問67
頻出度★★★
図に示す2台のWebサーバと1台のデータベースサーバから成るWebシステムがある。Webサーバの稼働率はともに0.8とし，データベースサーバの稼働率は0.9とすると，このシステムの小数第3位を四捨五入した稼働率は幾らか。ここで，2台のWebサーバのうち少なくとも1台が稼働していて，かつ，データベースサーバが稼働していれば，システムとしては稼働しているとみなす。また，それぞれのサーバはランダムに故障が起こるものとする。
令和6年度 ITパスポート試験 問67
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 67
Incorrectア
0.04 is (1-0.8)×(1-0.8)=0.04, that is, merely the probability that “both” of the 2 Web servers fail. What we want is the availability of the whole system, so we must subtract this from 1 to get the parallel availability 0.96, and then multiply by the database server. Taking the intermediate failure probability directly as the answer is the mistake.
Incorrectイ
0.58 is the value obtained by treating the 2 Web servers as “in series (both must operate)”, giving 0.8×0.8×0.9=0.576≈0.58. The question states that “it is enough that at least 1 server is operating”, so the 2 Web servers are in parallel, and the series calculation is wrong. For parallel, you evaluate using the product of the failure probabilities.
- ウ
正解 As shown in the figure, the 2 Web servers are arranged in parallel, with the database server connected in series after them. For the parallel part, since it is enough that “at least 1 server is operating”, take the probability that both stop at the same time, (1-0.8)×(1-0.8)=0.04, and subtract it from 1, giving the Web-side availability 1-0.04=0.96. Multiplying this in series by the database server's 0.9 gives 0.96×0.9=0.864. Rounded off at the third decimal place this is 0.86, so ウ is correct.
Incorrectエ
0.96 is only the availability of the parallel 2 Web servers themselves, 1-(1-0.8)(1-0.8)=0.96, and it forgets to multiply by the database server 0.9 that is connected in series afterward. Since the database server must also be operating, you have to carry the calculation through to 0.96×0.9.
ここがポイント
- The availability of a parallel (redundant) configuration is 1 minus “the probability that all units fail at the same time”: 1-(1-r1)(1-r2). Use it when it is enough for at least 1 unit to operate.
- The availability of a series configuration is the product of the individual availabilities. The key procedure is to first combine the parallel block into a single availability, then multiply it with the devices connected in series.
用語