There are four possible states in total: no machine is down, only machine 1 is down, only machine 2 is down, and both machines are down. Formulate and solve the balance equations based these four state
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A single repairperson looks after both machines 1 and 2. Each time it is repaired, machine i stays up for an exponential time with rate λi, i = 1,2. When machine i fails, it requires an exponentially distributed amount of work with rate i to complete its repair. The repairperson will always service machine 1 when it is down. For instance, if machine 1 fails while 2 is being repaired, then the repairperson will immediately stop work on machine 2 and start on 1. What proportion of time is machine 2 down? Then compute the probability that machine 2 is down.)
There are four possible states in total: no machine is down, only machine 1 is down, only machine 2 is down, and both machines are down. Formulate and solve the balance equations based these four states.
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- A copier machine has a mean time between failures of 400 operating hours. Repairs typicallyrequire an average of 10 hours from the time that the repair call is received until service is completed. Determine the availability of this copierToolco operates a machine shop with 22 machines. On the average, a machine breaks down every 2 hours. It takes an average of 12 minutes to complete a repair. When a machine breaks down, one of four repairpersons is called upon to do the repair. Both the time between breakdowns and the repair time are exponential. Toolco is interested in analyzing this situation and knowing the number of repairpersons needed to keep the shop running "smoothly." A = 12 = 0.5 breaks down per hour μ = 60/12 = 5 breaks down per hour System limit = K = 22 machines Source limit= K = 22 machines R = 1, 2, 3, 4. (M/M/R: GD/ K /K),Failsafe Textiles employs three highly skilled maintenance workers who are responsible for repairing the numerous industrial robots used in its manufacturing process. A worker can fix one robot every 8 hours on average, with an exponential distribution. An average of one robot fails every 3 hours, according to a Poisson distribution. Each down robot costs the company $100.00 per hour in lost production. A new maintenance worker costs the company $80.00 per hour in salary, benefits, and equipment. Should the manager hire any new personnel? If so, how many people? What would yourecommend to the manager, based on your analysis?
- Larry Ellison starts a company that manufactures high-end custom leather bags. He hires two employees. Each employee only begins working on a bag when a customer order has been received and then she makes the bag from beginning to end. The average production time of a bag is 1.7 days, with a standard deviation of 3 days. Larry expects to receive one customer order per day on average. The interarrival times of orders have a coefficient of variation of one. X Answer Is complete but not entirely correct. (Carry at least 4 decimal places in all intermediate calculations. Round your final answer to 2 decimal places.) What is the expected duration, in days, between when an order is received and when production begins on the bag? 30.39 8 daysA copier is able to operate for an average of 200 hours between repairs, and the mean repair time is two hours. Determine the availability of the copier.Users are connected to a database server through a network. Users request files from the Database server. The database server takes a period of time that is exponentially distributed with mean 5 seconds to process a request. Find the probability that 10 requests are processed by the server during the first 1 minutes. Determine the probability that no request is processed by the server during the first 2 minutes Determine the average number of requests processed in 2 minutes
- Suppose that a fire department receives an average of 24requests for fire engines each hour. Each request causes afire engine to be unavailable for an average of 20 minutes.To have at most a 1% chance of being unable to respond toa request, how many fire engines should the fire departmenthave?43. Six thousand light bulbs light a large hotel and casino marquee. Each bulb fails completely at random, and each has an average lifetime of 3,280 hours. Assuming that the marquee stays lit continuously and bulbs that burn out are replaced immediately, how many replacements must be made each year on the average? 14A crew of mechanics at the NCDOT repair NCDOT vehicles that break down at an average rate of λ = 4 vehicles per day. A bureaucrat in Raleigh has determined the cost associated with lost productivity due to breakdowns is $300/day. This same bureaucrat thinks it would be a good idea to have two repair crews instead of one. Vehicles still break down at the same rate of 4/day. Each crew can still service 5 /day. Assume that each crew handles half of the breakdowns. Each crew costs $400/day. The cost associated with the lost productivity of an idle vehicle is still $300/day. What is the cost of service for this new system?
- Suppose that 2000 students enter (and later leave) a classroom building over the 20 hours in which it is open. On average, there are 200 students in the building. Assuming the classroom building is operating in steady-state, which of the following statements are true? (Please tell me why C could be a right answer) A. The number of students in the building is 100, on average. B. Students spend an average of 120 minutes in the building. C. The arrival rate at the building is 83.33 students per hour. D. The building must have at least 5 classrooms. E. None of the answers are correct.A local cab company maintains a fleet of 10 cabs. Each time a cab breaks down, it isrepaired the same day. Assume that breakdowns of individual cabs occur completely atrandom at a rate of two per year.d. What is the probability that there are more than five breakdowns between Thanksgiving Day (November 28) and New Year’s Day (January 1)?Failsafe Textiles employs three highly skilled maintenanceworkers who are responsible for repairing the numerous in-dustrial robots used in its manufacturing process. A workercan fix one robot every 8 hours on average, with an exponen-tial distribution. An average of one robot fails every 3 hours,according to a Poisson distribution. Each down robot coststhe company $100.00 per hour in lost production. A newmaintenance worker costs the company $80.00 per hour insalary, benefits, and equipment. Should the manager hireany new personnel? If so, how many people? What would yourecommend to the manager, based on your analysis?