SOLUTION: 3. A system consists of three identical components, in order for the system to perform as intended; all of the components must perform. Each has the same probability of performance
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Question 1200592: 3. A system consists of three identical components, in order for the system to perform as intended; all of the components must perform. Each has the same probability of performance. If the system is to have a .92 probability of performance, what is the minimum probability of performance needed by each of the individual components? Found 2 solutions by ikleyn, Theo:Answer by ikleyn(52873) (Show Source):
Let x be the minimum probability of performance needed by each of the individual components
(x is the value under the problem's question).
Then the condition that the system performs properly is that each of the three
components works properly.
Since the components perform independently, this condition is
x^3 >= 0.92,
which gives
x >= = 0.972588826 (approximately), or 0.9726 (rounded). ANSWER
You can put this solution on YOUR website! let x be the probability that each component will perform.
you get x^3 = .92
solve for a to get:
x = .92^(1/3) = .9725888262.
each component must be able to perform at least 97.25888263% of the time in order for the combination to perform at least 92% of the time.
that's what i get.
