ITPEC FE Morning April 2019 Question 15
A system has devices with availability R, connected as shown in the figure below. Which of the following is the expression that represents the availability of the entire system? Here, a parallel connection only requires either of the two devices to be functional, whereas a series connection requires both the devices to be functional.
Explanation
(1 − (1 − R)²)² — reduce each parallel pair to one availability, then multiply the two pairs in series.
- •A parallel pair fails only if both devices fail: 1 − (1 − R)2
- •Two such pairs in series must both work: (1 − (1 − R)2) × (1 − (1 − R)2) = (1 − (1 − R)2)2
Answer (a)
Why not others:
- •(b) — 1 − (1 − R2) simplifies to R2, so this is R4: all four devices in series
- •(c) — all four devices in one parallel group, which ignores the series link between the pairs
- •(d) — two series pairs (R2 each) placed in parallel: the reverse of the configuration shown
Key rule: Series: multiply availabilities. Parallel: 1 − the product of the unavailabilities. Reduce the innermost groups first.
System Component · AI-written, may contain errors
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