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already low when scaled by spectral acceleration alone. Comparing results for the average twoparameterindex (Eq. 10) with Sa(T 1 ), the two-parameter index reduces the range of dispersionfrom 0.24-0.45 for Sa(T 1 ) to 0.19-0.29 for SaR Sa 0.5 .S a R Saα1.00.5α = 0.5T F = 2.0T 1CM92-RIOLA92-YERLP89-HCALP89-HSPLP89-WAHOMiyagiMendocinoValparaisoαS a R Sa1.00.5α = 0.5T F = 2.0T 10.00.00 0.02 0.04 0.06 0.08 0.10 0.12IDR MAX0 2 4 6 8 10 12 14λ u(a)(b)0.5Figure 7 – Updated Behavior Curves with IM = S a R Sa(a) IDA and (b) stability curves0.06. PROBABILITY ASSESSMENT OF COLLAPSE PREVENTIONUsing the inelastic time-history and stability analysis method described above, the “collapseprevention” performance for a given set of ground motion records is defined by the stabilitylimit,µˆλ f, defined in terms of the seismic hazard intensity – either Sa(T 1 ) or SaR 0.5 Sa . The nextstep in the performance assessment is to compare the stability limit to the seismic hazard,considering the uncertainty in both the calculated response indices and the site hazard curve.Mean Annual Probability of ExceedanceDefining failure (collapse) by the likelihood of the ground motion intensity exceeding thestability limitP fµˆλ fthe mean annual probability of collapse can be described by the following:[ ≥ µˆ ]= P IM(11)λfWhere P f is the mean annual probability of failure and IM is the seismic hazard demandexpressed using an intensity measure consistent with that used to define the stability limit,µˆλ f.In this case, the two alternative intensity measures considered are S aT ) or( 1SaR Sa0.5. The13