問57
頻出度★★★
図に示すあるシステムの運転状況において，区間 A における平均故障間隔（MTBF）は何時間か。 経過時間（横軸・右向き矢印）に沿ったシステムの運転状況。稼働中と故障修理中が交互に並ぶ。 - 故障修理中 10時間 - 稼働中 300時間 - 故障修理中 10時間 - 稼働中 200時間 - 故障修理中 20時間 - 稼働中 100時間 - 故障修理中 30時間 区間A は「稼働中 300時間」の開始時点から「故障修理中 30時間」の終了時点までを示す。
平成22年度 春期 ITパスポート試験 問57
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 57
Incorrectア
20 hours is not the MTBF but the value of MTTR (Mean Time To Repair). Dividing the repair time in section A, 10+20+30 = 60 hours, by the 3 failures gives 60 ÷ 3 = 20 hours. MTBF and MTTR use exactly opposite times in the numerator (operating time versus repair time), so mixing the two up produces this value.
Incorrectイ
110 hours comes from taking the whole length of section A, 300+10+200+20+100+30 = 660 hours, and dividing it by the 6 boxes without distinguishing operating from repair (660 ÷ 6 = 110). This averages operating time and repair time together, which departs from the definition of MTBF as dividing only the operating time by the number of failures, so it is wrong.
- ウ
正解 The correct answer is ウ, 200 hours. MTBF (Mean Time Between Failures) is the average time a system runs normally from one failure until the next failure, and it is found as MTBF = total operating time ÷ number of failures. In the figure, section A runs from the start of “Operating 300 hours” to the end of “Under failure repair 30 hours”, so the operating periods inside this section are the three of 300 hours, 200 hours and 100 hours, and the failures (repairs) are the three of 10 hours, 20 hours and 30 hours. The total operating time is therefore 300+200+100 = 600 hours, the number of failures is 3, and MTBF = 600 ÷ 3 = 200 hours. The key point is never to put failure-repair time into the numerator. MTBF averages only the time the system was running, so the repair time (60 hours in total) is excluded from the calculation.
Incorrectエ
220 hours is the whole 660 hours of section A divided by the 3 failures (660 ÷ 3 = 220), which corresponds to MTBF + MTTR = 200 + 20, that is, the average length of one cycle from the occurrence of one failure to the occurrence of the next. This is the mistake of including repair time in the numerator as well; MTBF takes only operating time in the numerator, so 200 is correct rather than 220.
ここがポイント
- MTBF (mean time between failures) = total operating time ÷ number of failures. The numerator contains only the time spent operating, not the time spent under failure repair. Learn how it differs from its counterpart MTTR (mean time to repair) = total repair time ÷ number of failures. The relation availability = MTBF ÷ (MTBF + MTTR) is also frequently tested.
- For this kind of figure question, the key is first to count up correctly the operating boxes and the repair boxes that fall inside the specified section (section A here). Check which box edges the start point and end point of the section are attached to in the figure, and be careful not to count the “Under failure repair 10 hours” outside the section as one of the failures.
用語