Lot Sampling Acceptance Probability & Inspection Cost Calculator

Compare lot acceptance probability alongside inspection cost

Two incoming inspection quotes may offer different sample sizes, acceptance numbers and prices.
This calculator compares two already agreed n/c plans for ordinary, non-safety-critical parts under the same assumed lot composition.
It helps small manufacturers and distributors prepare a discussion with quality staff before agreeing to sampling and follow-up costs.

What N, K, n and c mean

These input limits are product performance limits, not statutory or recommended sample sizes.
Use the plans actually proposed by the contracting parties.
Different defect definitions or inspection methods make the plans different in ways the probability model does not capture.

Exact hypergeometric probability without replacement

The model draws a uniform random sample from a finite lot without putting selected products back.
If X counts defective products in the sample, acceptance is X≤c.
Until both sampling confirmations are checked, probabilities, the OC table and expected costs are withheld; base inspection cost and time remain available.

The implementation starts at the distribution mode and sums relative weights in both directions, avoiding factorial overflow and subtraction of a tiny tail from one.
It uses the finite-population distribution without a binomial or normal approximation.
Floating-point rounding remains, and extreme tails may underflow: precision-bound displays do not guarantee zero risk.

Separate inspection cost, time and rejection treatment

Time accepts 0–86,400 seconds per item; each unit cost, fixed cost and extra cost accepts 0–1 billion KRW, with up to 6 decimal places.
The English and Korean versions both use KRW without currency conversion or automatic tax rates.
Expected cost is a conditional average, not this transaction’s invoice, cash deposit or return-loss estimate.
Entering an extra cost without treatment details produces an error.

How to compare two agreed plans

1. Enter the lot size N and a hypothetical whole-lot defective count K.
   Do not turn observed sample defects into a confirmed whole-lot count.
   
2. Enter each proposed n/c plan, unit price, time and fixed charge.
   Enter zero only for explicitly free items.
   
3. If rejection treatment and incremental cost are known, record them together.
   Otherwise leave the extra cost blank.
   
4. Add up to 15 K scenarios separated by spaces, newlines or semicolons, without commas.
   The table always includes 0, current K and N.
   
5. Verify uniform random sampling, no replacement and consistent defect definitions.
   The checkboxes record your verification rather than perform a statistical test.
   
6. Compare the starred current row and B−A differences, then save the TXT worksheet.
   Editing an input clears previous results and requires recalculation.
   

Worked example: a lot of 10 with 2 assumed defective products

This is a fictional arithmetic example, not a market price or recommended inspection plan.
N=10, K=2; A uses n=2,c=0 and B uses n=3,c=0.
Both charge 1,000 KRW per item plus 5,000 KRW fixed, and take 30 seconds per item.
Assume a documented rejection treatment with an incremental cost of 30,000 KRW.

A accepts with C(8,2)/C(10,2)=28/45; B accepts with C(8,3)/C(10,3)=7/15.
B−A is −15.555556pp for acceptance, +1,000 KRW for base inspection and +5,666.67 KRW for expected cost.
B rejects this assumed lot composition more often, so the incremental treatment cost increases its conditional average.
Leaving the extra costs blank withholds the final row rather than treating unknown costs as zero.

Read the OC table by varying only K

The OC table fixes N and both n/c plans and varies the assumed number of defective products.
The current K row has a ★ marker.
Up to 15 entered scenarios are sorted and deduplicated alongside 0, current K and N, producing at most 18 rows.
K/N is the assumed fraction defective, not an estimate from observed inspection data.

Do not linearly interpolate missing integer K rows for a contract figure.
Enter the needed K and recalculate under the same conditions.
Uniform sampling from one defined lot is essential to this interpretation.

Interpret probability differences and risk carefully

A 60% acceptance probability describes repeated sampling from lots with the assumed composition.
It does not mean the lot is 60% good or that inspection detects 60% of its defective products.
When c is positive, a sample can contain identified defective products and still accept the lot.

• A negative B−A means lower acceptance for B at this K, not an automatically superior contract across all quality levels.
  
• Percentage points (pp) subtract two percentages; they are not relative percentage changes.
  
• Formal producer and consumer risk analysis needs agreed definitions of acceptable and unacceptable lot quality.
  The tool does not select these quality levels.
  

Cost, consequences, delivery timing and treatment responsibility belong in the decision.
The calculator does not rank plans or recommend an optimal sample size.

Practical contract checks

All initial values are fictional.
Replace N, K, n/c and prices with current transaction inputs and verify the checkboxes again.
Keep dated worksheets separate when lot definitions or quote terms change.

Frequently asked questions