Sign In Sign Up Ask an AI advisor
Bobcat8395
Bobcat8395
30.04.2021 • 
Mathematics

An electronic device contains a number of interchangeable parts that operate independently. Each component is subject to random failure which renders it completely inoperable. All components are inspected at the end of every week. A component which is found to have failed is replaced with an identical new component. Based on historical data, a new component has 0.2 probability of failing in the first week. Components that are 1 week old have a 0.375 probability of failing in the second week. Components that are 2 weeks old have a 0.8 probability of failing in the third week. None of the components last more than 4 weeks. Let the process represented by the state variable Xt be in state

• 0 if a component is less than one week old in week t
• 1 if a component is one week old in week t
• 2 if a component is two weeks old in week t
• 3 if a component is three weeks old in week t

Provide solutions to the following questions:

a. What is the transition matrix P for this process?
b. Determine E(3). What is the value e(3) and what does it mean in the context of the problem?
c. If a device contains a component that is two weeks old, what is the probability that the next time it has a component that is two weeks old will be 5 weeks from now?
d. What is the mean recurrence time for components being new? Find your answer by taking the reciprocal of the steady state probability.

Solved
Show answers

Ask an AI advisor a question

I want advice