This case study integrates key topics learned during the first testing period. Review the Frito Lay SPC video if it will be helpful for seeing the SQC example with salt content again. Complete the problems below to answer the questions on Canvas.

Productivity

The video shows $9$ critical check points for the potato chip line. As shown, there is some product loss between potatoes coming in and bags of chips exiting the process. Assume Frito Lay produces $180$ cases of chips per $2000$ pounds of potatoes and each pound costs $$0\mathrm{.}50.$ It takes an hour to process this quantity at a labor cost of $$350/$hour and utility cost of $$50/$hour$.$ If higher grade potatoes are purchased, $200$ cases can be produced in an hour, but the cost increases to $$0\mathrm{.}70/$pound while the labor and utility costs stay the same. What is the productivity with each grade of potato? What is the $\%$ change in productivity if switching from the current to the higher grade of potato $($be sure to include $-$ if the productivity decreases$)?$ Round productivity answers to $3$ decimals

Prod of low grade $=0\mathrm{.}129$case$/$$

Prod of high grade $=0\mathrm{.}111$case$/$$

Decline in prod. $=-13\mathrm{.}953\%$

SQC

A QC employee for Frito Lay monitors the weight of potato chip bags. The target weight is

$1$ oz $($printed on bag$).$ Based on past data, the filling machine at this plant has an overall

average of $1\mathrm{.}04$ oz with an average range of $0\mathrm{.}10$ oz and a standard deviation of $0\mathrm{.}06$ oz$.$

a$.$ If a sample of $3$ bags is collected every half hour, set up the Xbar and R control charts for this process $(2$ decimals$).$

Xbar $=10\mathrm{.}99$

Rbar $=0\mathrm{.}06$

b$.$ Plot the most recent sample data below on your control charts. Is the process in control? $($don$$t use these for part a$)$

Sample Bag A Bag B Bag C

$10\mathrm{.}981\mathrm{.}090\mathrm{.}95$

$21\mathrm{.}051\mathrm{.}011\mathrm{.}01$

$31\mathrm{.}040\mathrm{.}961\mathrm{.}03$

$41\mathrm{.}041\mathrm{.}011\mathrm{.}02$

$50\mathrm{.}940\mathrm{.}960\mathrm{.}89$

c$.$ The specifications for the snack bags are $0\mathrm{.}80-1\mathrm{.}20$ oz$.$ Is this process capable?

Capacity and Layout

The packaging process requires $5$ tasks after the bags of chips exit the processing equipment to having stacked cases ready for shipping. Production demand is $180$ cases per hour. Use the information below to sketch a precedence diagram, assign tasks to workstations, and answer the questions that follow.

Task Time $($seconds$)$ Predecessor

A $12---$

B $15$ A

C $8$ A

D $5$ B$,$C

E $20$ D

a$.$ What is the maximum cycle time in seconds? $12$ secs

b$.$ Assign tasks to workstations. What is the actual number of workstations? $2$

c$.$ What is the capacity in cases per minute? $3$ cases$/$min

d$.$ What is the bottleneck time? $15$ secs

e$.$ Which station is the bottleneck? B

f$.$ What is the process throughput time? $($reminder it$$s based on stations, not tasks$)130$ secs Part b: Is the process in control?

Group of answer choices

Yes because both charts are in control

No because the range chart is out of control

No because the Xbar chart is out of control Part b: Value of last point you would plot on the range chart $(2$ decimals$)=$ Part c: Cpk $(2$ decimals$)=$