問77
頻出度★★★
2 台の処理装置が直列に接続されているシステムがある。両方の処理装置が正常に動作しないとシステムは稼働しない。両方の処理装置の故障の発生は独立しており，稼働率が等しい場合の，処理装置の稼働率とシステムの稼働率の関係を表すグラフの形はどれか。ここで，破線は処理装置の稼働率とシステムの稼働率が等しい場合を表す。
平成22年度 春期 ITパスポート試験 問77
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 77
Incorrectア
This shape lies always above the dashed line, meaning the system availability is higher than that of a single unit. That is the shape for a parallel (redundant) connection, whose availability is 1-(1-A)(1-A) and is higher than the original A. In a series connection the availability is a product and always drops, so it never takes this shape.
- イ
正解 A system connected in series operates only when every unit works normally. The two units have the same availability A, and their failures occur independently, so the availability of the system is the probability that both units are working at the same time, that is A×A=A². In the range 0<A<1, A² is always smaller than A: for example, A=0.9 gives 0.81, A=0.5 gives 0.25, and A=0.2 gives 0.04. The graph therefore meets the dashed line (the line where the system availability equals the processing-unit availability) at the two ends A=0 and A=1, but between them it always sags below the dashed line, forming a curve that is convex downward. Only イ has this shape, so the correct answer is イ.
Incorrectウ
This is an S-shaped curve that crosses from below the dashed line to above it at an availability of 0.5, but A² never exceeds A anywhere in the range 0<A<1. At A=0.5 it is 0.25, and even at A=0.9 it is only 0.81, so beyond 0.5 it still stays below the dashed line. There is no intersection with the dashed line other than at the two ends 0 and 1, so this is wrong.
Incorrectエ
This shape claims that the system availability is higher when the unit availability is below 0.5, but in fact A=0.2 gives A²=0.04 and A=0.4 gives 0.16; the lower the availability, the relatively wider the gap from the dashed line becomes, and the curve always stays below it. The above-below relationship is reversed, so this is wrong.
ここがポイント
- The availability of a series system is the product of the availabilities of its units (A×B), while the availability of a parallel (redundant) system is 1-(1-A)(1-B). Remember it as: series means “it works only when all of them work”, and parallel means “it works as long as any one of them works”.
- Because multiplying values that satisfy 0<availability<1 always gives a result smaller than the original, adding more units in series lowers the system availability, while adding more parallel redundancy raises it. On a graph, the former lies below the dashed line (convex downward) and the latter above it (convex upward).
用語