Consider a machine with the exponential reliability model. Assume that the breakdown rate, lamba, is 1...
Consider a machine with the exponential reliability model. Assume that the breakdown rate, lamba, is 1 and repair rate, mu, is 2.
(a) Calculate the probability that the machine is up for more than 10 units of time.
(b) Calculate the probability that the machine is down for less than 3 units of time.
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Consider a machine with the exponential reliability model.
Assume that the breakdown rate, lamba, is 1...
2. Consider the reliability model given in Assignment 5 Problem 1. You have discovered that the...
2. Consider the reliability model given in Assignment 5 Problem 1. You have discovered that the reliabilities given there were just rough estimates. After careful analysis of historical data, you know that each component has a random time until failure that is distributed according to the following table. Ideally, this machine shop should run for the next 2 years without the need to replace any components. Mean time until failure (MTTF); Time until failure (TTF) Component Distribution Exponential Parameters MTTF:...
Assume the inspection time of a machine follows an exponential distribution with parameter equal to 1....
Assume the inspection time of a machine follows an exponential distribution with parameter equal to 1. (a) Calculate the probability that the inspection time lasts more than 2 hours. (b) Calculate the probability that the total inspection time lasts more than 4 hours if we have already spent 2 hours inspecting the machine. (c) Every time we need to spend more that 2 hours inspecting a machine we get paid a bonus $1000. Calculate the probability that for the next...
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...
A production system relies on a single critical machine, the time until breakdown for this machin...
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=
The time, in hours, required to fix a machine is an exponential variable with parameter λ...
The time, in hours, required to fix a machine is an exponential variable with parameter λ = 1/2 (a) What is the probability that the repair time exceeds 2 hours? (b) What is the conditional probability that the repair time exceeds 10 hours, assuming it takes at least 9 hours?
3. Consider a fleet of N airplanes. Each airplane breaks down independently at rate μ, and is the...
3. Consider a fleet of N airplanes. Each airplane breaks down independently at rate μ, and is then sent to the hangar for repair. The repair facility can only repair one airplane at a time and each airplane takes an exponential time of parameter λ to repair of the number of airplanes in service. (b) when N 2, find the smallest value of λ/μ such that the limit probability that all are in service is greater th an 1/2
3....
The time between arrivals of customers at an automatic teller machine is an exponential random variable...
The time between arrivals of customers at an automatic teller machine is an exponential random variable with a mean of 5 minutes. A) What is the probability that more than three customers arrive in 10 minutes? B) What is the probability that the time until the 6th customer arrives is less than 5 minutes?
Oasis Corporation has a maintenance department that handles repair of electronic devices. The average rate of...
Oasis Corporation has a maintenance department that handles repair of electronic devices. The average rate of arrival of machines for repair, follow a Poisson distribution and occur at the rate of 3 per day. The maintenance department can handle 4 machines per day on average. The repair times follow an exponential distribution. What is the utilization rate of the service system? What is the average down time for a machine that is broken? How many machines are waiting to be...
(1) Consider a "two machine two repairman" problem, where each machine independently breaks down ...
(1) Consider a "two machine two repairman" problem, where each machine independently breaks down at rate μ (that is after an exponential waiting time with parameter μ) (a) If each repairman repairs a machine at rate λ, calculate the long term proportion of time when both machines are broken. [Hint: calculate the stationary probabilities.] You can also consider 4 marks] (b) Assume that repairman Abel works at rate X, and repairman Bernard works at rate Xb. When there is only...
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 ?? , ?...
2. Consider the reliability model given in Assignment 5 Problem 1. You have discovered that the reliabilities given there were just rough estimates. After careful analysis of historical data, you know that each component has a random time until failure that is distributed according to the following table. Ideally, this machine shop should run for the next 2 years without the need to replace any components. Mean time until failure (MTTF); Time until failure (TTF) Component Distribution Exponential Parameters MTTF:...
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...
3. Consider a fleet of N airplanes. Each airplane breaks down independently at rate μ, and is then sent to the hangar for repair. The repair facility can only repair one airplane at a time and each airplane takes an exponential time of parameter λ to repair of the number of airplanes in service. (b) when N 2, find the smallest value of λ/μ such that the limit probability that all are in service is greater th an 1/2
3....
(1) Consider a "two machine two repairman" problem, where each machine independently breaks down at rate μ (that is after an exponential waiting time with parameter μ) (a) If each repairman repairs a machine at rate λ, calculate the long term proportion of time when both machines are broken. [Hint: calculate the stationary probabilities.] You can also consider 4 marks] (b) Assume that repairman Abel works at rate X, and repairman Bernard works at rate Xb. When there is only...
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