Calculate LTPD — the defect rate at which a lot has a specified probability of rejection. Evaluate consumer risk of your sampling plan.
The Lot Tolerance Percent Defective (LTPD) is the defect rate at which the consumer wants the sampling plan to reject the lot with high probability — typically 90%. At the LTPD, the lot has only a 10% chance of being accepted (this 10% is called the consumer's risk, or β).
While AQL defines the quality level you want to accept, LTPD defines the quality level you want to reject. Together they characterize the sampling plan's discriminating power. A plan with a tight AQL-LTPD spread has high discrimination; a wide spread means the plan has a gray zone where lots might go either way.
This calculator takes a sampling plan's sample size and acceptance number and computes the LTPD at a given consumer's risk (default β = 10%). It helps you evaluate whether your sampling plan provides adequate protection against bad lots.
Understanding this metric in quantitative terms allows manufacturing leaders to prioritize improvement initiatives and allocate limited resources where they will deliver the greatest operational impact.
Knowing the LTPD tells you the worst-case quality that has a meaningful chance of slipping through your inspection. If the LTPD is too high — meaning lots with high defect rates still have a 10% chance of acceptance — you need a tighter plan. LTPD is the consumer's view of sampling plan adequacy.
LTPD is the value of p where P(accept | p) = β P(accept | p) = Σ C(n,d) × p^d × (1-p)^(n-d) for d = 0 to Ac Solve for p such that P(accept | p) = β (typically 0.10) This requires iterative numerical solution (bisection method).
Result: LTPD ≈ 7.4%
With n = 80 and Ac = 2, a lot with 7.4% defective has only a 10% chance of being accepted. Lots worse than 7.4% will almost always be rejected. This means the plan protects against lots exceeding 7.4% defective.
Every sampling plan has a non-zero probability of accepting bad lots. Consumer's risk quantifies this: at the LTPD quality level, there is still a β probability (usually 10%) that the lot passes inspection. Understanding this risk is essential for quality agreements between suppliers and customers.
Specify LTPD in your purchasing contracts: "Lots with defect rates exceeding X% have at least 90% probability of rejection under the agreed sampling plan." This gives your supplier a clear understanding of the quality bar and your inspection's teeth.
If your LTPD is too high, you have three options: increase the sample size (most effective), decrease the acceptance number (shifts the entire OC curve), or move to double or multiple sampling (provides better discrimination at similar average sample sizes).
Consumer's risk is the probability of accepting a lot at the LTPD defect rate. It's typically set at 10% (β = 0.10), meaning a 10% chance that a lot at the LTPD quality level passes inspection. Lowering β requires larger sample sizes.
AQL is the quality level you want to accept (producer-friendly). LTPD is the quality level you want to reject (consumer-friendly). The gap between them defines the plan's indifference zone — quality levels where acceptance is uncertain. A good plan has a narrow indifference zone.
For plans with high discrimination, the ratio is 3–5. For practical plans with moderate sample sizes, ratios of 5–10 are common. Extremely tight ratios (< 3) require very large sample sizes that may not be economical.
No. LTPD must always be greater than AQL. The AQL is the acceptable level (high acceptance probability) and LTPD is the rejectable level (low acceptance probability). LTPD < AQL would mean the plan rejects acceptable lots.
Increase the sample size. A larger sample gives the plan more information, allowing it to discriminate more sharply between acceptable and unacceptable lots. You can also reduce the acceptance number, but this shifts the entire OC curve.
Yes. Rejectable Quality Level (RQL) is an alternative name for LTPD. Both terms refer to the defect rate at which the lot should be rejected with high probability.