Double Sampling Plan Calculator

Work out double sampling plan instantly with clear inputs, formula shown and shareable results.

About Double Sampling Plan Calculator

A double sampling plan accepts or rejects on the first sample when the evidence is clear and draws a second sample only when it is ambiguous. Because most lots are decided on the smaller first sample, the average sample number is lower than a single plan of equivalent discriminating power.

Formulas

Double sampling

Pa = P(accept on first) + P(go to second) x P(accept on second)

Average sample number

ASN = n1 + P(second sample) x n2

Worked example

With the default values below, Double Sampling Plan Calculator returns Overall Probability Of Acceptance of 91.932%. Change any input above and every figure here is recalculated in your browser.

Inputs used

First Sample Sizeminimum 1: 80
Second Sample Sizeminimum 1: 160
First Acceptance Numberaccepts 0–1,000: 1
Lot Defect Rateaccepts 0–100 %: 1.5 %

Results

Overall Probability Of Acceptance: 91.932%
Accepted On First Sample: 66.263%
Second Sample Needed: 32.963%
Average Sample Number: 132.74

Step by step

1Values used
2Double sampling
3Average sample number
4Overall Probability Of Acceptance= 91.932
5Accepted On First Sample= 66.263
6Second Sample Needed= 32.963
7Average Sample Number= 132.74

Assumptions and limits

The result is derived only from the 4 inputs listed above. Anything not among them is not part of the calculation.
In particular, this calculator does not take inflation, tax, fees or charges or compounding frequency into account.
Figures are rounded for display to 3 decimal places, so totals built from several rounded parts can differ slightly from the unrounded arithmetic.

How these calculators are built and tested is described on the Methodology page. If a figure looks wrong, please report it.

Frequently Asked Questions

When is double sampling worth the complexity?

When inspection is expensive or destructive and most lots are clearly good or clearly bad. The saving in average sample size can be 25-40% against a single plan.

Why is the second acceptance number larger?

It applies to the combined sample. The cumulative count from both samples is compared with the second acceptance number, so it must scale with the larger total.