150
10 Defining Probabilities of Events
Fig. 10.7 Result for one dam (Dam 1), blue line, compounded with the potential failure of a second
one (Dam 2). The compounded case is the orange line
10.2.3 Summary of Conclusions on Elements’ Portfolios
(1) The probability of simultaneous failure of independent dams is the product
of their probabilities, i.e., an extremely small value for “normal dams”. For
example three dams with p f = 0.001 (1/1000) give 1/1,000,000,000 (one to one
billion).
(2) However, should those dams be interdependent, the system’s probability of
failure could rise as high as the original p f = 0.001 (1/1000), with consequences
increasing due to domino effects.
(3) In a real-life system of independent dams it is more efficient to define (and
mitigate) the “bad apples” rather than evaluating “cumulative” losses to justify
more reserves. The dams are then to be evaluated jointly (simultaneous failure,
i.e., product of the dams’ probabilities) to determine the maximum portfolio
potential loss and its probability.
(4) In a real-life portfolio dependent failures have to be studied with attention.
Oftentimes risks from dependent failures may be higher or smaller than what
intuition suggests. There is no “one size fits all” intuitive solution to these
estimations.
References
Ang A H-S, Tang WH (1975) Probability concepts in Engineering Planning and Design, Vol. I,
John Wiley and sons
Carlin, BP, Louis, TA (2008). Bayesian Methods for Data Analysis (Third ed.). CRC Press
NIST/SEMATECH e-Handbook of Statistical Methods, April, 2012
Oboni C, Oboni F (2013) Factual and Foreseeable Reliability of Tailings Dams and Nuclear Reactors
-a Societal Acceptability Perspective, Tailings and Mine Waste 2013, Banff, AB, November 6 to
9, 2013
10 Defining Probabilities of Events
Fig. 10.7 Result for one dam (Dam 1), blue line, compounded with the potential failure of a second
one (Dam 2). The compounded case is the orange line
10.2.3 Summary of Conclusions on Elements’ Portfolios
(1) The probability of simultaneous failure of independent dams is the product
of their probabilities, i.e., an extremely small value for “normal dams”. For
example three dams with p f = 0.001 (1/1000) give 1/1,000,000,000 (one to one
billion).
(2) However, should those dams be interdependent, the system’s probability of
failure could rise as high as the original p f = 0.001 (1/1000), with consequences
increasing due to domino effects.
(3) In a real-life system of independent dams it is more efficient to define (and
mitigate) the “bad apples” rather than evaluating “cumulative” losses to justify
more reserves. The dams are then to be evaluated jointly (simultaneous failure,
i.e., product of the dams’ probabilities) to determine the maximum portfolio
potential loss and its probability.
(4) In a real-life portfolio dependent failures have to be studied with attention.
Oftentimes risks from dependent failures may be higher or smaller than what
intuition suggests. There is no “one size fits all” intuitive solution to these
estimations.
References
Ang A H-S, Tang WH (1975) Probability concepts in Engineering Planning and Design, Vol. I,
John Wiley and sons
Carlin, BP, Louis, TA (2008). Bayesian Methods for Data Analysis (Third ed.). CRC Press
NIST/SEMATECH e-Handbook of Statistical Methods, April, 2012
Oboni C, Oboni F (2013) Factual and Foreseeable Reliability of Tailings Dams and Nuclear Reactors
-a Societal Acceptability Perspective, Tailings and Mine Waste 2013, Banff, AB, November 6 to
9, 2013