Simplified one can say that the production / injection system on a platform cons

Question

Simplified one can say that the production / injection system on a platform consist of wells, flowlines and closure systems to ensure that the well closes when needed.

Decommissioning system is tested regularly so that one should ensure that the christmas tree (XT) receives the correct signal by activating the relevant detectors. The system provides correct signal in 98% of cases, which means that the main hydraulic valve receives closing signal in 98% of cases where there is detected a high temperature or smoke.
For the hydraulic main valve satisfactory to shut and keep close so the valve must get proper signal, the valve should close (ie, the actuator must work) and when the valve is in the closed position must hold tight.
Tests show that the valve closes at 99% of cases and the valve remains sealed in 98% of cases.

a) What is the likelihood that hydraulic main valve closes and holds tight in a given situation?

Explanation / Answer

Here,

Probability that system provides correct signal, P(A) = 0.98

Probability that valve closes when it receives the signal, P(B) = 0.99

Probability that valve holds tight when once it is closed, P(C) = 0.98

Hence required probability that hydraulic main valve closes and holds tight in a given situation is P(A) * P(B) * P(C) = 0.98 * 0.99 * 0.98 = 0.9508

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