## 1 Introduction
CMR has been extensively applied to the collapse resistance assessment of different types of buildings [10; 11; 12]. To judge whether a structural system meets the performance objective, acceptable CMR values are defined in terms of an acceptably low probability of collapse for MCE ground motions in consideration of the uncertainty in collapse vulnerability in the FEMA P695 report [1]. These acceptable CMR values are appropriate for judging the collapse safety ability of any structure type and can guide the anticollapse design of building structures [13; 14]. The differences in theoretical background and seismic precautionary levels between the seismic design codes of China and the United States [15; 16] may cause a difference in the acceptable collapse probabilities of structures. Hence, the acceptable CMR proposed in FEMA P695 cannot be used to judge the collapse resistance ability of structures that are designed in accordance with China's code, and an acceptable CMR conforming to the seismic code of China must be proposed. An acceptable CMR is usually determined on the basis of the acceptable collapse probability. Collapse probabilities, such as that of MCE [9; 17], annualized collapse probability [18; 19], and that in the design reference period [20], are extensively used as assessment parameters for the collapse performance of structures. However, quantitative research on the acceptable values of these collapse probabilities remains deficient. Earlier editions of the provisions indicate that \"if a structure experiences a level of ground motion 1.5 times the design level, i.e., the MCE ground motion, the structure should have a low likelihood of collapse\" [21]. However, this provision is only a qualitative concept and is unquantified. In the following years, this \"low likelihood of collapse\" has been estimated as 10% [9] using the state-of-the-art IDA [22; 23] of structures designed in accordance with the National EarthquakeHazards Reduction Program (NEHRP) Recommended Seismic Provisions [20]. However, this value requires considerable experience and must be adjusted in accordance with actual situations, such as the importance of the structure and the owner's acceptable level. The acceptable probability of collapse at MCE was proposed for the first time in the newly implemented Code for the Anticollapse Design of Building Structures of China [24], and the acceptable probabilities of B- and C-class buildings are set to 1% and 5%, respectively. Such regulation of quantitative acceptable collapse risk at MCE improves the operability in collapse resistance design, but the explanation about various collapse uncertainty sources that influence collapse probability at MCE remains inadequate. Thus, the suggested values must be improved and adjusted through research development and adequate statistical data. With regard to the randomness of earthquake occurrence during a certain period, confining to the acceptable probability at a given earthquake intensity (such as MCE) is unsuitable regardless of seismic risk. The average annual collapse probability of structures obtained by coupling collapse vulnerability and seismic risk not only considers the acceptable probability at MCE but also exhibits the collapse uncertainty within the design life of structures, and hence it can reflect the exact collapse performance of structures. Risk targeting has recently emerged in the seismic design of structures; it considers many uncertainties that are disregarded in the uniform-hazard spectrum method and allows the achievement of consistent performance levels for structures with different properties through the definition of uniform risk design maps [25]. The 50-year collapse probability, which is derived from the average annual collapse probability, is suggested to be less than 1% in FEMA P-750 [20] as a uniform collapse risk target.