In the Table Below Are Selected Values for the OC

question 138

Essay

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

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Definitions:

Algorithm

A step-by-step procedure for calculations, data processing, and automated reasoning tasks.

Representativeness Heuristic

A cognitive shortcut where people categorize situations or individuals based on how similar they are to typical cases or categories they know.

Prototypes

Original models or first forms from which subsequent forms are derived or developed; in psychology, widely accepted examples of a certain category.

Heuristic

A mental shortcut or rule of thumb that simplifies decision-making but may not always lead to optimal outcomes.