What satisfaction sampling tells you at low n

You have shipped twenty orders. Twenty responses came back positive; nothing has been returned. It is tempting to conclude the product is fine. The correct conclusion is narrower, and it can be stated exactly.

The rule of three

If an event has not occurred in n independent trials, the upper bound of a 95% confidence interval for its rate is approximately 3/n. This follows directly: for a defect rate p, the chance of seeing none in n trials is (1−p)ⁿ, and setting that equal to 0.05 gives p ≈ 3/n for small p.

n =  10 → defect rate could be as high as 30%
n =  20 → defect rate could be as high as 15%
n =  50 → defect rate could be as high as  6%
n = 100 → defect rate could be as high as  3%
n = 300 → defect rate could be as high as  1%

Twenty clean orders are consistent with one customer in seven being dissatisfied. That is compatible with a product that is fine and equally compatible with one that will generate a steady stream of returns as volume grows. To establish that a defect rate is below 1% you need roughly three hundred clean observations, and no amount of enthusiasm about the first twenty substitutes.

Response bias makes it worse than the arithmetic suggests

The rule of three assumes you observe every trial. In satisfaction sampling you observe only the people who reply, and dissatisfied customers reply at a different rate from satisfied ones — sometimes higher, when there is something to complain about; often lower, when the disappointment is mild and returning the item is not worth the effort. Twenty replies out of eighty orders is a sample of twenty from a self-selected group, not a sample of eighty, and the honest n is the smaller number with an unquantified bias on top.

Sample for diagnosis, not for reassurance

At low n, satisfaction sampling has one job that it does superbly, and it is not estimating a rate. It surfaces specific, concrete failures — the item arrives with a scuff on one corner, the sizing runs small, the instructions omit a step. A single such report is actionable on its own and needs no confidence interval, because you are not estimating how often it happens; you are learning that it can happen and why. Ask open questions and read the answers. The score is nearly worthless at twenty responses; the sentences are not.

Figures in this lesson are illustrative inputs chosen so the arithmetic can be checked. They are not measurements. What FlowFinds Solutions actually measures is published, with its artifacts, in research.