Penn State Probability of A Leak Detection System Discussion

A leak detection system is available for the pipeline systems you analyzed in Memo 3. The cost of this leak detection system is $2,000,000.

The accuracy of such a system is described in the conditional probability below:

Leak

No Leak

Leak Detected

0.018

0.0098

No Leak Detected

0.002

0.9702

If a leak is detected, then it can be contained before any damages occur. The cost of fixing the leak is

$100,000. If a leak is not detected, then damages occur as described in the section below. 

A false alarm results in a cost of $25,000 to the company. 

The probability of a leak is 2 in 100.

Disasters may result from any of the natural gas transportation options.

 In these events, natural gas leaks from the transport vessel and is then ignited by sparks or high temperatures or open flames and an explosion results. 

If a leak occurs, the severity of such a leak in millions of dollars of damages is given by the following expression ? 

= 2(1.2?), where ? is a number following a Poisson distribution with a mean value of 5 (? = 5).