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Sampling and Trial Analysis

Single-Sample Acceptance Counts: A Fixed Number Is Not a Defect Percentage

Read the sample size and permitted count together. A single-sample count boundary does not automatically become a percentage applied to any quantity.

Library dates organize the collection. Actual publication and revision dates are shown separately.

Read the sample size and permitted count together. A single-sample count boundary does not automatically become a percentage applied to any quantity.

The statistical question

A single-sample attributes plan can be written as n,c: n identifies how many selected items are inspected, and c is the acceptance count of nonconforming items. Under that rule, a count greater than c rejects the lot. Changing n while retaining c changes the plan; replacing the count boundary with an invented percentage changes it again.

Primary reference: NIST Engineering Statistics Handbook.

An illustrative review example

For arithmetic only, suppose a fictional plan inspects 80 items and permits at most two nonconforming items. Two findings among those 80 meet its count boundary; three do not. Inspecting 160 items and permitting four findings is not the same n,c plan merely because both examples have a 2.5% boundary ratio. No operating-characteristic equivalence has been shown by dividing c by n.

Prepare the evidence for discussion

Ask the inspection team to put the approved plan reference beside the sample tally. Preserve the distinction between nonconforming items and multiple findings on one item. If a sample quantity changes because units were unavailable or damaged, record that departure and obtain the applicable decision from the responsible quality team. Do not silently rescale the acceptance count in a supplier trial spreadsheet.

Read n and c together

This blank worksheet is for your own project. It contains no H M machine trial result.

Read n and c together
Question to resolveEvidence to retain
Sample size nApproved inspection quantity
Acceptance count cNonconforming-item boundary
Actual tallyItem identities and findings
DepartureChanged quantity and disposition owner

Customer Questions

Is c a defect percentage?

It is a count boundary tied to the specified sample size in this n,c attributes plan.

Can the sample size be doubled without changing the plan?

Changing n changes the plan. Any revised acceptance rule needs its own agreed basis.

Do two findings on one item count as two items?

The record must distinguish nonconforming-item counts from individual defect or finding counts.

Primary References

These references support the technical principles discussed in this guide. The worked examples and review questions are educational.

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