The problem of estimating the error probabilities p and p', and the related problems of testing hypotheses of perfect inspection (p = 1) and/or p' = 0) are among the most challenging in the field of attribute sampling. It is not possible to solve any of these problems unless some at least of the items are inspected more than once. In our discussion we use repeated inspection in various forms. If we can identify each inspection of the same item, then any disagreement between decisions at different inspections provids clear evidence that inspection is not error-free. Whether this reflects values of p ≠ or p' ≠ 0, and what the values of p and/or p' may be, gives rise to much more difficult questions.