Question

The failure rate for a guided missile control system is 1 in \(1000 .\) Suppose that a duplicate, but completely independent, control system is installed in each missile so that, if the first fails, the second can take over. The reliability of a missile is the probability that it does not fail. What is the reliability of the modified missile?

Short answer

Answer: The reliability of the modified missile is \(\frac{999999}{1000000}\).

Step-by-step solution

Understand the information given and find the probability of failure for each control system

We are given that the failure rate of one guided missile control system is 1 in 1000. We can write this as a probability: P(failure of one control system) = \(\frac{1}{1000}\)

Find the probability of both control systems failing at the same time

Since the two control systems are independent, we can find the probability of both failing by multiplying their individual failure probabilities: P(both control systems fail) = P(failure of control system 1) * P(failure of control system 2) = \(\frac{1}{1000} * \frac{1}{1000} = \frac{1}{1000000}\)

Find the reliability of the modified missile

The reliability of the modified missile is the probability that it does not fail, which can be found by subtracting the probability of both control systems failing from 1: Reliability of modified missile = 1 - P(both control systems fail) = \(1 - \frac{1}{1000000} = \frac{999999}{1000000}\) Therefore, the reliability of the modified missile is \(\frac{999999}{1000000}\).