Free Acceptance Sampling & AQL Lab

Step 1: Configure Batch & Inspection Plan

Acceptance Sampling Parameters

Total Lot Size (N Units)

Total batch or shipment delivery volume.

Sample Inspection Size (n Units)

Number of randomized units tested.

Acceptance Number (c)

Max allowed defectives in sample before rejection.

Incoming Defect Rate (p %)

True process/supplier defect fraction.

Inspection Cost per Unit ($)

Cost to screen or test a single component.

Escaped Defect Penalty ($)

Warranty, recall, or downstream rework cost.

Lot Acceptance Prob (Pa)

55.8%

Moderate lot risk zone

Average Outgoing Quality (AOQ)

0.653% Defect Rate

Max AOQL Ceiling: 0.67%

Average Total Inspection (ATI)

2,280 Units

Average Total Inspection per Lot

Expected Quality Cost

$19,340

Inspection ($10,260) + Risk ($9,080)

Operating Characteristic (OC) Curve & Quality Distribution

Incoming Defect Rate (p)	Acceptance Probability (Pa)	Rejection Probability (Pr)	Average Outgoing Quality (AOQ)	Average Total Inspection (ATI)

Statistical Quality Control Principles

Acceptance Sampling & Risk Balance

Acceptance sampling balances producer inspection costs against consumer defect exposure:

Producer's Risk (α, Type I Error): The probability of rejecting a lot whose defect rate is at or below the acceptable AQL standard.
Consumer's Risk (β, Type II Error): The probability of accidentally accepting a bad lot whose defect rate exceeds the Lot Tolerance Percent Defective (LTPD / LQ).
Rectifying Inspection: When rejected lots undergo 100% screening and defect replacement, the outgoing quality is capped by the Average Outgoing Quality Limit (AOQL).
Zero-Defect (c = 0) Plans: Provide steep OC discrimination but increase Producer's Risk if incoming lots have minor non-critical variations.

Measure process capability in the Process Capability Lab.

Mathematical Quality Equations

Acceptance sampling formulas

Poisson Parameter (λ) = n × p

P(a) = ∑ [e^(-np) × (np)^k ÷ k!] for k = 0 to c

AOQ = [P(a) × p × (N - n)] ÷ N

ATI = n + [1 - P(a)] × (N - n)

Expected Quality Cost = (ATI × Cost_insp) + (Escaped_Defects × Penalty)

Calculate DPMO and Sigma levels in the Six Sigma Lab.

FAQ

Acceptance sampling & AQL quality questions

What is Acceptance Sampling?

Acceptance sampling is a statistical quality control procedure where a random sample of n units is drawn from a lot of N units to determine whether to accept or reject the entire lot based on an acceptance number c.

What is an Operating Characteristic (OC) curve?

An OC curve graphically illustrates the relationship between the true incoming lot defect rate (p) and the probability of accepting the lot (Pa), demonstrating the plan's statistical discriminating power.

What is the difference between AQL and LTPD?

Acceptance Quality Limit (AQL) is the worst quality level acceptable to the producer with low rejection risk (Alpha), while Lot Tolerance Percent Defective (LTPD) is the poorest quality the consumer will tolerate with low acceptance risk (Beta).

What is Average Outgoing Quality (AOQ) and AOQL?

AOQ is the expected average defect rate leaving inspection under rectifying screening (where rejected lots are 100% inspected). AOQL is the peak ceiling defect rate that can ever reach customers regardless of incoming defect spikes.

What is Average Total Inspection (ATI)?

ATI represents the average number of units inspected per lot, calculated as ATI = n + (1 - Pa)(N - n), factoring in both sample inspections and full screening of rejected lots.

Can I export the acceptance sampling analysis to CSV?

Yes. You can export complete OC curve coordinates, Pa, AOQ, ATI, and cost breakdowns as a UTF-8 CSV spreadsheet with formula defense.

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