Question

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 of? service, that? is, waiting to be repaired or being repaired is 2.68

machines. ?(Enter your response rounded to two decimal places?.)

c. The average time a machine is out of service is 28.88

hours. (Enter your response rounded to two decimal places?.

Answer 1

Average machine failure rate ( 1 failure every 25 hours) = a = 1/25 hours= 0.04 per hour

Average machine servicing rate ( 1 repair every 10 hours ) = s = 1/10 hours = 0.1 per hour

1. Jimmy’s utilization ( %) = a/s x 100 = 10/25 x 100 = 40%

1. Average number of machines out of service ( i.e. waiting to be repaired or being repaired)

= a^2/S x ( S – a ) + a/s

= 0.04 x 0.04 / 0.1 x( 0.1 – 0.04)+ 0.04/0.1

= 0.04 x 0.04 /0.1 x 0.06+ 0.4

= 0.266 + 0.4

= 0.666

1. Average time machine is out of service ( i.e. time required to wait for service + time taken for being serviced)

= a/ S x ( S – a )hour

= 0.04 / 0.1 x ( 0.1 – 0.04)+ 1/ 0.1

= 0.04 / 0.1 x 0.06 + 10

= 6.66 + 10 hours

= 16.66 hours