A University Web server has 5 main components, each with the same reliability. All 5 components must work for the server to function as intended. If the University wants to have a 93 percent reliability, what must be the reliability of each of the components? (Round answer to 4 decimal places, e.g. 15.2512.)

You want the reliability of each of 5 components with the same reliability if each is required, and the system reliability is 0.93.

Reliability

The reliability of the system is the product of the reliabilities of the components. If that value is r, we require ...

r⁵ = 0.93

r = 0.93^(1/5) ≈ 0.9856

The reliability of each component must be about 0.9856.

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Additional comment

When probability of failure is small enough, the probability of system failure is approximately the sum of the probabilities of component failure. Here, that would mean the probability of component failure could be estimated as (1 - 0.93)/5 = 0.014. Hence component reliability needs to be approximately 1 - 0.014 = 0.9860.

This sort of method of reliability estimation is often used where a large number of components of relatively high reliability are combined in a system that must meet specific reliability requirements.