(Problem 3:) ABC Manufacturing Co. uses a single sampling plan to determine the acceptability of shipments of a wheel assembly used in the manufacture of childrens bicycle. For lots of 500 wheels assembly, samples of n = 15 are taken. The lot is rejected if any defectives are found in the sample. Suppose that AQL = 0.01 and LTPD = 0.05.

1. Find the probability of the producers risk (a) and the consumers risk (b) for the current sampling plan. Is this plan more advantageous for the consumer or the producer?
2. The company realized that the consumers risk and the producers risk under the current sampling plan are not balanced. Thus, both parties agreed to modify the current sampling plan to balance the risks at about 5% (a) and 10% (b), respectively. What is the suggested new sampling plan, i.e., what are n and c, for this goal?