A new aircraft control system is being designed that must be

A new aircraft control system is being designed that must be 97.5% reliable. This system consists of four components in series. If all four of the components are to have the same level of reliability, then the level of reliability required for each component (enter your response as a percentage rounded to two decimal places)

Solution

Desired Reliability of aircraft control system is 97.5%

As there are four components to be placed in series. Let x be the reliability of each component, hence total reliability of the system is given by

x * x * x * x = 0.975

x^4 = 0.975

x = sqrt(sqrt(0.975)) = 0.9937

Hence reliability of each componenet should be 99.37%