A system has two components that operate in parallel, as shown in the following

Question

A system has two components that operate in parallel, as shown in the following diagram. The components operate in parallel so for the system to function properly at least one of the components must function properly. Let F1 denote the event that component 1 fails during one period of operation and F2 denote the event that component 2 fails during one period of operation. P(F1) = 0.20 P(F2) = 0.03 The chance either component fails is independent of one another. The probability the above system fails during one period of operation is P(F1 and F2) = P(F1) times P(F2) P(F1 and F2) = P(F1) + P(F2) P(F1 or F2) = P(F1) + P(F2) P(Not F1 and Not F2) = P (Not F1) times P(Not F2)

Explanation / Answer

Solution:-

As here we need the probability that the above system fails during one period of operation, we need to be sure that both the systems have failed in the operation. Reason is that, as we have the two components in parallel that is, even if one of the two components fail the system will still work.

So, in order to get the system fail during operation, both the systems must fail in the operation.

The first option is correct, i.e., P(F1 and F2) = P(F1) x P (F2).

[Note :- the second option is itself incorrect, the third option will pass the system as one of the two components will be functional here, and the last option is a pure functional system as both components will be functional in this one.]

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