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

Answer:

$E(x) = \frac{1}{2}$ -- Component A

$E(x) = \frac{1}{3}$ -- Component B

Step-by-step 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:

$E(x) = \frac{1}{\lambda}$

We have:

$\lambda = 2$ --- Component A

$E(x) = \frac{1}{2}$

Solving (b): The mean time of B

The mean of an exponential distribution is:

$E(x) = \frac{1}{\lambda}$

We have:

$\lambda = 3$ --- Component B

$E(x) = \frac{1}{3}$