What makes an OC curve "good"?

A good OC curve drops steeply from near 100% acceptance at acceptable quality to near 0% at unacceptable quality. The transition zone should be narrow. This means the plan has high discrimination and low risk at both ends.

How does sample size affect the OC curve?

Larger sample sizes make the OC curve steeper, reducing the indifference zone between AQL and LTPD. This provides better discrimination but at higher inspection cost. Doubling the sample size roughly halves the LTPD-to-AQL ratio.

What is the ideal OC curve shape?

The ideal would be a vertical step function at the desired quality level — accepting everything better and rejecting everything worse. This requires infinite sample size. Practical plans approximate this with sigmoid-shaped curves.

Can I compare two plans using OC curves?

Yes, this is the primary use. Overlay OC curves for different n/Ac combinations on the same chart. The plan with the steeper curve provides better discrimination. Select the plan that gives acceptable producer's and consumer's risk at your target quality levels.

Does the OC curve depend on lot size?

For binomial approximation (large lots), no. For hypergeometric computation (small lots where sample is > 10% of lot), yes — smaller lots have steeper OC curves at the same sample size because the sample represents a larger fraction of the lot.

How do I use the OC curve in negotiations with suppliers?

Share the OC curve with your supplier and say: "At X% defective, you have a Y% chance of lot rejection." This provides a clear, quantitative understanding of the quality bar and the risk each party faces.

Operating Characteristic (OC) Curve Calculator

Generate the OC curve for a sampling plan: probability of acceptance vs. actual defect rate. Visualize plan discrimination and risk.

Sample Size (n)

Acceptance Number (Ac)

AQL (95% acceptance)

0.72%

LTPD (10% acceptance)

7.56%

LTPD / AQL Ratio

10.6

Wide indifference zone

Defect Rate (%)	P(Accept) (%)	Visual
0.0	100.0
0.5	97.4
1.0	91.1
2.0	73.6
3.0	55.5
5.0	27.9
7.0	12.6
10.0	3.4
15.0	0.3
20.0	0.0
25.0	0.0
30.0	0.0

Planning notes, formulas, and examples

About the Operating Characteristic (OC) Curve Calculator

The Operating Characteristic (OC) curve is the fundamental tool for evaluating a sampling plan. It plots the probability of accepting a lot (y-axis) against the true fraction defective in the lot (x-axis). A perfect plan would be a vertical line — accepting all lots below the quality threshold and rejecting all above. In practice, the OC curve is an S-shaped curve that transitions gradually.

The shape of the OC curve reveals the plan's discrimination: a steep curve that drops quickly from near 100% to near 0% provides strong discrimination. A shallow curve means the plan struggles to distinguish between acceptable and unacceptable quality levels. The steepness is primarily controlled by the sample size.

This calculator generates OC curve data points for any single sampling plan defined by sample size (n) and acceptance number (Ac). It also identifies the AQL (at 95% acceptance) and LTPD (at 10% acceptance) from the curve, providing a complete risk picture.

When This Page Helps

You cannot properly evaluate or compare sampling plans without seeing their OC curves. Two plans with the same sample size but different acceptance numbers perform very differently. The OC curve makes this visible, letting you select the plan that best balances producer's and consumer's risk.

How to Use the Inputs

Enter the sample size (n) for the sampling plan.
Enter the acceptance number (Ac).
Review the computed OC curve data table.
Note the AQL (where P(accept) ≈ 95%) and LTPD (where P(accept) ≈ 10%).
Compare multiple plans by changing n and Ac to see the effect.
Select the plan that provides the best risk balance for your application.

Formula used

P(accept) = Σ C(n,d) × p^d × (1-p)^(n-d) for d = 0 to Ac

where n = sample size, Ac = acceptance number, p = true fraction defective

The curve is evaluated at p = 0%, 0.5%, 1%, 2%, 3%, 5%, 7%, 10%, 15%, 20%, 25%, 30%

Example Calculation

Result: AQL ≈ 0.8%, LTPD ≈ 9.3%

With n = 50, Ac = 1: at 0.8% defective, there is a 95% chance of acceptance (AQL). At 9.3% defective, there is only 10% chance of acceptance (LTPD). The plan provides moderate discrimination with a ratio of about 11.6.

Tips & Best Practices

Steeper OC curves come from larger sample sizes — they distinguish good and bad lots more sharply.
Increasing Ac shifts the curve to the right (more lenient); decreasing Ac shifts it left (more strict).
Plot OC curves for normal, tightened, and reduced plans on the same chart to visualize the switching effect.
For critical items, choose plans with steep OC curves even if they require larger samples.
The ideal plan depends on the relative cost of inspecting vs. the cost of accepting defective lots.
OC curves assume random sampling from a homogeneous lot — stratified or biased sampling invalidates the analysis.

The Anatomy of an OC Curve

The left end of the OC curve (low defect rate) shows the probability of accepting good lots — ideally near 100%. The right end (high defect rate) shows the probability of accepting bad lots — ideally near 0%. The slope of the transition between these endpoints measures the plan's discrimination power.

Producer's Risk and Consumer's Risk

At the AQL point on the OC curve, the probability of rejection is the producer's risk (α, typically 5%). At the LTPD point, the probability of acceptance is the consumer's risk (β, typically 10%). Both risks are visible on the OC curve and can be read directly from the table or chart.

Using OC Curves for Plan Selection

To select a sampling plan: (1) define your AQL and LTPD targets, (2) plot OC curves for candidate plans, (3) select the plan whose curve passes through both target points (95% acceptance at AQL, 10% acceptance at LTPD). If no single plan meets both targets, increase the sample size until one does.

Sources & Methodology

Last updated: February 10, 2026

Frequently Asked Questions

A good OC curve drops steeply from near 100% acceptance at acceptable quality to near 0% at unacceptable quality. The transition zone should be narrow. This means the plan has high discrimination and low risk at both ends.