The defect rate in Six Sigma is defined as the number of defects divided by the number of opportunities to create defects.

$($a$)$ Some practitioners define the number of opportunities as the number of inspections and$/$or tests. Why is this not a valid way to determine defect rate? $($Hint: the best manufacturers tend to do very little test and inspection.$)$

$($b$)$ Another school of quality thought defines opportunities as value$-$added transformations. That is$,$ a product or service is changed by the process, the change matters to the customer $($i$.$e$.,$ if a step removes scratches from a previous step, it doesn't count$),$ and only first$-$time operations count $($i$.$e$.,$ rework steps are not opportunities$).$ Will this lead to a more reliable measure of defect rate than the previous definition? How might an unscrupulous practitioner manipulate the calculation of opportunities to make the defect rate look better than it actually is$?$