random variable and signal processing
Each time a machine is repaired, it remains up for an exponentially distributed time with rate ?. It then fails, and its failure is either of two types: - Each failure is, independently of the time it took the machine to fail, a type 1 failure with probability ? and a type 2 failure with probability 1 − ?. - If it is a type ? failure, the time to repair the machine is exponential with rate ?? , ? = 1,2. Consider the machine in either of three states: (0) working, (1) down due to type 1 failure, and (2) down due to type 2 failure. (a) (10 pts) Draw the transition rate diagram and specify the instantaneous transition rates. (b) (10 pts) What proportion of time is the machine in each of the three states?
Homework Answers
Request Answer!
We need at least 10 more requests to produce the answer.
0 / 10 have requested this problem solution
The more requests, the faster the answer.
Q3. Each time a machine is repaired it remains "up" for an exponentially distributed time with rate A. It then fails and "down", and its failure is either of two types. If it is a typ...
Q3. Each time a machine is repaired it remains "up" for an exponentially distributed time with rate A. It then fails and "down", and its failure is either of two types. If it is a type 1 failure, then the time to repair the machine is exponential with rate μ!, if it is a type 2 failure, then the repair time is exponential with rate H2. Each failure is, independently of the time it took the machine to fail, a...
4. Each time a machine is repaired, it remains up and working for an exponentially distributed ti...
4. Each time a machine is repaired, it remains up and working for an exponentially distributed time with rate λ. It then fails, and its failure is either of two types. If it is type 1 failure, then the time to repair the machine is exponentially distributed with mean μ1; if it is a type 1 failure, then the time to repair the machine is exponentially distributed with mean μ2. Each failure is, independently of the time it took the...
Homework Assignment 3.5 Summer 2018 Question 3: Continuous-time Markov Chains (a) A facility has three that...
Homework Assignment 3.5 Summer 2018 Question 3: Continuous-time Markov Chains (a) A facility has three that are identical. Each machine fails independently with an exponential distribution with a rate of 1 every day; repairs on any machine are also exponentially distributed with a rate of 1 every 12 hours. Create a continuous-time Markov chain to model this (identify the rates, and the transition probabilities) (b) Now, assume the facility above has three machines, but one of them is of Type...
A system is subject to two types of failure. When a failure occurs, it is type...
A system is subject to two types of failure. When a failure occurs, it is type 1 with 40% probability The time from when the system is repaired until a new failure occurs exponentially distributed with mean of 30 days. If the failure is type 1, two different components are repaired by two repairmen in exponentially and independently distributed periods each with a mean of 2 days. If the failure is type 2, one component is repaircd by one repairman...
Q3. Commodore 64's computer has three critical parts, each of which is needed for the computer to work. The com...
Q3. Commodore 64's computer has three critical parts, each of which is needed for the computer to work. The computer runs continuously as long as the three required parts are working. The three parts have mutually independent exponential lifetimes before they fail. The expected lifetime of parts 1, 2 and 3 are 10 weeks, 20 weeks and 30 weeks, respectively. When a part fails, the computer is shut down and an order is made for a new part of that...
. A facility of m identical machines is sharing a single repair person. The time to...
. A facility of m identical machines is sharing a single repair person. The time to repair a failed machine is exponentially distributed with mean 1/λ. A machine, once operational, fails after a time that is exponentially distributed with mean 1/μ. All failure and repair times are independent. (a) Draw state transition diagram (b) Find out expression for the steady-state proportion of time where there is no operational machine.
The Acme Machine Shop has five machines that periodically break down and require service. The average...
The Acme Machine Shop has five machines that periodically break down and require service. The average time between breakdowns for any one machine is 4 days, distributed according to an exponential distribution. The average time to repair a machine is 1 day, distributed according to an exponential distribution. One mechanic repairs the machines in the order in which they break down. Use q.xls. a. Determine the probability that the mechanic is idle. (Hint: Pn is given in q.xls, and is...
I. A computer has five processing units (PUs). The lifetimes of the PUs are iid Exp(A) random var...
Answer question in RED box:
I. A computer has five processing units (PUs). The lifetimes of the PUs are iid Exp(A) random variables. When a PU fails, the computer tries to isolate it automatically and reconfigure the system using the remaining PUs. However, this process succeeds with probability c, called the coverage factor. If the reconfiguring succeeds, the system continues with one less PU. If the process fails, the entire system crashes. Assume that the reconfiguring process is instantaneous and...
5 Multiplication Rule Consider a parallel system, that is, a system of n machines in which...
5 Multiplication Rule Consider a parallel system, that is, a system of n machines in which the failure of any machine is mutually independent of the failure of any other machine (i.e. machines fail in isolation, and the failure of any machine or group of machines is independent of the failure of another machine or group of machines). Let P(Fi) denote the probability that machine 1 fails at some point in a one day period, ..., P(F) denote the probability...
5. (15 Points) Let T be a random variable that is the time to failure (in...
5. (15 Points) Let T be a random variable that is the time to failure (in years) of certain type of electrical component. T has an exponential probability density function f(x,A) =e, if >0 10, otherwise. Compute the probability that a given component will fail in 5 years or less.
5. (15 Points) Let T be a random variable that is the time to failure (in years) of certain type of electrical component. T has an exponential probability density function...
Q3. Each time a machine is repaired it remains "up" for an exponentially distributed time with rate A. It then fails and "down", and its failure is either of two types. If it is a type 1 failure, then the time to repair the machine is exponential with rate μ!, if it is a type 2 failure, then the repair time is exponential with rate H2. Each failure is, independently of the time it took the machine to fail, a...
4. Each time a machine is repaired, it remains up and working for an exponentially distributed time with rate λ. It then fails, and its failure is either of two types. If it is type 1 failure, then the time to repair the machine is exponentially distributed with mean μ1; if it is a type 1 failure, then the time to repair the machine is exponentially distributed with mean μ2. Each failure is, independently of the time it took the...
Homework Assignment 3.5 Summer 2018 Question 3: Continuous-time Markov Chains (a) A facility has three that are identical. Each machine fails independently with an exponential distribution with a rate of 1 every day; repairs on any machine are also exponentially distributed with a rate of 1 every 12 hours. Create a continuous-time Markov chain to model this (identify the rates, and the transition probabilities) (b) Now, assume the facility above has three machines, but one of them is of Type...
A system is subject to two types of failure. When a failure occurs, it is type 1 with 40% probability The time from when the system is repaired until a new failure occurs exponentially distributed with mean of 30 days. If the failure is type 1, two different components are repaired by two repairmen in exponentially and independently distributed periods each with a mean of 2 days. If the failure is type 2, one component is repaircd by one repairman...
Q3. Commodore 64's computer has three critical parts, each of which is needed for the computer to work. The computer runs continuously as long as the three required parts are working. The three parts have mutually independent exponential lifetimes before they fail. The expected lifetime of parts 1, 2 and 3 are 10 weeks, 20 weeks and 30 weeks, respectively. When a part fails, the computer is shut down and an order is made for a new part of that...
Answer question in RED box:
I. A computer has five processing units (PUs). The lifetimes of the PUs are iid Exp(A) random variables. When a PU fails, the computer tries to isolate it automatically and reconfigure the system using the remaining PUs. However, this process succeeds with probability c, called the coverage factor. If the reconfiguring succeeds, the system continues with one less PU. If the process fails, the entire system crashes. Assume that the reconfiguring process is instantaneous and...
5 Multiplication Rule Consider a parallel system, that is, a system of n machines in which the failure of any machine is mutually independent of the failure of any other machine (i.e. machines fail in isolation, and the failure of any machine or group of machines is independent of the failure of another machine or group of machines). Let P(Fi) denote the probability that machine 1 fails at some point in a one day period, ..., P(F) denote the probability...
5. (15 Points) Let T be a random variable that is the time to failure (in years) of certain type of electrical component. T has an exponential probability density function f(x,A) =e, if >0 10, otherwise. Compute the probability that a given component will fail in 5 years or less.
5. (15 Points) Let T be a random variable that is the time to failure (in years) of certain type of electrical component. T has an exponential probability density function...
Most questions answered within 3 hours.
-
Where is the error in this code sequence?
String s1 = "Hello";
String s2 = "ello";...
asked 10 months ago -
Financial data for Joel de Paris, Inc., for last year
follow:
Joel de Paris, Inc.
Balance...
asked 10 months ago -
Consider this reaction:
Al2(SO4)3 (aq)+ BaCl3
(aq) Al2Cl6 (aq)- +
3BaSO4(s) . What is the...
asked 10 months ago -
Suppose that Savneet is considering increasing her
recent random sample from 20 car rentals to 40...
asked 10 months ago -
Trucks arrive at an unloading terminal at an average rate of 120
per hour.
Trucks arrive...
asked 10 months ago -
Why are methanol and ethanol completely soluble in water while
octanol is not very little soluble....
asked 10 months ago -
A facilities manager at a university reads in a research report
that the mean amount of...
asked 10 months ago -
When the CuSO4 is rehydrated by adding water to the anhydrous
compound, is this an endothermic...
asked 10 months ago -
A ray of sunlight is passing from diamond into crown glass; the
angle of incidence is...
asked 10 months ago -
A block of mass 0.249 kg is placed on top of a light, vertical
spring of...
asked 10 months ago -
how do the kidneys compensate in the presences of acidosis
a) trigger hyperventilate
b) reserve acid...
asked 10 months ago -
Question 501 pts
The rental rate of capital to the firm increases. Which of the
following...
asked 10 months ago