5. Consider a process where a fraction p (if p = .07 then 7 parts out of 100 parts are defective) of the items processed turn out defective. Suppose a defective item has two particular types of defects that determine the ability to rework it. Given that an item has been identified as defective, inspector 1 inspects it for the first type of defect. As shown in the Figure below, if he/she finds that the item has the first type of defect, then the item is scrapped (with probability q₃), or it is sent back for reprocessing (with probability q₁). Otherwise, the defective item is directly passed to the second inspector who inspects it for the second type of defect.

With probability (1-r), inspector 2 finds that the item has the second type of defect and the item is scrapped. Otherwise, the defective item is considered to be reworkable and it is sent back for reprocessing. It is assumed that an item can be reprocessed indefinitely and that, regardless of the number of times an item has been reprocessed, it turns out defective with probability p. It is also assumed that the two types of defects occur independently.

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