Question

The failure rate for a guided missile control system is 1 in 1,000. 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

Answer 1

Answer:

The reliability is 0.999999.

Step-by-step explanation:

The failure rate for a guided missile control system is 1 in 1,000.

Hence, the probability that the missile will not fail is $\frac{1000 - 1}{1000} = \frac{999}{1000}$.

According to the new system, if the first fails, the second can take over.

There are two possibilities, either the first one will be fail or not.

If the first one will not fail, then the probability will be $\frac{999}{1000}$ = 0.999.

If the first one will fail, then the probability will be $\frac{999}{1000} \times\frac{1}{1000} = 0.000999$.

The reliability of the modified missile is 0.999 + 0.000999 = 0.999999.