimation when the maximum responses by multiple excitations are combined by the absolute sum rule, while this may result in underestimation when the maximum responses by the multiple excitations are combined by the square root of sum of squares rule. Then authors have developed an advanced method of the ISM approach named SATH (spectrum method assisted by time history analysis). In the SATH method, both floor response spectra and time histories of floor acceleration are used as independent inputs of support excitations. The information of the mode shapes, frequencies, and damping values for the supporting structure is not necessary. The maximum responses by multiple excitations are combined using correlation coefficients calculated by taking into account each time history of modal response due to independent inputs of support excitations. In this paper, it was confirmed that the SATH method has the advantage to derive a more realistic rule for combining the maximum responses by multiple excitations, and that it can be easily applied to the actual design as a response spectrum method.