A flame stability diagram in a partially premixed flame is typically expressed using the axis coordinates of heat input rate and equivalence ratio. These diagrams are inadequate for identifying changes in combustion conditions and flame stability when a reference fuel is substituted with other fuels under identical operating conditions. This study proposes a new type of diagram and validates it experimentally. In this new diagram, the axis coordinates are air flow rate and Wobbe fuel flow rate, defined as the fuel flow rate multiplied by the square root of the relative density. The diagram was validated in trials using various fuels, including $CH_4$, $C_{3}H_{8}$, and LFG-$C_{3}H_{8}$ mixed fuels, in a domestic gas-range and an gas interchangeability test burner. The results of these trials show that the new diagram can provide information useful for assessing gas interchangeability of combustion conditions and flame stability when one fuel is substituted with another under identical operating conditions.