Question

A system has two components: A and B. The operating times until failure of the two components are independent and exponentially distributed random variables with parameter 2 for component A, and parameter 3 for component B. The system fails at the first component failure.

(a) - Read section 1.5.2 in the textbook.
(b) - What is the mean time to failure for component A and for component B

Answer 1

`E(x) = (1)/(2)` -- Component A

`E(x) = (1)/(3)` -- Component B

Explanation:

Given

Distribution = Exponential

`\lambda = 2` --- Component A

`\lambda = 3` --- Component B

Solving (a): The mean time of A

The mean of an exponential distribution is:

`E(x) = (1)/(\lambda)`

We have:

`\lambda = 2` --- Component A

`E(x) = (1)/(2)`

Solving (b): The mean time of B

The mean of an exponential distribution is:

`E(x) = (1)/(\lambda)`

We have:

`\lambda = 3` --- Component B

`E(x) = (1)/(3)`