In a company two mechanics maintain two very important machines in a production process, which usually break down on average every 16 hours. This time between breakdowns has an exponential distribution. A mechanic spends on average 10 hours repairing a machine (time with exponential distribution). Determine how much time a machine spends on average in the system.
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- Find a Doctor is a small startup that helps people find a physician who best meets their needs (location, insurance accepted, etc.). During a “slow” time for it, it has 8 staff members taking calls from customers. On average, one call arrives every 5 minutes (with a standard deviation of 5 minutes). Each staff member spends on average 18 minutes with each customer (with a standard deviation of 27.00 minutes). How long does one of their customers spend, on average, waiting on hold before he or she can start speaking to a representative?At the SuperSpeedy drive-through the time between consecutive customerarrivals has a mean of 50 seconds and a standard deviation of 30 seconds. Thereare two servers whose service time averages 80 seconds with a standard deviationof 20 seconds. Assume that no customers leave the drive-through after entry.a. What is the utilization of the employees?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. Do not provide handwritten solution. Maintain accuracy and quality in your answer. Take care of plagiarism. Do not provide Excel Screet shot rather use tool table
- In the production shop of a company, the breakdown of the machines is found to be Poisson distributed with an average rate of 3 machines per hour. Breakdown time at one machine cost 400 birr per hour to the company. There are two choices before the company for hiring the repairmen. One of the repairmen is slow but cheap, the other is fast but expensive. The slow cheap repairman demands 200 birr per hour and will repair the broken down machines exponentially at the rate of 5 per hour. The fast expensive man demands 300 birr per hour and will repair machines exponentially at an average rate of 6 per hour. Which repairman should be hired?A graphics reproduction firm has four units of equipment that are automatic but occasionally become inoperative because of the need for supplies, maintenance, or repair. Each unit requires service roughly twice each hour, or, more precisely, each unit of equipment runs an average of 30 minutes before needing service. Service times vary widely, ranging from a simple service (such as pressing a restart switch or repositioning paper) to more involved equipment disassembly. The average service time, however, is five minutes. Equipment downtime results in a loss of $20 per hour. The one equipment attendant is paid $6 per hour.Using finite queuing analysis, answer the following questions: a. What is the average number of units in line? b. What is the average number of units still in operation? c. What is the average number of units being serviced?d. The fi- rm is considering adding another attendant at the same $6 rate. Should the firm do it?A machine can operate for an average of 10 weeks before it needs to be overhauled, a process which takes two days. The machine is operated five days a week. Compute the availability of this machine. (Hint: All times must be in the same units.)
- 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?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.Customers send emails to a help desk of an online retailer every 2.9 minutes, on average, and the standard deviation of the interarrival time is 90 seconds. The online retailer has three employees answering emails. It takes on average 7.5 minutes to write a response email. The standard deviation of the service times is 3.5 minutes. How many emails would there be, on average, that have been submitted to the online retailer, but their senders have not received the response email yet?
- At a book store, one customer arrives every 4 minutes. The bookstore has one cashier, and it takes 3 minutes to serve one customer with a standard deviation of 4.9. The arrival process has a standard deviation of 7. What is the average number of customers in the queueA tractor shop that is staffed only by one employee. Suppose that the arrival table corresponds to a Poisson process, so that service times follow exponential distributions. Let us consider that, after observing the evolution of the workshop, it is estimated that the arrival rate is 10 vehicles per day and that the service time is one hour. Assuming that the employee fixes the tractors in strict order of arrival and taking a 12-hour working day, the following questions are asked: a) Average time each tractor must wait to be repaired. b) Probability that a tractor is in the workshop for more than one day. c) Average time that a vehicle is in the system.