Final answer:
To construct the OC curve for the given sampling plan, calculate the probability of acceptance (Pa) for different lot quality levels (p) and plot them on a graph.
Step-by-step explanation:
An OC curve, also known as Operating Characteristic curve, is used to evaluate the performance of a sampling plan in terms of its ability to accept or reject a lot of items based on a specific acceptance number and rejection number. The sample size (n), acceptance number (c), and rejection number (r) are given as n=24, c=7, and r=8.
To construct the OC curve, you can calculate the probability of acceptance (Pa) for different lot quality levels (represented by the proportion of defective items, p). The OC curve can be graphed by plotting the values of p on the x-axis and the corresponding values of Pa on the y-axis.
Here's the step-by-step process to construct the OC curve:
- Choose a range of values for p. For example, you can choose p values from 0 to 1 (representing 0% to 100% defective items).
- For each value of p, calculate the probability of acceptance (Pa) using the binomial distribution formula: Pa = (nCr) * (p^c) * ((1-p)^(n-c)), where n is the sample size, c is the acceptance number, and r is the rejection number.
- Plot the values of p on the x-axis and the corresponding values of Pa on the y-axis.