ITPEC FE Subject A April 2025 Question 12
In a system that is composed of two processing devices, what is the difference in availability between the two conditions below? Here, the availability of each processing device is 0.9, and no other factors besides the processing devices are considered.
[Conditions]
Explanation
0.18 — compute each condition's availability, then subtract.
- •Condition (1), parallel: the system fails only if both devices fail, 1 − (1 − 0.9)2 = 1 − 0.01 = 0.99
- •Condition (2), series: both must run, 0.9 × 0.9 = 0.81
- •Difference: 0.99 − 0.81 = 0.18
The difference is exactly the probability that one device runs and the other does not: 2 × 0.9 × 0.1 = 0.18.
Answer (c)
Why not others:
- •(a) 0.09 — 0.9 × 0.1 counts only one of the two cases where exactly one device runs
- •(b) 0.10 — the unavailability of a single device, 1 − 0.9, not a difference between the two systems
- •(d) 0.19 — 1 − 0.81: treats condition (1) as always available, forgetting that both devices can fail at once (0.01)
Key rule: Series: multiply the availabilities. Parallel: multiply the unavailabilities and subtract the product from 1.
System Component · AI-written, may contain errors
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