In the table below are selected values for the OC curve associated with the acceptance sampling plan n = 50, c = 1. (Watch out-the points are not evenly spaced.) Assume that 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 = 0.0050, α = 0.05; LTPD = 0.05, β = 0.10? Discuss.
$0.0050.973870.010.910560.020.735770.030.555280.040.400480.050.279430.060.190000.080.08271\begin{array} { | c | c | } \hline \begin{array} { c } \text { Population percent } \\\text { defective }\end{array} & \begin{array} { c } \text { Probability of } \\\text { acceptance }\end{array} \\\hline 0.005 & 0.97387 \\\hline 0.01 & 0.91056 \\\hline 0.02 & 0.73577 \\\hline 0.03 & 0.55528 \\\hline 0.04 & 0.40048 \\\hline 0.05 & 0.27943 \\\hline 0.06 & 0.19000 \\\hline 0.08 & 0.08271 \\\hline\end{array}$

Question

In the table below are selected values for the OC curve associated with the acceptance sampling plan n = 50, c = 1. (Watch out-the points are not evenly spaced.) Assume that 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 = 0.0050, α = 0.05; LTPD = 0.05, β = 0.10? Discuss.

0.0050.973870.010.910560.020.735770.030.555280.040.400480.050.279430.060.190000.080.08271\begin{array} { | c | c | } \hline \begin{array} { c } \text { Population percent } \\\text { defective }\end{array} & \begin{array} { c } \text { Probability of } \\\text { acceptance }\end{array} \\\hline 0.005 & 0.97387 \\\hline 0.01 & 0.91056 \\\hline 0.02 & 0.73577 \\\hline 0.03 & 0.55528 \\\hline 0.04 & 0.40048 \\\hline 0.05 & 0.27943 \\\hline 0.06 & 0.19000 \\\hline 0.08 & 0.08271 \\\hline\end{array}

Jailene Laureano · Accepted Answer

Final Answer :  This plan does not meet the specification very well. At .005 defective, the probability of acceptance is not 95% but over 97. At 0.05 defective, the acceptance rate is not 5% but 28.      Population   percent   defective   Probability of   acceptance   AOQ  0.005 0.97387 0.004869  at AQL  0.01 0.91056 0.009106 0.02 0.73577 0.014715 0.03 0.55528 0.016658  maximum  0.04 0.40048 0.016019 0.05 0.27943 0.013972  at LTPD  0.06 0.19000 0.0114 0.08 0.08271 0.006617 \begin{array} { | c | c | c | c | } \hline \begin{array} { c } 	ext { Population } \	ext { percent } \	ext { defective }\end{array}  &  \begin{array} { c } 	ext { Probability of } \	ext { acceptance }\end{array}  &  	ext { AOQ }  &  \\hline 0.005  &  0.97387  &  0.004869  &  	ext { at AQL } \\hline 0.01  &  0.91056  &  0.009106  &  \\hline 0.02  &  0.73577  &  0.014715  &  \\hline 0.03  &  0.55528  &  0.016658  &  	ext { maximum } \\hline 0.04  &  0.40048  &  0.016019  &  \\hline 0.05  &  0.27943  &  0.013972  &  	ext { at LTPD } \\hline 0.06  &  0.19000  &  0.0114  &  \\hline 0.08  &  0.08271  &  0.006617  &  \\hline\end{array}  Population   percent   defective  ​ 0.005 0.01 0.02 0.03 0.04 0.05 0.06 0.08 ​  Probability of   acceptance  ​ 0.97387 0.91056 0.73577 0.55528 0.40048 0.27943 0.19000 0.08271 ​  AOQ  0.004869 0.009106 0.014715 0.016658 0.016019 0.013972 0.0114 0.006617 ​  at AQL   maximum   at LTPD  ​ ​

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