問94
頻出度★★★
稼働率0.9の装置で並列システムを構成したい。このシステムの稼働率を0.999とするためには, 最低何台の装置で並列システムを構成する必要があるか。ここで, 並列システムを構成したときに, 少なくとも1台の装置が稼働していればシステムは正常に稼働しているものとする。
令和7年度 ITパスポート試験 問94
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 94
Incorrectア
With 2 devices, the probability of all failing at once is 0.1²=0.01, and the system availability is 1-0.01=0.99. This does not reach the target of 0.999, so it is insufficient.
- イ
正解 In a parallel system, the system is normal “as long as at least one device is running,” so it stops only when all devices fail at the same time. The failure probability of a single device is 1-0.9=0.1. With n devices in parallel, the probability that all of them fail simultaneously is 0.1ⁿ, so the system availability is 1-0.1ⁿ. The target is 0.999, so we look for the smallest n satisfying 0.1ⁿ≤0.001. When n=3, 0.1³=0.001 and the availability is 1-0.001=0.999, exactly meeting the target. When n=2, 0.1²=0.01 and the availability is only 0.99, which is not enough. Therefore at least 3 devices are required, and the correct answer is “イ”.
Incorrectウ
With 4 devices, 0.1⁴=0.0001 and the availability is 0.9999, which meets the target of 0.999; however, 3 devices already achieve 0.999, so this is not the 'minimum number' (excessive).
Incorrectエ
With 5 devices, the availability is 0.99999, which meets the target; but 3 devices are enough, so this is not the minimum number, and it uses even more devices.
ここがポイント
- Parallel system availability = 1 - (failure rate of each device)ⁿ. Failure rate = 1 - availability, and the system stops only when all devices fail at the same time.
- Distinguish this from a series system (where availabilities are multiplied), and find the minimum number of devices meeting the target availability via the inequality 0.1ⁿ≤(1-target).
用語