ITPEC FE Subject A October 2024 Question 12
Which of the following is the approximate availability of the system comprising five devices, namely, A, B, C, D, and E as shown in the figure below? The numeric value in parentheses represents the availability of each device. The system is operational if either device connected in parallel is available.
Explanation
0.795 — reduce each parallel pair to one block first, then multiply the three blocks in series.
A parallel pair is down only when both of its devices are down:
- •A and B: 1 − (1 − 0.8)(1 − 0.7) = 1 − 0.2 × 0.3 = 0.94
- •D and E: 1 − (1 − 0.7)(1 − 0.8) = 0.94
The blocks in series must all be up: 0.94 × 0.9 × 0.94 ≈ 0.795
Answer (d)
Why not others:
- •(c) 0.282 — multiplies all five devices as if they were in series, 0.8 × 0.7 × 0.9 × 0.7 × 0.8 ≈ 0.282, ignoring the parallel spares
- •(a) 0.003 — takes each pair's failure probability 0.06 as its availability, dropping the “1 −”: 0.06 × 0.9 × 0.06 ≈ 0.003
- •(b) 0.031 — below even the all-series 0.282; adding a device in parallel can only raise availability, so the result must exceed 0.282
Key rule: Series: multiply the availabilities. Parallel: multiply the unavailabilities and subtract from 1. Collapse each parallel group into one block before combining in series.
System Component · AI-written, may contain errors
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