ITPEC IP April 2019 Question 14
Among the system configurations shown below, which of the following has the lowest probability of causing the entire system to stop at the occurrence of a failure? Here, ─▭─ represents an identical device. When the devices are connected in parallel, only one device must be running, and when the devices are connected in serial, all devices must be running.
Explanation
Three devices in parallel — the system stops only if all three devices fail at once.
Let p be the probability that one device fails. Then the probability that each system stops is:
- •(a) two in series: stops if either fails, 1 − (1 − p)2, about 2p
- •(b) two in parallel: stops only if both fail, p2
- •(c) three in series: stops if any fails, 1 − (1 − p)3, about 3p
- •(d) three in parallel: stops only if all three fail, p3
For any p between 0 and 1, p3 < p2, and both are far below the series cases, so (d) is the least likely to stop.
Answer (d)
Why not others:
- •(a) — in series every device must run, so one failure out of two stops the whole system
- •(b) — redundant, but only two devices must fail to stop it, p2 > p3
- •(c) — the worst of the four: three devices in series give three chances for a single failure to stop the system
Key rule: Adding a device in series multiplies the chances to stop; adding one in parallel multiplies the failure probability by p again, so each parallel device lowers the chance of stopping.
System Component · AI-written, may contain errors
This question comes from an official ITPEC past paper. ITPEC Practice is an independent study tool and is not affiliated with ITPEC. See the official IP past-paper collection or Report an issue.