10.2 Probability of Failure in a Portfolio
149
spots at the top left correspond respectively to the p f of Samarco and Mount Polley
evaluated using the data that were available to us before their respective failures.
Using the client’s data, we evaluate the system’s probability p fS on the maximum estimates of the client’s dams (yellow bars) to be 4.37 * 10
−2 /year or roughly
(4.5/100)/year. As it can be immediately seen, the system is heavily influenced by the
few “poor dams” present in the system. This stresses the need to perform quantitative
prioritization of systems, in order to swiftly detect the “bad apples” which affect the
whole system.
As additional proof of the statement above, we added to the previous analysis
first one and then both, green examples (top left) of Fig. 10.6. As stated above,
those correspond to the estimates of Samarco and Mount Polley, developed with the
data that were available before their respective failures. This addition corresponds to
considering one or two extra “bad apple” in the portfolio. As expected, the system’s
probability increases to 1.39 * 10
−1 /year (13.9/100)/year if we include Mount Polley,
and further to 23.4 * 10
−1 /year (23.4/100)/year if we include both Mount Polley and
Samarco. This shows again the serious effect of “bad apples” on a whole system.
Conclusions on Independent Elements
In a real-life system of independent dams it is more efficient to define (and mitigate) the “bad apples” rather than evaluating “cumulative” potential losses to justify
more reserves. This bears particular interest for insurers interested in insuring entire
portfolios.
10.2.2 Dependent Elements
As introduced earlier, the case of dependent facilities is very complex. The dependencies can be physical, intrinsic or external, related to common cause failure (CCF),
etc.
Dependent facilities also have the potential to generate MFLs which are larger
than the single facility failure would generate by domino effects. Thus the reasoning
has to cover simultaneously the probability and the consequences, i.e., a full risk
assessment has to be performed.
Example of Two Cascading Dams
Figure 10.7, again from a real-life study, shows the 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.
As can be seen, the compounded failure of the two dams is less likely than the
failure of Dam 1 alone, but the consequences are more than double (of course,
depending on the reservoirs volumes and many other factors to be determined).
Conclusions on Interdependent Elements
In a real-life portfolio, dependent failures must 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.
149
spots at the top left correspond respectively to the p f of Samarco and Mount Polley
evaluated using the data that were available to us before their respective failures.
Using the client’s data, we evaluate the system’s probability p fS on the maximum estimates of the client’s dams (yellow bars) to be 4.37 * 10
−2 /year or roughly
(4.5/100)/year. As it can be immediately seen, the system is heavily influenced by the
few “poor dams” present in the system. This stresses the need to perform quantitative
prioritization of systems, in order to swiftly detect the “bad apples” which affect the
whole system.
As additional proof of the statement above, we added to the previous analysis
first one and then both, green examples (top left) of Fig. 10.6. As stated above,
those correspond to the estimates of Samarco and Mount Polley, developed with the
data that were available before their respective failures. This addition corresponds to
considering one or two extra “bad apple” in the portfolio. As expected, the system’s
probability increases to 1.39 * 10
−1 /year (13.9/100)/year if we include Mount Polley,
and further to 23.4 * 10
−1 /year (23.4/100)/year if we include both Mount Polley and
Samarco. This shows again the serious effect of “bad apples” on a whole system.
Conclusions on Independent Elements
In a real-life system of independent dams it is more efficient to define (and mitigate) the “bad apples” rather than evaluating “cumulative” potential losses to justify
more reserves. This bears particular interest for insurers interested in insuring entire
portfolios.
10.2.2 Dependent Elements
As introduced earlier, the case of dependent facilities is very complex. The dependencies can be physical, intrinsic or external, related to common cause failure (CCF),
etc.
Dependent facilities also have the potential to generate MFLs which are larger
than the single facility failure would generate by domino effects. Thus the reasoning
has to cover simultaneously the probability and the consequences, i.e., a full risk
assessment has to be performed.
Example of Two Cascading Dams
Figure 10.7, again from a real-life study, shows the 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.
As can be seen, the compounded failure of the two dams is less likely than the
failure of Dam 1 alone, but the consequences are more than double (of course,
depending on the reservoirs volumes and many other factors to be determined).
Conclusions on Interdependent Elements
In a real-life portfolio, dependent failures must 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.