Question

- A manufacturing facility has a repair shop with two repairmen who repair failed machines on a first-fail-first-serve basis. They work together on the machine if there is one machine down (the repair still takes the same amount of time), and otherwise, each works on a separate machine. Thus, if there are more than two machines down, new failures simply wait for their turn to be repaired. Assume that machine failures arrive in a combined failure stream, so that we do not need to track machine identity. More specifically, assume that the times between machine failures are equally likely between 10 and 20 hours, and that repair times are equally likely between 5 and 55 hours for each machine.

To manually simulate the manufacturing facility, use the approach of items (a) and (b) of Exercise 1 utilizing the following sequence of uniform random numbers (between 0 and 1), U ¼ {0.2, 0.5, 0.9, 0.7, 0.8, 0.1, 0.5, 0.2, 0.7, 0.4, 0.3} to generate times to failure and repair times. Simulate the manufacturing facility manually for five machine repair completions, and calculate the following statistics:

- Fraction of time a machine is down Average number of down machines waiting to be repaired
- Fraction of time each repairman is busy (repairman utilization) Fraction of time the repair facility is idle
- Average time a failed machine waits until its repair starts
- Throughput of the repair facility (number of repair completions per hour)

** Note**: These
manual procedures will simulate the system for a short period of
time. The tedium involved in simulating the system should make you
realize that you need a computer program for long simulations or of
even those of moderate complexity.

Answer #1

please post solutions using R
a manufacturing facility has a repair shop with two repairmen
who repair failed machines on a first-fail-first-serve basis. They
work together on the machine if there is one machine down (the
repair still takes the same amount of time), and otherwise, each
works on a separate machine. Thus, if there are more than two
machines down, new failures simply wait for their turn to be
repaired. Assume that machine failures arrive in a combined failure...

. 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.

Question: ?Benny's Arcade has five video game machines. The
average time between machine failures is 25 hou...
?Benny's Arcade has five
video game machines. The average time between machine failures
is 25
hours.? Jimmy, the maintenance? engineer, can repair a machine
in 10
hours on average. The machines have an exponential failure?
distribution, and Jimmy has an exponential? service-time
distribution.
a. ?Jimmy's utilization is ?.
?(Enter your response rounded to three decimal?
places.)
b. The average number of machines out...

Consider a batch manufacturing process in which a machine
processes jobs in batches of three units. The process starts only
when there are three or more jobs in the buffer in front of the
machine. Otherwise, the machine stays idle until the batch is
completed. Assume that job interarrival times are uniformly
distributed between 2 and 8 hours, and batch service times are
uniformly distributed between 5 and 15 hours.
Assuming the system is initially empty, simulate the system
manually...

please post solutions using R
Consider a batch manufacturing process in which a machine
processes jobs in batches of three units. The process starts only
when there are three or more jobs in the buffer in front of the
machine. Otherwise, the machine stays idle until the batch is
completed. Assume that job interarrival times are uniformly
distributed between 2 and 8 hours, and batch service times are
uniformly distributed between 5 and 15 hours.
Assuming the system is initially...

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