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.
$0.001.000000.010.994080.020.866500.030.556230.040.265160.050.100560.060.032170.070.009050.080.002310.090.000540.100.00012\begin{array} { | c | c | } \hline \text { Population percent defective } & \text { Probability of acceptance } \\\hline 0.00 & 1.00000 \\\hline 0.01 & 0.99408 \\\hline 0.02 & 0.86650 \\\hline 0.03 & 0.55623 \\\hline 0.04 & 0.26516 \\\hline 0.05 & 0.10056 \\\hline 0.06 & 0.03217 \\\hline 0.07 & 0.00905 \\\hline 0.08 & 0.00231 \\\hline 0.09 & 0.00054 \\\hline 0.10 & 0.00012 \\\hline\end{array}$

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.

0.001.000000.010.994080.020.866500.030.556230.040.265160.050.100560.060.032170.070.009050.080.002310.090.000540.100.00012\begin{array} { | c | c | } \hline \text { Population percent defective } & \text { Probability of acceptance } \\\hline 0.00 & 1.00000 \\\hline 0.01 & 0.99408 \\\hline 0.02 & 0.86650 \\\hline 0.03 & 0.55623 \\\hline 0.04 & 0.26516 \\\hline 0.05 & 0.10056 \\\hline 0.06 & 0.03217 \\\hline 0.07 & 0.00905 \\\hline 0.08 & 0.00231 \\\hline 0.09 & 0.00054 \\\hline 0.10 & 0.00012 \\\hline\end{array}

Emma Wilkerson · Accepted Answer

Final Answer :

The plan meets the α and the β specification fairly well.

0.060.0330.00200.070.0090.00060.080.0020.00020.090.0010.0001\begin{array} { | c | c | c | c | } \hline \begin{array} { c } \text { Population percent } \\\text { defective }\end{array} & \begin{array} { c } \text { Probability of } \\\text { acceptance }\end{array} & \mathrm { AOQ } & \\\hline 0.00 & 1.000 & 0.0000 & \\\hline 0.01 & 0.994 & 0.0099 & \\\hline 0.015 & 0.958 & 0.0144 & \text { At AQL } \\\hline 0.02 & 0.867 & 0.0173 & \text { maximum } \\\hline 0.03 & 0.558 & 0.0167 & \\\hline 0.04 & 0.267 & 0.0107 & \\\hline 0.05 & 0.102 & 0.0051 & \text { At LTPD } \\\hline 0.06 & 0.033 & 0.0020 & \\\hline 0.07 & 0.009 & 0.0006 & \\\hline 0.08 & 0.002 & 0.0002 & \\\hline 0.09 & 0.001 & 0.0001 & \\\hline\end{array}

$The plan meets the α and the β specification fairly well. \begin{array} { | c | c | c | c | } \hline \begin{array} { c } \text { Population percent } \\ \text { defective } \end{array} & \begin{array} { c } \text { Probability of } \\ \text { acceptance } \end{array} & \mathrm { AOQ } & \\ \hline 0.00 & 1.000 & 0.0000 & \\ \hline 0.01 & 0.994 & 0.0099 & \\ \hline 0.015 & 0.958 & 0.0144 & \text { At AQL } \\ \hline 0.02 & 0.867 & 0.0173 & \text { maximum } \\ \hline 0.03 & 0.558 & 0.0167 & \\ \hline 0.04 & 0.267 & 0.0107 & \\ \hline 0.05 & 0.102 & 0.0051 & \text { At LTPD } \\ \hline 0.06 & 0.033 & 0.0020 & \\ \hline 0.07 & 0.009 & 0.0006 & \\ \hline 0.08 & 0.002 & 0.0002 & \\ \hline 0.09 & 0.001 & 0.0001 & \\ \hline \end{array}$

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