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# Re: Probability..

• To: seaoc(--nospam--at)seaoc.org
• Subject: Re: Probability..
• From: "Bill Sherman" <SHERMANWC(--nospam--at)cdm.com>
• Date: Fri, 3 Jan 1997 10:07:22 +0500

```Thanks again to Ahmed Nisar for clarifying terms of probability:

>The difference in probability of exceedence and probability of occurrence can
>be understood this way..

>Suppose you throw two dice, the probability of getting an exact seven, no
more,
>no less is the probability of occurrence of seven.  the probability of
>exceedence will be the probability of getting anything greater than an exact
>seven.

It occurred to me after asking the question that probability of occurrence
refers to the probability of a single event occurring whereas probability of
exceedance refers to any event "equal to or exceeding".  Thus when ASCE 7
refers to "annual probability" for wind speed, it is referring to probability
of exceedance; similarly, for floods we refer to expected return period which
relates to exceedance probability.

Thus looking back at the original message which prompted my questions, Frank
McClure questioned the following statement: "probabilistic methods could help
inform the decision, with consideration of the likelihood of a significant
seismic event occurring in the time before remedial work, the risk of collapse
due to that event relative to the risk of collapse of some other "typical"
building during a similar exposure period, etc.".

His response was "We start down a very slippery slope if we starting telling
our clients or the public that the probability of occurrence can be given in
terms of a certain number of years for earthquakes of a certain magnitude or
ground motion
strength.  Earthquake ground motion strength parameters are usually, for
building code purposes or earthquake risk assessments, expressed in terms of
"MEAN (average) ANNUAL FREQUENCY OF EXCEEDANCE ( not OCCURRENCE). "

While I concur that probability of occurrence of a single event is different
than probability of exceedance based on the magnitude of an event, I don't see
how that prevents us from discussing seismic events based on the probability
of a certain magnitude event during a given number of years (if that was the
point).  Nevertheless, I do think that expressing the probability in terms of
the probability of exceedance over a given design life is more meaningful than
stating the "mean" return period, as a return period longer than the design
life seems to give a false sense of security - e.g., a 100-year flood design
for a 50-year design life sounds conservative, but a 40% probability of
exceedance in 50-years sounds risky.  It would be beneficial if all such
events - earthquake, wind, flood, etc - were expressed using consistent terms.

```