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
Question
Answer:
[tex]E(x) = \frac{1}{2}[/tex] — Component A
[tex]E(x) = \frac{1}{3}[/tex] — Component B
Step-by-step explanation:
Given
Distribution = Exponential
[tex]\lambda = 2[/tex] — Component A
[tex]\lambda = 3[/tex] — Component B
Solving (a): The mean time of A
The mean of an exponential distribution is:
[tex]E(x) = \frac{1}{\lambda}[/tex]
We have:
[tex]\lambda = 2[/tex] — Component A
[tex]E(x) = \frac{1}{2}[/tex]
Solving (b): The mean time of B
The mean of an exponential distribution is:
[tex]E(x) = \frac{1}{\lambda}[/tex]
We have:
[tex]\lambda = 3[/tex] — Component B
[tex]E(x) = \frac{1}{3}[/tex]