To establish the rate at which materials were falling off the building, the consultant focused on seventeen damaged walls, examining every brick for evidence of spalling – when water entering the brick repeatedly freezes and thaws, damaging the wall. Then, they extrapolated the spalling rate to include every brick in the complex. With over one million bricks, the estimated cost for replacing the damaged ones exceeded $20 million.
In reviewing the engineers’ report, a principal at Analysis & Inference, found that the locations for assessing the damage were not selected in a biased fashion (in particular without “randomization”). By focusing on the most affected upper and north-facing walls which received the brunt of the weather, the engineers applied the highest level of damages to every wall.
A second engineering team, WDP & Associates, conducted a new survey of spalling at wall sites. But they faced a fresh challenge: due to obstructed camera angles, many of the jumbo bricks could not be assessed from a photographic survey.
In the real world, statisticians must often cope with missing, mis-measured, “dirty” or “messy” data. To circumvent the lack of data, A&I constructed a statistical model that predicted the values of the missing data – by location. The model took into account factors such as the direction and height of the wall, and whether it was an inner or outer wall. A&I demonstrated that this properly detailed model could predict with reasonable accuracy the spalling rate in every location throughout the complex.
The Figure here shows the step in the process in
which the relatively inexpensive photo survey of the spalling was converted, by
calibration, to the gold standard of measured spalls on exterior scaffold drop surveys
of small sections of wall (the “true” or “drop” spall rate). The photo spall
rate was converted to a true spall rate by multiplying the photo rate by 2.8
and adding 2.5.
The brick manufacturer was enormously relieved when Analysis & Inference showed conclusively that the predicted spalling rate was just one-third that of the original survey. The testimony from the A&I principal in the Federal District Court for the Southern District of New York substantially reduced the owner’s claim, and the brick manufacturer settled with the owner.
The manufacturer’s attorney wrote: “Without your dedication and insight, a satisfactory result would not have been possible. My deepest personal thanks for all of your help. It was a joy working with you.” And later the attorney added: “It would certainly be useful in resolving future construction disputes if the practice [was] to insist on information as precise as your conclusions...before attempting to fix blame.”
