問83
頻出度★★★
次の式で求まる信頼性を表す指標の説明はどれか。 MTBF ÷ (MTBF + MTTR)
平成25年度 春期 ITパスポート試験 問83
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 83
Incorrectア
This describes MTBF (mean time between failures) itself; it explains only the numerator, not the whole formula. The average length of time until the system fails is expressed by MTBF alone, and its unit is time. In contrast, the MTBF ÷ (MTBF + MTTR) asked about here is time divided by time, so it has no unit and expresses a proportion rather than an average value. If you overlook the division by the denominator MTBF + MTTR, this choice is easy to pick.
Incorrectイ
This describes MTTR (mean time to repair). The average length of time required to restore the system is expressed by MTTR alone, and it appears in the formula only as part of the denominator. The formula asked about here has MTBF in its numerator, so it is not a formula for the repair time itself. Note also that the smaller the MTTR, the higher the maintainability (the speed of recovery); it is a metric from a viewpoint different from availability.
- ウ
正解 The correct answer is ウ, “The proportion of the total time during which the system is operating.” MTBF ÷ (MTBF + MTTR) is the formula for availability. MTBF (mean time between failures) is the average length of the period from when the system is restored until it fails again, that is, the time it is running normally. MTTR (mean time to repair) is the average length of the period from when a failure occurs until the system is restored, that is, the time it is stopped. A system repeats the cycle “operating → failure → repair → operating”, so MTBF + MTTR represents the total time of one cycle (operating time + downtime). Therefore, the value obtained by dividing the numerator MTBF by the denominator MTBF + MTTR is the proportion of the total time during which the system was running. For example, if MTBF is 95 hours and MTTR is 5 hours, then 95 ÷ (95 + 5) = 0.95, which reads as an availability of 95 %. If you notice that the numerator and the denominator of the formula are not “time itself” but “a ratio of one time to another”, you can also see that the answer must be the choice expressing a proportion rather than an average value.
Incorrectエ
The proportion of the total time during which the system is down is unavailability, and its formula is MTTR ÷ (MTBF + MTTR), that is, the value obtained by subtracting the availability from 1. Its numerator must be MTTR, not MTBF, so it does not match the formula in this question. Availability and unavailability add up to 1, and which of the two times is placed in the numerator makes the meaning exactly opposite; that is the dividing point of this question.
ここがポイント
- Availability = MTBF ÷ (MTBF + MTTR). MTBF is the average of the operating time and MTTR is the average of the downtime, and their sum is the total time of one cycle, so this formula expresses the proportion of the total time that is operating time. Unavailability is MTTR ÷ (MTBF + MTTR) = 1 − availability.
- The larger the MTBF (mean time between failures), the less prone to failure and the more reliable the system is; the smaller the MTTR (mean time to repair), the faster the repair and the higher the maintainability. Both are “average values” whose unit is time, whereas availability is a ratio of them and is therefore a “proportion” with no unit; distinguish between the two.
用語