(Question 6: 10 points) Consider a following configuration of a system (a collec

Question

(Question 6: 10 points) Consider a following configuration of a system (a collection of components). The system has two components arranged in a sequential manner, i.e, the input has to pass through both the components before exiting the system. System Input Output Component 1 Component 2 (a) Under what conditions does the system cease to operate (b) If the failure probability of each of the components is equal to P (0PP, P)? Provide an intuitive reasoning for your answer Consider the following system. The system has two components arranged in parallel. In this case, the input can pass through cither of the components before exiting as the output System Component Input Output Component 2 (c) Under what conditions does the system cease to operate? (d) If the failure probability of each of the components is equal to P (0 P

Explanation / Answer

(a)

The system ceases to operate if either Component 1 alone fails OR Component 2 alone fails OR both Components 1 and Component 2 Fail.

(b)

Failure probability of the system > P,

since the possibilities of failure of the system increases since the failure can be due failure of either of the components OR both.

(c)

The system ceases to operate ONLY if BOTH Component 1 and Component 2 fail at the same time.

(d)

Failure probability of the system < P,

since the possibilities of failure probability of the system decreases since the failure can be due to failure of both Component 1 and Component 2 TOGETHER AT THE SAME TIME only.

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