What it means
Checking every unit is thorough but slow, expensive and, where the test destroys the item, impossible. Acceptance sampling replaces total inspection with a statistical rule: inspect a sample of n units, accept the lot if defects found are at or below an acceptance number c, and reject the lot otherwise.
Plans come in several shapes. A single sampling plan takes one sample and decides immediately, a double plan allows a second sample when the first result is borderline, and a sequential plan tests unit by unit until the evidence is conclusive, which usually needs the smallest average sample size of the three.
Every plan carries two risks that pull against each other. Producer's risk is rejecting a lot that was actually fine, consumer's risk is accepting a lot that was not, and tightening the plan to reduce one of them raises inspection cost while only partly reducing the other.
The commercial value shows up in contracts and supplier scorecards rather than on the inspection bench. Sampling results feed defect trend data, justify rework charges and decide which suppliers earn reduced inspection over time and which are moved to tightened inspection or dropped.
In practice
Real-world examples.
Example
A brewery tests 20 bottles from every 10,000-bottle run for fill volume and seal integrity. The test destroys the sample, so total inspection is impossible and a sampling plan is the only workable option.
Example
A car parts distributor moves a reliable supplier from normal to reduced inspection after ten consecutive lots pass, cutting sample sizes and inspection labour while keeping the right to switch back after any failure.
Example
A clothing importer uses double sampling on a new factory: a first sample of 80 garments, and where the result is borderline a second sample of 80 before deciding, which avoids rejecting a whole container on ambiguous evidence.
Formula
Calculation
Accept the lot if d is at or below c, where d is the defects found in a sample of n units. Sample defect rate = d / n.
A manufacturer receives lots of 5,000 electronic components and applies a single sampling plan with n = 125 and c = 3. Inspection costs $0.80 per unit, so full inspection of a lot would cost 5,000 x $0.80 = $4,000, while sampling costs 125 x $0.80 = $100. The saving is $4,000 - $100 = $3,900 per lot, and across 40 lots a year that is 40 x $3,900 = $156,000. On the current lot the inspector finds 2 defects. The sample defect rate is 2 / 125 = 1.6%, and because 2 is at or below the acceptance number of 3, the lot is accepted. Had 5 defects been found, the lot would be rejected because 5 exceeds 3, and the sample rate would have been 5 / 125 = 4.0%.Case study
Seen in the real world.
Fenwick Tooling is a fictional company used purely to illustrate the idea. It buys precision fasteners in lots of 8,000 at $1.25 each, giving a lot value of 8,000 x $1.25 = $10,000, and until recently it inspected every incoming unit at a cost of $0.15 per piece, or 8,000 x $0.15 = $1,200 per lot.
With 60 lots a year, total inspection was costing 60 x $1,200 = $72,000, roughly 12% of the annual purchase value of 60 x $10,000 = $600,000. The quality manager introduces a single sampling plan with a sample of 200 and an acceptance number of 2. Inspection now costs 200 x $0.15 = $30 per lot, or 60 x $30 = $1,800 a year, saving $72,000 - $1,800 = $70,200.
The trade-off is accepted deliberately. Fenwick knows some defective fasteners will slip through, so it keeps 100% inspection for the two part numbers used in safety-critical assemblies, adds a quarterly supplier audit and writes a rework clause into the contract. Two years later the escaped defect rate is marginally higher than under total inspection, but the savings comfortably fund the audits and the rework, and inspection is no longer the bottleneck at goods inwards.
Watch out
Common mistakes.
- Drawing the sample from whatever is easiest to reach, usually the units nearest the door, which destroys the randomness the whole method depends on.
- Using acceptance sampling for safety-critical characteristics where the only defensible standard is zero defects and full inspection or in-process control is required.
- Reading a passed lot as proof of a good supplier. A single acceptable sample says little; the value comes from the trend across many lots.
Questions
People also ask.
How is acceptance sampling different from statistical process control?
Sampling judges finished lots after production, while process control monitors the process while it runs so problems are corrected before defective output accumulates.
How is the sample size decided?
It comes from a published standard that maps lot size, inspection level and the chosen acceptable quality level to a sample size and acceptance number, rather than from a fixed percentage of the lot.
Is a bigger sample always better?
A larger sample reduces the risk of a wrong decision but costs more, so the right size is the one where the cost of extra inspection matches the cost of the errors it prevents.
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