IPA FE Subject A 2025 Question 4
A question IPA Japan published in 令和７年度 基本情報技術者試験 科目A 公開問題 問4, translated into English. ITPEC is based on the same exams.
There is a device with an MTBF of 4,000 hours and an MTTR of 1,000 hours. Over the next 6 years, the plan is to improve the MTBF by 100 hours every year compared with the previous year through preventive maintenance, and to improve the MTTR by 100 hours every year compared with the previous year through remote maintenance. What is the availability after 6 years have elapsed?
Explanation
0.92 — after 6 years the MTBF is 4,600 hours and the MTTR 400 hours, and availability is MTBF ÷ (MTBF + MTTR).
- •MTBF after 6 years: 4,000 + 100 × 6 = 4,600 hours
- •MTTR after 6 years: 1,000 − 100 × 6 = 400 hours (improving the MTTR means shortening it)
- •Availability: 4,600 ÷ (4,600 + 400) = 4,600 ÷ 5,000 = 0.92
Because the MTBF grows by as much as the MTTR shrinks, their sum stays 5,000 hours, and the availability rises by 100 ÷ 5,000 = 0.02 a year: 0.80 now, 0.92 after 6 years.
Answer (c)
Why not others:
- •(a) 0.88 — the value after only 4 years, 4,400 ÷ 5,000
- •(b) 0.90 — the value after 5 years, 4,500 ÷ 5,000: one year too few
- •(d) 0.94 — the value after 7 years, 4,700 ÷ 5,000: one year too many
Key rule: Availability = MTBF ÷ (MTBF + MTTR); a longer MTBF and a shorter MTTR both raise it, so improving the MTTR means subtracting hours.
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This question comes from the past questions IPA Japan publishes, translated into English by ITPEC Practice. ITPEC Practice is an independent study tool and is not affiliated with IPA or ITPEC. See the original paper (PDF) or Report an issue.