CODEWITHSUNDEEP
probabilityreliabilitysubsystem
raulgabriel9999
raulgabriel9999

Reputation: 1

subsystem configuration

What is the minimum number of subsystems that need to be configured in parallel in order to increase the availability of the entire system to 99% or more, if the availability of each subsystem in the parallel system shown below is 70%?

Assume that the entire system is running as long as one subsystem is running.

diagram:

diagram http://postimage.org/image/tdv2xfwk/

The answer is 4 but I don't know why?

Upvotes: 0

Views: 117

Answers (1)

bdonlan
bdonlan

Reputation: 231203

This isn't a programming question such as a probability question. Assuming that subsystem failures are independent events (this is NOT obvious - the question is flawed for leaving this out, but unsolvable if we don't assume it), we can consider the probability for NOT all subsystems being NOT available.

Since "NOT-available" are independent events, we can compute the probability of "all subsystems being NOT available" by multiplying the probabilities of each individual event, as in (1-p)^n, where p is the probabilty of a system being available (0.7 in this case), and n is the number of subsystems.

Then to get back the probability of at least one being available - that is, NOT all being NOT available, just invert the probability, with 1-(1-p)^n. Now just find the lowest value of n for which this comes out to be at least 0.99.

Upvotes: 1

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