Proportion of time is the system shut down

Assignment Help Basic Statistics

Reference no: EM131005870

Consider an n-component system where component i, i = 1, ... , n, functions for an exponential time with rate λi and then fails; upon failure, repair begins on component i, with the repair taking an exponentially distributed time with rate μi . Once repaired, a component is as good as new. The components act independently except that when there is only one working com- ponent the system is temporarily shut down until a repair has been completed; it then starts up again with two working components.

(a) What proportion of time is the system shut down?

(b) What is the (limiting) averaging number of components that are being repaired?

Reference no: EM131005870

Questions Cloud

What is the total future worth of these savings : Southwestern Moving and Storage wants to have enough money to purchase a new tractor-trailer in 5 years at a cost of $290,000. If the company sets aside $100,000 in year 2 and $75,000 in year 3, how much will the company have to set aside in year ..

Conditional expected time : In a semi-Markov process, let tij denote the conditional expected time that the process spends in state i given that the next state is j. (a) Present an equation relating μi to the tij .

Proportion of passengers write angry letters : At what rate does the shuttle bus arrive at the terminal without any passengers? Suppose that each passenger that has to wait at the bus stop more than c time units writes an angry letter to the shuttle bus manager.

How much will you invest each year : How much will you invest each year? Even $50 a month is a start ($600 a year), you'll be surprised at how much it will earn. You can chose a number you think you can afford on your life circumstances or you can dream big

Proportion of time is the system shut down : (a) What proportion of time is the system shut down? (b) What is the (limiting) averaging number of components that are being repaired?

Average number of machines : We shall attempt to answer these questions: (a) What is the average number of machines not in use? (b) What proportion of time is each machine in use?

What is the economic service life of the machine : The operating cost of the dozer will be constant at $75,000 per year. At an interest rate of 12% per year, what is the economic service life of the machine? What is the associated AW value?

Number of storms during the ?rst : In good years, storms occur according to a Poisson process with rate 3 per unit time, while in other years they occur according to a Poisson process with rate 5 per unit time. Suppose next year will be a good year with probability 0.3. Let N(t) de..

Events of a nonhomogeneous poisson process : Let T1, T2, ... denote the interarrival times of events of a nonhomogeneous Poisson process having intensity function λ(t).

User Account

All Pages