Consider an assembly line with 50 steps that are carried out sequentially. Each
ID: 3201163 • Letter: C
Question
Consider an assembly line with 50 steps that are carried out sequentially. Each of the 50 steps has a defect probability of 1%. The final product produced on the assembly line is defective if any one of the 50 steps made a defect.
At the end of the assembly line there are two operators independently inspecting the product. Each of them is recognizing a defective product with a 90% probability. Assuming that the product is not defective, it is moved to the shipping department. Otherwise, the product is scrapped.
Probability that a defective product is produced (independent of the defect being found or not) (in decimal form):
What is the probability that a defective product is moved to the shipping department?
Explanation / Answer
Probability that a defective product is produced = 1- Probability that a non defective product is produced
= 1- (0.99)50 = 1- 0.605 = 0.395
probability that a defective product is moved to the shipping department = 1- (0.9)(0.9) = 0.19