What is the difference between AQL and LTPD?

AQL is the maximum defect rate considered acceptable (lots at AQL are accepted ~95% of the time). LTPD is the defect rate that should be rejected (lots at LTPD are accepted only ~10% of the time). They define the two key points on the OC curve.

What is a typical consumer risk (β)?

The standard consumer's risk is 10% (β = 0.10). This means lots at the LTPD quality level will be accepted 10% of the time. For critical applications, β can be set lower (e.g., 5%).

How does LTPD relate to the OC curve?

LTPD is the point on the OC curve where the acceptance probability equals the consumer's risk (β). It is typically on the right side of the curve where acceptance probability is low.

Can I reduce LTPD without increasing sample size?

Reducing the accept number (Ac) while keeping sample size constant will reduce LTPD but also increases producer's risk (more rejections of good lots). Increasing n is the safest way to reduce LTPD.

Is LTPD the same as RQL?

Yes. Rejectable Quality Level (RQL) is another name for the same concept. It is the quality level associated with the consumer's risk point on the OC curve.

What if my process defect rate is close to the LTPD?

This is a warning sign. Your sampling plan may not adequately distinguish between your current quality and unacceptable quality. Improve the process or adopt a more discriminating sampling plan.

LTPD Calculator (Lot Tolerance Percent Defective)

Calculate LTPD — the defect rate at which consumer risk equals beta (typically 10%). Evaluate worst-case lot quality for sampling plans.

Sample Size (n)

Accept Number (Ac)

Consumer Risk (β)

LTPD

6.52%

Lot Tolerance Percent Defective

P(accept) at LTPD

10.00%

≈ 10% consumer risk

Planning notes, formulas, and examples

About the LTPD Calculator (Lot Tolerance Percent Defective)

Lot Tolerance Percent Defective (LTPD) is the defect rate at which a sampling plan provides only a specified consumer's risk (β, typically 10%) of acceptance. In other words, lots at the LTPD quality level will be accepted only 10% of the time — providing strong consumer protection against poor quality.

LTPD sits at the opposite end of the OC curve from AQL. While AQL defines the quality level that a good supplier should consistently achieve (with high acceptance probability), LTPD defines the worst-case lot quality that the plan guards against (with low acceptance probability).

This calculator finds the LTPD for a given sampling plan by computing the defect rate where P(accept) equals the consumer's risk level, helping you evaluate whether your plan provides adequate protection.

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

LTPD tells you the worst quality level that your sampling plan still has a chance of accepting. Knowing LTPD helps you evaluate whether your plan is strict enough for your risk tolerance and product application.

How to Use the Inputs

Enter the sample size (n) of your sampling plan.
Enter the accept number (Ac).
Enter the desired consumer risk (β), typically 10%.
Review the LTPD — the defect rate at which P(accept) = β.
Compare LTPD against your process capability to ensure adequate margin.
If LTPD is too high, increase sample size to lower it.

Formula used

LTPD is the value of p where:
P(accept) = Σ from x=0 to Ac of C(n,x) × p^x × (1−p)^(n−x) = β

Typically β = 0.10 (10% consumer risk)

Solved numerically by finding p such that P(accept | p) = β.

Example Calculation

Result: LTPD ≈ 7.2%

For n = 80 and Ac = 2 with β = 10%, the LTPD is approximately 7.2%. This means lots with a true defect rate of 7.2% will be accepted only 10% of the time. Lots worse than 7.2% have even lower acceptance probability.

Tips & Best Practices

A lower LTPD means better consumer protection but requires larger sample sizes.
Compare LTPD with your process average defect rate — there should be a safety margin between them.
LTPD is especially important for safety-critical products where accepting bad lots has severe consequences.
When comparing sampling plans, the plan with the lower LTPD provides more consumer protection.
For very tight LTPD requirements, consider 100% inspection or tightened sampling.
Document the LTPD of your plans to demonstrate due diligence in quality planning.

AQL and LTPD: The Two Key Points

Every sampling plan is characterized by its AQL (the good quality level, P(accept) ≈ 95%) and its LTPD (the bad quality level, P(accept) ≈ 10%). The gap between AQL and LTPD is called the indifference zone — within this zone, the plan provides moderate discrimination.

Designing Plans by LTPD

Some approaches design sampling plans starting from the LTPD rather than the AQL. The Dodge-Romig tables, for example, specify plans that guarantee a particular LTPD while minimizing average inspection. This consumer-focused approach prioritizes protection over cost.

LTPD in Regulated Industries

Pharmaceutical, medical device, and aerospace industries often specify LTPD requirements alongside AQL. Regulatory auditors may require evidence that sampling plans provide adequate consumer protection, making LTPD documentation essential.

Sources & Methodology

Last updated: February 9, 2026

Frequently Asked Questions

AQL is the maximum defect rate considered acceptable (lots at AQL are accepted ~95% of the time). LTPD is the defect rate that should be rejected (lots at LTPD are accepted only ~10% of the time). They define the two key points on the OC curve.