ITPEC FE Morning October 2019 Question 16
Topic: System Component
There exists a device with an MTBF of forty-five (45) hours and an MTTR of five (5) hours. What is the availability of a system that connects two (2) such devices in series?
Explanation
0.81 — find one device's availability, then multiply, because a series system works only while both devices work.
- •One device: 45 ÷ (45 + 5) = 45 ÷ 50 = 0.90
- •Two in series: 0.90 × 0.90 = 0.81
Answer (a)
Why not others:
- •(b) 0.90 — the availability of a single device, ignoring the second one in the chain
- •(c) 0.95 — higher than one device, but adding a device in series can only lower availability, so no series calculation gives it
- •(d) 0.99 — the parallel result, 1 − (1 − 0.90)2 = 1 − 0.01 = 0.99
Key rule: Availability = MTBF ÷ (MTBF + MTTR); in series multiply the availabilities, in parallel multiply the unavailabilities (1 − A) and subtract from 1.
System Component · AI-written, may contain errors
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