問70
頻出度★★★
2台の処理装置からなるシステムがある。両方の処理装置が正常に稼働しないとシステムは稼働しない。処理装置の稼働率がいずれも0.90であるときのシステムの稼働率は幾らか。ここで，0.90の稼働率とは，不定期に発生する故障の発生によって運転時間の10%は停止し，残りの90%は正常に稼働することを表す。2台の処理装置の故障には因果関係はないものとする。
平成21年度 春期 ITパスポート試験 問70
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 70
- ア
正解 The correct answer is ア (0.81). The question states that the system operates only when both processing units are operating normally, so these 2 units form a series configuration. The availability of a series system is obtained as the product of the availabilities of the individual units. In addition, the statement that the failures of the two processing units are not causally related means that the operation of the two units is mutually independent, so the probability that both are operating at the same time can be obtained simply by multiplication. The availability of the system is therefore 0.90 × 0.90 = 0.81. Intuitively, during the 90% of the operating time in which the first unit is running, the second unit is running for only 90% of that time as well; thinking of it as “90% of 0.90” gives 0.81. Conversely, the system is down whenever either one of the units has failed, and that proportion is 1 − 0.81 = 0.19, about 19%.
Incorrectイ
0.90 simply takes the availability of a single processing unit as the answer. In a series configuration the system does not work unless both units are operating at the same time, so as long as the availability of the other unit is less than 1, the overall availability is necessarily lower than the 0.90 of a single unit. The overall value stays at 0.90 only when the other unit never fails (availability 1.00), which does not apply here because both units have an availability of 0.90.
Incorrectウ
0.95 corresponds to an incorrect calculation that splits the 10% failure rate between the 2 units, as in 1 − 0.10 ÷ 2 = 0.95, or to a guess that takes the midpoint between 0.90 and 1.00. Availabilities are not added or averaged; in a series configuration they are obtained as a product, so the availability of the whole system can never exceed the 0.90 of a single unit.
Incorrectエ
0.99 is the availability of a parallel configuration (a redundant configuration in which the system operates as long as at least 1 unit is running). For a parallel configuration it would be 1 − (1 − 0.90) × (1 − 0.90) = 1 − 0.01 = 0.99. This question states that the system operates only when both processing units are operating normally, that is, a series configuration in which both units are required, so this formula does not apply.
ここがポイント
- The availability of a series configuration (all units are required) is the product of the individual availabilities, p1 × p2, and the availability of a parallel configuration (a redundant configuration in which only 1 unit needs to be running) is 1 − (1 − p1) × (1 − p2). The statement that the failures are not causally related indicates that the units operate independently, which is the precondition for using this multiplication.
- The first step is to read carefully whether the question says the system works only when both units operate normally or that only 1 unit needs to be running, and to judge from that whether the configuration is series or parallel. Remembering that a series configuration becomes less available as more units are added (always lower than with a single unit), while a parallel configuration becomes more available as more units are added (always higher than with a single unit), lets you narrow down the choices before calculating.
用語