Consider a processing time that has three independent sub$-$tasks. These are:

the job setup time S$,$ normal processing time P$,$ and job removal time R from the

machine. The distributional parameters for these sub$-$tasks are:

E$[$S$]=10$ min, C$2[$S$]=3,$

E$[$P$]=1$ hr$,$ C$2[$P$]=1$

$2,$

E$[$R$]=5$ min, C$2[$R$]=1.$

$($a$)$ Determine the mean and squared coefficient of variation for the job residence

time $($total processing time$).$

$($b$)$ After careful study the engineering department has come up with a jig for performing a sizeable proportion of the job setup time off line $($while the machine is

busy processing another job$).$ The result is that the $$on$-$line$$ machine setup time is

reduced, with resulting parameters E$[$S$]=1$ min and C$2[$S$]=1.$ In addition, due to

an operator suggestion, the job removal time variability was reduced toC$2[$R$]=1/3.$

Note that no improvement was made in the actual machine processing time. Determine the mean of the new total processing time $($job residence time$)$ and its squared

coefficient of variation. What are the percentage improvements over the $$old$$ job

residence time parameters?