問69
頻出度★★★
あるコンピュータシステムの故障を修復してから60,000時間運用した。その間に100回故障し, 最後の修復が完了した時点が60,000時間目であった。MTTRを60時間とすると, この期間でのシステムの MTBF は何時間となるか。
平成26年度 春期 ITパスポート試験 問69
テクノロジ系システム構成要素 › システムの評価指標
This question's explanation and your answers so far.
解説
問 69
Incorrectア
480 hours is what you get by subtracting the MTTR of 60 once more from the correctly obtained MTBF of 540. The repair time only needs to be subtracted once from the 60,000 hours; there is no reason to subtract it twice. MTBF is simply «total operating time ÷ number of failures», and this calculation subtracts too much.
- イ
正解 MTBF means «mean time between failures», that is, the average of the time the system was actually operating between one failure and the next; it does not include the time spent on repairs. In this question the 60,000 hours start at the moment one repair was completed and end at the moment the last repair was completed. So this period is filled exactly by 100 complete cycles of «operate → fail → repair», and the total of 100 operating times plus 100 repair times comes to 60,000 hours. Total repair time = MTTR × number of failures = 60 × 100 = 6,000 hours. Therefore the total operating time = 60,000 − 6,000 = 54,000 hours. MTBF = total operating time ÷ number of failures = 54,000 ÷ 100 = 540 hours, so the correct answer is イ. As a check, MTBF + MTTR = 540 + 60 = 600 hours is the length of one cycle, and 600 × 100 = 60,000 hours, which matches the data given.
Incorrectウ
599.4 hours is the value obtained as (60,000 − 60) ÷ 100, subtracting only one repair time of 60 hours. Since the system failed 100 times, repairs were carried out 100 times as well, so what must be subtracted is 60 × 100 = 6,000 hours. This is a mistake that comes from misunderstanding the point that MTTR is the average repair time per occurrence.
Incorrectエ
600 hours is the value obtained as 60,000 ÷ 100, without subtracting any repair time at all. It corresponds to the average length of one cycle (operation + repair), that is, MTBF + MTTR. MTBF is the average of only the time that was spent operating, so you must remove the 6,000 hours of repair time before dividing.
ここがポイント
- MTBF (mean time between failures) = total operating time ÷ number of failures; MTTR (mean time to repair) = total repair time ÷ number of failures. The whole period = operating time + repair time, so the basic procedure is to subtract MTTR × number of failures from the period first, and only then divide.
- The length of one cycle is MTBF + MTTR. If you memorize this together with the relation «availability = MTBF ÷ (MTBF + MTTR)», you can also use it to double-check your calculated results.
用語