Question

a production system relies on a single critical machine, the time until breakdown for this machine follows an exponential distribution with average rate of 3 breakdowns per week
1， probability the machine will operate for one week without failure=  
2， probability that the machine, which has operated for 2 weeks without breakdown, will operate for an additional week without failure=
3， The mean time to failure, measured in weeks=

Answer 1

Ans:

P(T<=t)=1-e^-3t

1)

P(no failure)=P(T>1 week)=e^-3=0.0498

2)Use memoryless property of exponential distribution

P(T>2+1/T>2)=P(T>1)=e^-3=0.0498

3)

Mean time to failure=1/3