Abstract
I congratulate the authors for their first time showing the data upon which the fragility functions were based. Transparency is important so that engineers can make informed decisions when using the functions.
The purpose of my discussion is to point out that despite the mathematical elegance and care that went into deriving the functions, they are based on an assumed relationship that does not appear to be supported by the data. My impression is that peak acceleration alone is a poor predictor of failure probability when looking at the data points in Figures 1 through 15 (e.g., see air handling units, chillers, or engine generators).
I can understand the desire of having the fragility based on a single intuitively logical variable (peak floor acceleration); unfortunately, the reality appears to be more complex, with additional variables entering into the problem. Hence, I think the fragility functions presented are more like expert opinion rather than objective, statistical, science-based relations, and the next step of creating performance modification factors (PMFs) amounts to adding another layer of expert opinion. Engineers should be alerted of this prior to using them on their particular projects so that they can make sure to incorporate their own judgments.
I would appreciate the authors presenting coefficient of determination (R2) statistics for several of the equipment types to see if my impression is correct. The R2 from standard linear regression would be very informative since this measure is well understood by engineers. I suspect the R2 is near zero, thus indicating no association of failure probability with peak floor acceleration. I would also appreciate the authors’ thoughts regarding why the data points do not show upward trends as postulated by the derived fragility functions (higher failure probability with increasing peak floor acceleration).
In closing, I commend the authors for their efforts to advance our knowledge in the challenging area of equipment seismic fragilities, even in view of my concerns above.