The independent support motion response spectrum method (ISM) is currently used for seismic analysis to calculate the response of multiply supported piping with independent inputs of support excitations. This approach may derive considerable overestimation in the combination of group responses under the absolute sum rule of NUREG-1061 . 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 of floor response spectra and time histories of floor acceleration are used as independent inputs of support excitations. The group responses are summed with correlation coefficients which are calculated by considering each time history of modal response by independent inputs of support excitations. In this paper, the necessity of taking the effects of correlation coefficients for the group responses into account in the ISM approach is examined. The SATH method has advantage to derive a more realistic sum rule of the group responses and applicability for the actual design.