Statistical Sampling Plan, OC Curve & Average Outgoing Quality

The formula

This is the expression the tool evaluates. Every term is named underneath, with the unit it must be supplied in.

How the result is derived

Step by step, from the values you type to the figure on screen.

1. The 5 inputs are read from the form on every keystroke: Lot Size, General Inspection Level, Acceptable Quality Limit, Acceptance Number Ac and Actual Process Defect Rate.
2. Each value is checked against the accepted range in the input table below. A value outside its range stops the calculation rather than producing a misleading figure — the results blank out and a message appears.
3. The validated values are substituted into the expression above, which resolves Sample Size together with every supporting figure in one pass — no value is carried over from a previous entry.
4. The supporting outputs — Acceptance Probability at the AQL, Producer's Risk, Quality Rejected 9 Times in 10 (LTPD), Indifference Quality (50% Accept), Average Outgoing Quality, Average Outgoing Quality Limit, Average Total Inspection and Rejection Number Re — come from the same pass, so they always describe the same case as the headline figure.
5. Results are rounded for display only. The full-precision value is used throughout the chain, so reading a rounded intermediate figure back into the tool by hand can shift the last digit.

What each input means

Where to read each value on the floor, the unit it must be in, and the range the tool accepts.

What the tool returns

The headline figure and every supporting value it is built from.

Worked example

Substituting

The gap between 1.5% and 4.5879% is the honest reading of this plan: a lot at the AQL passes nine times in ten, and a lot three times worse still passes one time in ten. A sampling plan is a sorting device with a wide grey band, not a guarantee. Anyone promising that AQL 1.5 means no more than 1.5% defective in delivered goods has read the label and not the curve.

How to use it

1. Work through the input groups in order — The Lot and The Plan. The defaults are a realistic case, so you can change one value at a time and watch what moves.
2. There is no calculate button. Every figure recalculates as you type or drag, which is what makes this usable for a what-if sweep rather than a single answer.
3. Read Sample Size in the dark results panel — that is the headline figure, expressed in units.
4. Check the supporting rows underneath (Acceptance Probability at the AQL, Producer's Risk, Quality Rejected 9 Times in 10 (LTPD), Indifference Quality (50% Accept), Average Outgoing Quality, Average Outgoing Quality Limit, Average Total Inspection and Rejection Number Re) before acting on the headline — they are where an implausible input usually shows itself first.
5. Reset to defaults returns every field to the reference case, which is the quickest way to check whether a surprising result came from the tool or from an input you had changed earlier.

Where this is used

• Process planning — establishing Sample Size before a trial is booked, so machine time and material in Fiber Testing, Bale Management & Laboratory Sampling are committed against a calculated figure rather than an estimate.
• Costing and quotation — Sample Size is an input to the cost sheet, and quoting from a worked number rather than a remembered one is what keeps a margin intact.
• Troubleshooting — when the floor result drifts from plan, entering the measured values (starting with Lot Size) shows how much of the gap in Sample Size each variable explains.
• Teaching and study — the accepted ranges bracket normal Fiber Testing, Bale Management & Laboratory Sampling practice, so moving one variable at a time shows the shape of the relationship rather than a single answer.

Reading the result

Typical bands and what each one is telling you.

Assumptions and limits

• The sample size comes from the ISO 2859-1 general inspection level code letters, with Level I and Level III taken as one code letter either side of Level II - which is how the general levels are laid out in Table 1. Special levels S-1 to S-4, used for destructive or expensive tests, are not covered and must be taken from the standard. The acceptance number is an input, not a lookup: Table 2-A contains arrow cells that redirect to a different sample size, and reproducing those without the table in front of you is how plans get misquoted. The operating characteristic is exact binomial for a single sampling plan under normal inspection; double, multiple and sequential plans have different curves. Where the sample would exceed the lot it is capped at the lot size, which is 100% inspection. Switching rules between normal, tightened and reduced inspection are a separate mechanism and change the effective protection substantially.
• Every input is bounded to the range normal practice occupies (Lot Size 2 to 5000000 units, General Inspection Level Level I - reduced discrimination · Level II - normal, the default · Level III - tightened discrimination and Acceptable Quality Limit 0.01 to 15 %, and so on for the rest). Those bounds are guard rails against typing errors, not a claim that the formula fails one unit outside them.
• The calculation is deterministic: the same inputs always give the same result. It carries no allowance for machine condition, operator skill, ambient conditions or lot-to-lot material variation unless an input above explicitly represents one.
• Nothing is sent anywhere. The maths runs in your browser, so the numbers you type never leave the page.

Standards and further reading

• ISO 2859-1 - sampling procedures for inspection by attributes, indexed by AQL.
• ANSI/ASQ Z1.4 - the North American equivalent scheme.
• ISO 2859-2 - sampling plans indexed by limiting quality (LQ) for isolated lots.
• ISO 3951-1 - sampling procedures for inspection by variables, where a measured characteristic is available.

Questions people ask