To save money, some project specifications for piling require that some percentage (say 10 percent) of the piles shall be subject to integrity testing. Marilyn vos Savant, once regarded as the most intelligent person in the world (IQ of 228) investigated this approach. The following analysis is based on her reasoning:
Assumptions:
Of all piles in quality-controlled projects 10 percent may have some degree of flaws (Faiella and Superbo 1998).
All piles are tested with modern instrumentation that is 90 percent accurate.
Question: A pile randomly selected is tested positive (flawed). What is the probability that it is really flawed?
Solution: Assume that on a given site there are 1,000 piles of which 100 are flawed. From the 900 sound piles the test will confirm that 810 (90%) are sound and 90 are flawed (False positive). Of the 100 flawed piles the tests will find ninety flawed (True positive) and 10% sound ones.
Marylin’s solution: Since the number of false positives is equal to that of true positives, random testing of a single pile is no better than flipping a coin!
As more piles are being tested, the confidence increases, and when all piles are tested, the confidence is as good as the accuracy of the test.
Our advice: Test all piles!
References
Faiella, D. and Superbo, S. (1998): Integrity non destructive tests of deep foundations by means of sonic methods - analysis of the results collected on 37 sites in Italy, 3rd. Conf. Deep Foundations on Bored and Augered Piles, Ghent, pp. 209-213