Consider an assembly line with 20 stations. Each station has a 0.5% probability of making a defect. At the end of the line, an inspection step singles out the defective units. The inspection step catches 80% of all defects. From inspection, units that are deemed to be non-defective are moved to the shipping department.
If a defect is found at inspection, it is sent to the rework department. Rework fixes about 95% of the defective units. units are directly shipped from the rework department with no further inspection taking place.
a) what is the likelihood (probability) tha ta unit ends up in rework?
b) what is the likelihood that a defective unit is shipped
hint: figure out the probability that a unit is Not defective coming out of each station. Assuming independence between stations, then calculate the probability o fnon-defective after going through all the 20 stations. Then answer part (a) after considering inspection (probabiliyt of making a defect in assembly and catching it for rework).
For part b), probability of shipping a defective unit = probability o fmaking a defect in assembly and not noticing it + probability of a defect in assembly and noticing it and not get fixed by rework.