Lot Tolerance Percent Defective (LTPD) Calculator

About the Lot Tolerance Percent Defective (LTPD) Calculator

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.

When This Page Helps

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.

How to Use the Inputs

1. Enter the sample size (n) from your sampling plan.
2. Enter the acceptance number (Ac).
3. Enter the consumer's risk β (default 10%).
4. Review the computed LTPD.
5. Compare LTPD against your tolerance for bad lots.
6. Adjust the plan if LTPD is unacceptably high.

Example Calculation

Tips & Best Practices

• For critical applications, LTPD should be no more than 2–3× the AQL.
• If the LTPD is too high, increase the sample size or lower the acceptance number.
• Share LTPD information with suppliers so they understand the rejection risk at various quality levels.
• The ratio LTPD/AQL indicates plan discrimination — lower ratios mean sharper plans.
• Consider both AQL and LTPD when selecting a sampling plan, not just one.
• For safety-critical items, use plans with very low LTPD (< 1%).

Understanding Consumer's Risk

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.

LTPD in Practice

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.

Adjusting the Plan for Better Protection

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).

Frequently Asked Questions

• What is consumer's risk (β)?

  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.

• How does LTPD relate to AQL?

  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.

• What is a good LTPD-to-AQL ratio?

  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.

• Can LTPD be lower than AQL?

  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.

• How do I reduce the LTPD?

  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.

• Is LTPD the same as RQL?

  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.