Now, let's see an example of how to apply a PRA
or probabilistic risk analysis.
For this, you can think, for example,
of all the times you arrive late for work,
and want to solve it.
By thinking of an event tree model,
with different possibilities and different branches,
and calculating the different probabilities,
you can figure out how to improve your performance.
The initiator event, in this case, is being a work day.
And also, you have mitigating systems,
in form of an alarm clock and a back-up person
that can wake you up if the other system fails.
The main idea here is to solve the model
and to calculate an estimated "career damage frequency"
by calculating the initiating event frequency
and determining, for each branch of the model, their probabilities.
First, we set the different events.
The first one is if we are in a work day.
Then, you have your first mitigating system
in the form of the clock.
Then, you can, as an operator, listen to the clock or not,
and answer to that alarm.
And finally, you have your back-up person
as the second mitigating system.
Lets see how our tree model works.
First, we have that every time that we find a branch,
we are going to have the successful situations at the top
and the failures at the bottom.
The first branch is going to be if the alarm rings.
The second branch depends on if we listen or not listen to the alarm.
And finally, the third is regarding the back-up person
when the clock fails or we don't respond to the alarm.
Let's calculate the frequencies.
First, we can say that each year
has approximately 250 work days,
based on an average of 5 days per week and 50 weeks a year.
Based also on our experience, we know that when the clock alarm works,
we listen to it 90% of the times
and we fail to respond to it 10% of the times.
We also know, based on past experiences, the performance of the back-up person.
This is the operator action regarding human reliability analysis
or past experience.
Next, we have the operator action
regarding the back-up person.
The probabilities here are different from the previous ones.
But there is another probability that we need to know and calculate,
that is how many times does the alarm fail.
Let's calculate it.
To solve this, we can do a diagram
with the main three probabilities that affect the alarm.
Like, setting incorrectly or not setting the alarm,
having electrical power loses or blackouts,
and finally, that the alarm clocks fails for whatever reason
that it's not included in the first two.
So, based on our experience, we know that we don't set properly the alarm
four times each work year.
So we have approximately 0.016 times
of doing this.
Then, we know that, by our experience once again,
we have electrical power loses 3 times each work year.
We have a probability of 0.012.
And finally, the clock company's experience data says
that the failure is 1 in 10 000 demands,
which is a very small probability.
We have all these, and if we calculate the overall failure probability,
we'll have approximately 3% of the times.
Using the rare event approximation and adding the probabilities
under "OR" gate.
So, now we know the probabilities for the alarm to fail.
And we set it here.
Now, we know the frequency of being late
because the alarm fails, we don't respond to the alarm,
and our back-up person fails too.
That is approximately 2.4 times per year.
Also, we can calculate the frequency of being late due to the failure
of the two mitigating systems.
And we set it in 6 times a year.
With these two probabilities or frequencies, sorry,
we can calculate our career damage frequency.
that will be the sum of both, 8.4 days late for work per year.
Now, let's think that you add another clock.
How does the career damage frequency change?
So, please, calculate your career damage frequency
for that case.
Consider that all the probabilities regarding you responding to the alarm
and the back-up person failing to wake you up
and the possible clock failures are the same.
Answer to this question in the next slide.