Question

• In the table below are selected values for the OC curve for the acceptance sampling plan n = 210, c = 6. Upon failed inspection, defective items are replaced. Calculate the AOQ for each data point. (You may assume that the population is much larger than the sample.) Plot the AOQ curve. At approximately what population defective rate is the AOQ at its worst? Explain how this happens. How well does this plan meet the specifications of AQL = 0.015, α = 0.05; LTPD = 0.05, β = 0.10? Discuss.

Population percent defective	Probability of acceptance
0.00	1.00000
0.01	0.99408
0.02	0.86650
0.03	0.55623
0.04	0.26516
0.05	0.10056
0.06	0.03217
0.07	0.00905
0.08	0.00231
0.09	0.00054
0.10	0.00012

Answer 1

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(1)ANSWER::-

AS FOR GIVEN DATA....

• In the table below are selected values for the OC curve for the acceptance sampling plan n = 210, c = 6. Upon failed inspection, defective items are replaced. Calculate the AOQ for each data point. (You may assume that the population is much larger than the sample.) Plot the AOQ curve. At approximately what population defective rate is the AOQ at its worst? Explain how this happens. How well does this plan meet the specifications of AQL = 0.015, α = 0.05; LTPD = 0.05, β = 0.10? Discuss.

Population percent defective	Probability of acceptance
0.00	1.00000
0.01	0.99408
0.02	0.86650
0.03	0.55623
0.04	0.26516
0.05	0.10056
0.06	0.03217
0.07	0.00905
0.08	0.00231
0.09	0.00054
0.10	0.00012

The Average outgoing Quality (AOQ) value is obtained using the following formula,

Fraction defective, Pd	Probability of accepting lot, Pa	AOQ
0	1	0.00000
0.01	0.99408	0.00994
0.02	0.8665	0.01733
0.03	0.55623	0.01669
0.04	0.26516	0.01061
0.05	0.10056	0.00503
0.06	0.03217	0.00193
0.07	0.00905	0.00063
0.08	0.00231	0.00018
0.09	0.00054	0.00005
0.1	0.00012	0.00001

The scatter plot for AOQ and fraction defective is obtained in excel by following this step;

Select the data value > INSERT > Recommended Charts > All Charts > Scatter with Smooth Lines and markers. the screenshot is shown below,

From the scatter plot we can find the value AOQ and Probability of acceptance for percentage of defective = 0.015,

Fraction defective	Probability of accepting lot	AOQ
0	1	0.00000
0.01	0.99408	0.00994
0.015	0.96	0.01440	At AQL
0.02	0.8665	0.01733	Maximum
0.03	0.55623	0.01669
0.04	0.26516	0.01061
0.05	0.10056	0.00503	At LTPD
0.06	0.03217	0.00193
0.07	0.00905	0.00063
0.08	0.00231	0.00018
0.09	0.00054	0.00005
0.1	0.00012	0.00001

From the above table, at percentage defective =0.015, the probability of acceptance is about 95% (alpha = 0.05) and at percentage defective =0.05, the probability of acceptance is about 10% (beta = 0.10). hence the plan meets the specification very well.

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