Hi,

Please allow me to apologize in advance for the length of this post.

That being said, I have a problem used for calculating the tolerability limits of the consequence of a hazard.

For this problem, please allow me to define a few terms that I use:

• Hazard ? root condition or circumstance that can lead to an undesirable state.
• Consequence ? the potential outcome or outcomes of a hazard.
• Triggering Frequency ? rate of occurrence of the initiating event or circumstance that permits or causes a hazard to develop into a consequence. Triggering Frequency values are limited to: 1.E 00 (practically always), 1.E-01 (almost always), 1.E-02 (frequently), 1.E-03 (reasonably probable), 1.E-04 (occasionally), 1.E-05 (remote), 1.E-06 (extremely remote), and 1.E-07 (extremely improbable).
• Undesirable Operational State (UOS) ? the stage in an accident scenario where the scenario has escalated so far that (excluding luck) the accident can be avoided only through successful recovery measures.
• Avoidance Barrier ? risk control designed to prevent the occurrence of an accident by reducing the probability of reaching an undesirable operational state. The values to calculate that barriers will succeed in AVOIDING the UOS are: 1.E-07 (practically always), 1.E-06 (almost always), 1.E-05 (frequently), 1.E-04 (reasonably probable), 1.E-03 (occasionally), 1.E-02 (remote), 1.E-01 (extremely remote), 1.E 00 (extremely improbable).
• Recovery Barrier ? risk control designed to prevent the occurrence (or mitigate the impact) of an accident after the operations has reached an undesirable operational state. The values to calculate that barriers will succeed in succeed in recovering from an UOS are the same as the Avoidance Barriers.
• Detectability ? the ability to recognize reaching the OUS, there by applying the Recovery Barrier activities to the equation. Detectability is quantified using the same values as Triggering Frequency.
• Accident Severity ? is a classification of the impact of a potential accident, measures as: 1.E-09 (catastrophic), 1.E-07 (major), 1.E-05 (minor), and 1.E 00 (negligible)
• Tolerability ? the level of acceptance for assuming the risk of a hazard. Tolerability values are: 1.E-02 (accept), 1.E-01 (monitor), 1.E 00 (secure), 1.E 01 (improve), and 1.E 02 (stop).

The formula that I use is:

UOS = Triggering Frequency X Avoidance Barrier

Tolerability = UOS X Recovery Barrier / Accident Severity

The problem with the formula is it is too basic for an actual assessment of hazards since it leaves out other relevant factors that impact on the effectiveness of the risk controls (avoidance/recovery barriers).

Question 1:
Let?s say that we have an Avoidance Barrier that has an effectiveness value of 1.E-06, IF it is fully deployed throughout an organization. What if only 50% of the organization knows about the risk control? Is it simply 1.E-06 X 0.5?

After addressing risk control deployment, of an individual control, we address the affect of multiple risk controls as explained in: https://www.askmehelpdesk.com/mathem...01163-new.html

Question 2:
If there is a potential for multiple triggers (brings the consequence(s) of a hazard to fruition), acting independently (only requires one), would we calculate their affect in the same manner as we did with the affect of compounding risk controls (barriers)?

Question 3:
The ability to detect the UOS will (may) impact the likelihood of employing the appropriate Recovery Barrier. If the Detectability value is 1.E-01 and the Recovery Barrier Value is 1.E-06, would the ?real? Value of the effectiveness of the Recovery Barrier be 1.E-01 X 1.E-06?

As a math person, are there other factors that you would consider relevant to this calculation?

Thank you very much for your time.

Before diving into the specific questions, please clarify your notation. When you write 1.E-06 do you mean the probability of occurrence is ? If so, then your definition of 1.E00 is wrong - because this equals 1 which means it ALWAYS occurs, not "practically always." And 1.E-1 isn't "almost always" but rather is a 1 in 10 chance of occurring. If I'm misunderstanding your notation please correct me. But if you're going to build mathematical formulas from these you need to be precise about the terms. For example, perhaps the scale should be based on estimated probabilities such as these:

0.99 = practically always
0.9 = almost always
0.5 = frequently
0.2 = reasonably probable
0.05 = occasionally
0.001 = remote
0.0001 = extremey remote
0.00001 = extremely improbable

Once we get the scale properly defined we can then work on probability models.

I'm sorry I wasn't cear. For all notations, please use:

1.E+00 1.0000000
1.E-01 0.1000000
1.E-02 0.0100000
1.E-03 0.0010000
1.E-04 0.0001000
1.E-05 0.0000100
1.E-06 0.0000010
1.E-07 0.0000001

Please note that for "Probability of Occurance" I use:

1.E+00 = 1.0000000 = Practically always
1.E-01 = 0.1000000 = Almost every flight
1.E-02 = 0.0100000 = Frequently
1.E-03 = 0.0010000 = Reasonably probable
1.E-04 = 0.0001000 = Occasionaly
1.E-05 = 0.0000100 = Remote
1.E-06 = 0.0000010 = Extreamly remote
1.E-07 = 0.0000001 = Extremely improbable


And for affectiveness of barries I use probability of SUCCESS:

1.E-07 = 0.0000001 = Practically always
1.E-06 = 0.0000010 = Almost every flight
1.E-05 = 0.0000100 = Frequently
1.E-04 = 0.0001000 = Reasonably probable
1.E-03 = 0.0010000 = Occasionaly
1.E-02 = 0.0100000 = Remote
1.E-01 = 0.1000000 = Extreamly remote
1.E+00 = 1.0000000 = Extremely improbable

Thank you

Oops. Sorry I didn't read you question closely. I understand you question now, regarding:

1.E00 is wrong - because this equals 1 which means it ALWAYS occurs, not "practically always." And 1.E-1 isn't "almost always" but rather is a 1 in 10 chance of occuring

Infortunately my vales are predetermined by the standards sent to me. If you could work through the formula using my values, and point out where they are flawed, that would help a lot. I will then address the flaws after "selling" the folks of the error of their ways. Then I will substitue the correct values.

Again. Thanks!