Lot Sampling Versus Defect Counting

A four-point inspection on fabric records defects against a surface, so the result is a defect rate per unit area. A sampling plan applied to a control component records a count against a lot, so the result is a decision about that lot. The two scales are not interchangeable, and treating one as the other is a common source of wrong acceptance decisions.

A fabric check answers how much visible defect exists per hundred square yards or per hundred linear yards. A lot check answers whether the proportion of nonconforming units in a submitted lot falls below a stated acceptance number. When a buyer applies a per-area rate to a per-lot decision, a lot with a low average defect density can still contain individual pieces that fail a functional requirement. When a supplier applies a per-lot acceptance number to a per-area question, a conforming production run can be rejected because one localized defect inflates the count.

The distinction matters beyond textiles. Buyers who work across materials, including those who consult a technical guide in English on denim specification and inspection covering spinning, dyeing, finishing, and testing, meet the same two scales in different vocabularies. The underlying arithmetic does not change with the substrate.

What does a four-point check measure?

A four-point system assigns penalty points to defects according to their length or size, then sums the points over the inspected length or area. The result is expressed as points per hundred square yards, or points per hundred linear yards when width is fixed. The unit of analysis is the surface, not the piece. A single roll can carry a high point total in one zone and remain acceptable overall if the average stays below the agreed limit.

Because the unit is area, the four-point result is a density. It supports comparisons between rolls, between dye lots, and between suppliers, provided the inspected length and the width are recorded. It does not by itself state how many rolls in a shipment are nonconforming, and it does not define an acceptance number for the shipment. Those belong to the sampling plan.

A four-point count is also blind to defect type unless the inspector records it. A hole and a slub may carry the same penalty points while having entirely different consequences downstream. The point total is a screening figure, and the defect classification is the diagnostic figure.

What does a sampling plan decide?

A sampling plan decides whether to accept or reject a lot on the basis of a sample drawn from it. The plan states the sample size, the acceptance number, and the rejection number. The unit of analysis is the lot, and the output is a binary decision with a known producer's risk and consumer's risk at stated quality levels.

A sampling plan does not measure the lot. It measures the sample and infers the lot. The inference is probabilistic, so a lot at the acceptance quality limit will be rejected some fraction of the time, and a lot above the limit will be accepted some fraction of the time. Those fractions are properties of the plan, not of the supplier.

The plan also requires a defined nonconformity. A unit is nonconforming if it fails a stated requirement, and the requirement must be written before the sample is drawn. Without a written requirement, the acceptance number has no referent, and the decision reduces to opinion.

Which tests qualify a component?

Qualification tests establish whether a component meets its stated requirements under defined conditions. The test method, the specimen preparation, and the pass or fail threshold are part of the specification, not of the inspection. The table below lists common test families and the property each one addresses.

Test families, the property each addresses, and the typical reporting unit.

Test family	Property addressed	Typical reporting unit
Tensile or grab	Breaking strength	Newtons or pounds-force
Tear	Resistance to propagation	Newtons or grams-force
Abrasion	Surface durability	Cycles to endpoint
Colorfastness	Resistance to transfer or fading	Gray scale rating
Leak or pressure	Seal integrity	Pressure held over time

Each row answers a different question. A tensile result does not predict abrasion behavior, and an abrasion result does not predict seal integrity. A qualification file is a set of answers to separate questions, and a single passing figure does not qualify a component for all uses.

How do defect rate and lot rate differ?

A defect rate is a count divided by an exposure measure: defects per hundred square yards, defects per thousand units, or defects per hour of operation. It describes intensity within a population and can be averaged across a production run.

A lot rate is a proportion of nonconforming units within a defined lot. It describes the composition of that lot and supports an accept or reject decision. The two figures can move in opposite directions. A process can reduce average defect density while increasing the proportion of units that fail a functional requirement, if the remaining defects concentrate in critical locations.

Converting between the two requires an assumption about how defects distribute across units. If defects cluster, the conversion from density to proportion is not linear, and a low density can coexist with a high proportion of nonconforming units. That is why a four-point result cannot be substituted for a sampling decision, and why a sampling decision cannot be substituted for a four-point result.