Generate the OC curve for a sampling plan: probability of acceptance vs. actual defect rate. Visualize plan discrimination and risk.
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.
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. Consistent measurement creates a reliable baseline for tracking improvements over time and demonstrating return on investment for process optimization initiatives.
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%
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.