Question

Benny's Arcade has five video game machines. The average time between machine failures is 50 hours.​ Jimmy, the maintenance​ engineer, can repair a machine in 15 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 nothing machines. ​(Enter your response rounded to two decimal places​.)

c.The average time a machine is out of service is nothing hours. ​(Enteryour response rounded to two decimal places​.)

Answer 1

Given the data in the problem :

Average rate of machine failure = a = 1/50 hours

Average rate of machine repair = S = 1/15 hours

1. Jimmy’s utilization is = a/s = ( 1/50)/(1/15) = 15/50 = 0.30

c)Average time machine is out of service ( i.e. waiting to be repaired or being repaired)

= a/S x ( s -a ) + 1/s

= S/ S x ( s -a )

= 1/ ( s – a )

= 1/ ( 1/15 – 1/50) hours

= 1 / ( ( 50 – 15) / 15 x 50)

=( 15 x 50 )/35 hours

= 21.428 hours ( 21.43 hours rounded to 2 decimal places )

1. Average number of machines out of service ( i.e. waiting to be repaired or being repaired0

= a^2/S x ( S -a ) + a/s

= a/ ( S -a )

= a x Average time machine is out of service ( in hours)

= 1/50 x 21.43

= 0.4286 ( 0.43 rounded to 2 decimal places )