Question 4.89

4.89 Supplier Quality.

A manufacturer of an assembly product uses three different suppliers for a particular component. By means of supplier audits, the manufacturer estimates the following percentages of defective parts by supplier:

Supplier 1 2 3
Percent defective 0.4% 0.3% 0.6%

Shipments from the suppliers are continually streaming to the manufacturer in small lots from each of the suppliers. As a result, the inventory of parts held by the manufacturer is a mix of parts representing the relative supplier rate from each supplier. In current inventory, there are 423 parts from Supplier 1, 367 parts from Supplier 2, and 205 parts from Supplier 3. Suppose a part is randomly chosen from inventory. Define “S1” as the event the part came from Supplier 1, “S2” as the event the part came from Supplier 2, and “S3” as the event the part came from Supplier 3. Also, define “D” as the event the part is defective.

  1. Based on the inventory mix, determine , , and .
  2. If the part is found to be defective, use Bayes's rule to determine the probability that it came from Supplier 3.

4.89

(a) (b) 0.3057.