Can any help me how to solve below problem.? I am student and learning OC curve and double sampling plan. Can you someone help me how to understand this concept?

A shipment of 1000 items is to be inspected on a sampling basis. The producer and the consumer have agreed to adopt a plan as shown below:

Quality Level Risk
AQL = 0.01 Alafa = 0.05
LTPD = 0.05 Beta = 0.10

Construct an OC curve of the sampling plan n=100,c<=2, and indicate whether the plan satisfied the requirement. You can use approximation of binomial with Poisson distribution.

To solve this problem and understand the concept of the OC curve and double sampling plan, follow these steps:

Step 1: Understand the Terminology
- AQL (Acceptable Quality Level): The maximum defective rate that the consumer is willing to accept.
- LTPD (Lot Tolerance Percent Defective): The maximum defective rate that the producer is willing to tolerate.
- Alpha (Type I Error): The probability of rejecting a good lot.
- Beta (Type II Error): The probability of accepting a bad lot.

Step 2: Determine the Sample Size (n) and the Acceptance Number (c)
In this case, the sample size (n) is 100, and the maximum acceptable number of defects (c) is 2. This means that if the sample contains 2 or fewer defects, the lot will be accepted; otherwise, it will be rejected.

Step 3: Calculate the Operating Characteristic (OC) Curve
The OC curve shows the probability of accepting a given defective rate for different levels of inspection.

To construct the OC curve, you will need to calculate the cumulative distribution function (CDF) of the binomial distribution. However, in this problem, you can use an approximation of the binomial distribution with the Poisson distribution.

The formula to calculate the CDF of the Poisson distribution is as follows:

CDF(x; λ) = ∑ (e^(-λ) * λ^k) / k!
k=0 to x

Where λ is the average number of defects per inspection, and k is the number of defects.

For this problem, you can use λ = n * AQL, since the average number of defects is the defect rate (AQL) multiplied by the sample size (n).

Step 4: Calculate the OC Curve and Evaluate the Sampling Plan
To construct the OC curve, calculate the CDF for different defective rates and plot the results on a graph.

For example, calculate the CDF for defect rates of 0, 0.01, 0.02, 0.03, 0.04, ..., 0.20. Plot the defect rates on the x-axis and the corresponding CDF values on the y-axis.

Evaluate whether the sampling plan satisfies the requirements by checking if the OC curve stays below the LTPD (0.05 in this case).

Step 5: Interpretation
After plotting the OC curve, analyze the results. If the curve stays below the LTPD line, the sampling plan is acceptable. If the curve crosses above the LTPD line, the sampling plan fails to meet the required standards.

By following these steps, you should be able to construct the OC curve and evaluate the given sampling plan.