A manufacturer receives large batches of components daily and decides to institute an acceptance sampling scheme. Three possible plans are considered, each of which requires a sample of 30 components to be tested:

Plan A: Accept the batch if non-conforming components are not found, otherwise reject.
Plan B: Accept the batch if not more than one non-conforming component is found, otherwise reject.
Plan C: Accept the batch if two or fewer non-conforming components are found, otherwise reject.

(a) For each plan, calculate the probability of accepting a batch containing

(i) 2 per cent non-conforming components (ii) 8 per cent non-conforming components

(b) Sketch the operating characteristic of each plan on the same axes without further calculation.

(c) Which plan would be most appropriate in each of the circumstances listed below?

(i) There should be a high probability of accepting batches containing 2 per cent nonconforming items.

(ii) There should be a high probability of rejecting batches containing 8 per cent non-conforming items.
(iii) A balance is required between the risk of accepting batches containing 8 per cent defective items and the risk of rejecting batches containing 2 per cent nonconforming items.