Construct and evaluate an event tree diagram. System description: An offshore oil and gas production platform is equipped with a safety system to prevent the release of flammable gases. In the event of a loss of containment in the gas section, the detection system should function to identify the gas release. In the event detection occurs, there are two isolation valves located, in series, in the gas line. The first, the primary isolation valve, is automatically commanded by the gas detection system. To provide redundancy in the event the primary isolation valve fails, a sensor is located in the line downstream $($past$)$ the primary isolation valve. If the primary isolation valve fails and gas is detected by the sensor$,$ it will sound an alarm alerting the operator to manually close the backup isolation valve. Finally, a blowdown valve then opens to de$-$pressurize the sections by allowing the gas in the line to be flared.

Probabilities of failure:

$$ Initiating event: Loss of containment in gas section $(0\mathrm{.}025)$

i$.$ Gas detection system fails: $(0\mathrm{.}05)$

ii$.$ Primary isolation valve fails to close: $(0\mathrm{.}005)$

iii. Sensor$/$Alarm to detect gas downstream of primary isolation valve fails: $(0\mathrm{.}08)$

iv$.$ Backup isolation valve fails to close $($includes operator error$)$: $(0\mathrm{.}025)$

v$.$ Blowdown valve fails to open: $(0\mathrm{.}055)$

Description of potential outcomes:

$$ If neither of the isolation valves closes and the blowdown valve fails to open to allow the gas to be flared, explosion of the platform and personnel death can occur.

$$ If neither of the isolation valves closes but the blowdown valve opens $($an uncontrolled amount of gas is flared$),$ some damage to the platform or injuries to personnel could result.

$$ If either isolation valve closes but the blowdown valve fails to open, the amount of gas trapped in the lines could result in minor system damage.

$$ If either isolation valve closes and the blowdown valve opens, a limited amount of gas is flared from the system resulting in only short$-$term disruption of oil and gas production.

$1.(20$ pts$)$ Develop an Event Tree which shows:

$$ Initiating event

$$ All pivotal events

$$ Each path outcomes and associated probability.

$$ Compute the probability for each outcome.