Learning Activity: Ensuring Quality in the Supply Chain

Background: When you put multiple machines together in a production line, even

small errors in each machine can create terrible quality in your finished products. This

gets even worse when you consider your hundreds or thousands of suppliers, each who

may sell you materials with good quality products, but errors combine and may create

too many customer defects.

Rolled Yield $=$ Yield $1**$ Yield$2*$ Yield$3*...($where Yield $=\%$ quality items$)$

Additional Background: "When a product or service is complex, it is important that

suppliers maintain very high levels of quality to ensure that the final product has the

required quality. A concept called rolled yield accounts for the cumulative defect rate

observed by the final customer. For example, suppose a product or service has $100$

components or parts and each part has a yield of $99$ percent $(1$ percent defective$).$

Then the overall yield of the final product is obtained by multiplying the yields of all the

individual parts. Since there are $100$ parts with the same yield $(\mathrm{.}99),$ in this case the

rolled yield is $\mathrm{.}99\mathrm{.}99\mathrm{.}99$dots$\mathrm{.}99(100$ times$)=0\mathrm{.}366=$ only $36\%!!!"($Schroeder

and Goldstein, $2021,$ p$.151)$

Activity: Using the data below, compute your supply chain's Rolled Yield.

Tip: Defect Rate $=$ Defective Items $\frac{?}{?}$ Quantity Delivered

Tip: The Product formula can help you multiply several cells

at one time.

Rolled Yield $=$

Question: With such good suppliers, does this Rolled

Yield pose a concern?