company is concerned about the total processing time required for one of its major products. To

investigate, the process manager decides to measure the processing time $($in hours$)$ for one product on each shift $($they

operate two shifts$)$ and to place this data on an Average and Range Control Chart to see if the process is stable. See

the data and Control Chart below for $15$ days of production.

Questions:

$1.$ Is this a stable $($in$-$control$)$ process? Yes or No$.$ Explain $($that is$,$ what does your answer mean in this case?$).$

$2.$ When the company priced this particular product, they did so assuming the total processing time would not exceed

$70$ hours. Are they capable of meeting this objective? Yes or No$.$ Explain $($that is$,$ what does it mean to be capable

or not?$)$

$3.$ Currently, the company doesn$$t have the resources to make any changes to this process to improve it$.$ If they

continue to operate this process as it is $($without changes$),$ what risk do they incur that a processing time will exceed

$70$ hours?

$4.$ Suppose the company currently completes about $1000$ units of this product per month. Using your risk estimate in

#$3,$ what is your estimate of the number of units per month that will exceed the $70-$hour total processing time?