ITPEC FE Morning October 2021 Question 16
In the time-chart of a system shown below, the shaded parts represent the normal working hours of the system, and the white parts represent the time when the system is not available due to failure. The numbers inside each part indicate the start and end hours of each state. Which of the following is the availability of the system?
Explanation
0.90 — availability is the working time divided by the total time on the chart.
- •Working (shaded): 0~60, 70~145, 150~240, 255~300, so 60 + 75 + 90 + 45 = 270 hours
- •Failed (white): 60~70, 145~150, 240~255, so 10 + 5 + 15 = 30 hours
- •Availability: 270 ÷ 300 = 0.90
The same result via MTBF and MTTR: three failures give MTBF = 270 ÷ 3 = 90 hours and MTTR = 30 ÷ 3 = 10 hours, and 90 ÷ (90 + 10) = 0.90.
Answer (c)
Why not others:
- •(a) 0.10 — the downtime ratio 30 ÷ 300, the unavailability
- •(b) 0.82 — would mean about 54 hours down, but the three white parts total only 30
- •(d) 0.98 — would mean only 6 hours down out of 300
Key rule: Availability = uptime ÷ (uptime + downtime) = MTBF ÷ (MTBF + MTTR); read each segment's start and end carefully and add the lengths.
System Component · AI-written, may contain errors
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