ITPEC FE Morning October 2018 Question 16
As shown in the figure below, one (1) server, three (3) clients, and two (2) printers are connected via a LAN. This system prints data located on the server in response to instructions from the clients. When the availability of each device is as shown in the table below, which of the following is the expression that represents the availability of the system? Here, the system is considered available when the server, one (1) of the three (3) clients, and one (1) of the two (2) printers are running.
Explanation
a(1 − (1 − b)³)(1 − (1 − c)²) — the server is in series with a parallel group of clients and a parallel group of printers.
- •The server has no backup, so it contributes a
- •The clients fail as a group only if all three fail, with probability (1 − b)3, so the group's availability is 1 − (1 − b)3
- •The printers likewise: 1 − (1 − c)2
- •The LAN is 1, and all three parts must work, so multiply: a(1 − (1 − b)3)(1 − (1 − c)2)
Answer (d)
Why not others:
- •(a) — ab3c2 requires every client and every printer to run, a pure series system
- •(b) — 1 − b3 is the probability that not all three clients run, not that at least one does
- •(c) — (1 − b)3(1 − c)2 is the probability that every client and every printer is down
Key rule: In series, multiply availabilities; for "at least one of n" in parallel, use 1 − (1 − x)n, one minus the chance that all fail.
System Component · AI-written, may contain errors
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