# Question 250-Step Assembly Line

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?

Question 3

Process with Scrap

Consider the following four-step assembly operation with quality problems:

• The first resource has a processing time of 5 minutes per unit and one employee doing the operation.
• The second resource has a processing time of 4 minutes per unit. It also has one employee doing the operation. However, this is a very delicate task and 80% of all products have to be scrapped after this step.
• Two workers are staffed for the third resource. No quality problems occur at this resource and the processing time is 20 minutes per unit.
• At the fourth and final resource, one operator handles the product. No quality problems exist at this step and the processing time is 12 minutes per unit.

For every unit of demand, how many units have to flow through the second step in the process?