Question

please answer to question 10-36.

10-33 A double sampling plan is desired that has a producer's risk of 0.05 at AQL-1.8% nonconforming and a consumer's risk of 0.10 at LQL = 8.5% nonconforming. The lot size is 1500, and the sample sizes are assumed to be equal. Find the sampling plan if the producer's stipulation is to be satisfied exactly. Find the average sample number for lots that are 1.8% nonconforming. 10-35 Refer to Exercise 10-33. Find the double sampling plan if the second sample is to be twice as large as the first sample and the consumer's stipulation is to be satisfied exactly Refer to Exercise 10-33. Find the sampling plan if it is desired to accept batches that are 5% nonconforming with a probability of 0.5. 10-36

Answer 1

AQL = p_1 = 1%. Producer's risk, alpha = 100% - 95% = 5% RQL = p_2 = 8%. Consumer's risk, beta = 10% n_2 = 2n_1 Steps 1. Determine the ratio of p_2/p_1. Here we have calculated as 8. 2. Obtain c_1, c_2, the acceptance levels, from the table below by using the nearest ratio of p_1/p_2. Here, with a ratio of p_1/p_2 equal to 8, we can choose to have c_1 at 0 c_2 at 2. Determine the simple sizes by holding either alpha or beta at specified level. If hold beta at 0.10. the sample sizes can be calculated as: n_1 = (p_2n_1)/p_2 = 2.42/0.08 almostequalto 30 n_2 = 2n_1 = 60. If use the same values but hold alpha at 0.05, the sample sizes can be calculated as: n_1 = (p_1n_1)/p_1 = 0.30/0.01 almostequalto 30 n_2 = 2n_1 = 60. According to the above, there is only one eligible sampling plan which is: n_1 = 30,