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# Risk Analysis and Management: Fragility versus Loads and Fire Explosion Safety Issues

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1. A propane tank is located 100 m away from the nearest buildings. The fragility to explosion can be expressed by

p = 0 for I < 0.7 MPa ? s
p = aI for 0.7 < I < 1.3 MPa ? s
p = 1 for I > 1.3 MPa ? s

Accounting for various release and ignition scenarios, including uncertainties, the estimated probability distribution of impulses resulting from such explosions is given by the following set of values:

I (MPa ? s) 0.1 0.3 0.5 0.7 0.9 1.2
pload 0.06 0.1 0.4 0.3 0.1 0.04

Supposing that you can improve the building so that you can affect the threshold of damage, increasing it above 0.7 MPa ? s, and supposing the high end at 1.3 MPa ? s remains the same, and so is the linear in-between behavior:

(a) Where would you place the lower threshold if you wanted the failure probability not to exceed 5%?
(b) What would you do if your answer in (a) was the best you could do to improve the fragility, and you wanted a failure probability of less than 0.1% (moral certainty for no failures)?

#### Solution Preview

(a) Where would you place the lower threshold if you wanted the failure probability not to exceed 5%?

At I = 1.3 MPa.s, the cumulative probability of fragility to explosion is equal to 1, so a = 1/1.3 = 0.7692.

If the lower threshold is 0.7 MPa.s, the discrete cumulative probability of fragility to explosion is given as follows:
I (MPa ? ...

#### Solution Summary

The concept of fragility to explosion is explored. Probability distributions are used to calculate threshold for failure.

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