Three decisions people make by feel
Most quality decisions come with arithmetic attached, and three of them are almost always made without it. Not because people are careless — because the arithmetic is unfamiliar and the guess feels reasonable. Each of these has a right answer, and each is quietly wrong when estimated by eye.
1. How many should I inspect? The usual answer is a fraction: ten per cent of the lot, or twenty pieces because twenty is a round number. Both are arbitrary. What actually matters is the pair of risks you are willing to carry: at what quality level should a lot be accepted (the producer's side), and at what level must it be rejected (the consumer's side). Fix those two and the sample size and accept number follow — there is nothing left to guess.
The curve that shows what a plan really does is the operating characteristic: true defect rate along the bottom, probability of accepting the lot up the side. Every plan has one, including the plan you invented. SenSight draws it and marks your two risk points on it. The usual surprise is how gentle the curve is: a plan that feels strict often accepts a bad lot far more often than anyone expected.
One number worth knowing is the AOQL — the worst average outgoing quality. If rejected lots get fully inspected and corrected, the quality that reaches the customer is bounded, and the AOQL is that bound. It is the single honest summary of a sampling scheme, and most tools never show it.
2. What range do the parts fall in? Here is the mistake that reaches customers. You have thirty measurements, you compute a 95% confidence interval, and you write it into the report as "99% of parts fall between these limits". Those are two different questions. A confidence interval is about the mean, and it gets narrower as you measure more. A tolerance interval is about the individual parts, and more data makes it more certain but not much narrower — because the parts really do vary that much.
The gap is not subtle. On typical data the tolerance interval is several times wider than the confidence interval. Quoting the narrow one is promising a spread your process cannot hold.
Two cautions. The usual factor assumes the data is roughly normal; on skewed measurements it puts the limits in the wrong place, so SenSight tests normality first and says so. And there is a distribution-free alternative that assumes nothing about the shape — but it is not free: covering 99% with 95% confidence from the smallest and largest values needs several hundred measurements. The panel tells you how many, so you can see what the assumption is buying you.
3. Is the new one the same as the old one? New supplier, new machine, new operator. You run a t-test, the p-value comes out at 0.4, and the conclusion goes in the report as "no significant difference — the two are equivalent". That inference is invalid, and it is probably the most expensive statistical mistake in manufacturing.
A large p-value means the test could not demonstrate a difference. That happens when there is no difference — and equally when you measured six parts and the test had no power to see one. Absence of evidence is being read as evidence of absence.
Showing that two things are the same requires its own test, and it requires something the data cannot give you: a statement of how much difference is small enough to ignore. That margin is an engineering decision. Two MPa on a tensile spec may be irrelevant; on a safety-critical dimension it may not be. Once you state it, the two one-sided test procedure (TOST) asks the right question: does the difference stay inside your margin?
The clearest way to read the result is not the p-value but the interval. If the whole interval for the difference sits inside ±margin, the two are equivalent. If it sits entirely outside, they are genuinely different. And if it straddles the margin, the honest answer is that you cannot say either way — which usually means you need more measurements, not a different conclusion. SenSight reports all three outcomes separately, because that third one is the one people skip.
1. How many should I inspect? The usual answer is a fraction: ten per cent of the lot, or twenty pieces because twenty is a round number. Both are arbitrary. What actually matters is the pair of risks you are willing to carry: at what quality level should a lot be accepted (the producer's side), and at what level must it be rejected (the consumer's side). Fix those two and the sample size and accept number follow — there is nothing left to guess.
The curve that shows what a plan really does is the operating characteristic: true defect rate along the bottom, probability of accepting the lot up the side. Every plan has one, including the plan you invented. SenSight draws it and marks your two risk points on it. The usual surprise is how gentle the curve is: a plan that feels strict often accepts a bad lot far more often than anyone expected.
One number worth knowing is the AOQL — the worst average outgoing quality. If rejected lots get fully inspected and corrected, the quality that reaches the customer is bounded, and the AOQL is that bound. It is the single honest summary of a sampling scheme, and most tools never show it.
2. What range do the parts fall in? Here is the mistake that reaches customers. You have thirty measurements, you compute a 95% confidence interval, and you write it into the report as "99% of parts fall between these limits". Those are two different questions. A confidence interval is about the mean, and it gets narrower as you measure more. A tolerance interval is about the individual parts, and more data makes it more certain but not much narrower — because the parts really do vary that much.
The gap is not subtle. On typical data the tolerance interval is several times wider than the confidence interval. Quoting the narrow one is promising a spread your process cannot hold.
Two cautions. The usual factor assumes the data is roughly normal; on skewed measurements it puts the limits in the wrong place, so SenSight tests normality first and says so. And there is a distribution-free alternative that assumes nothing about the shape — but it is not free: covering 99% with 95% confidence from the smallest and largest values needs several hundred measurements. The panel tells you how many, so you can see what the assumption is buying you.
3. Is the new one the same as the old one? New supplier, new machine, new operator. You run a t-test, the p-value comes out at 0.4, and the conclusion goes in the report as "no significant difference — the two are equivalent". That inference is invalid, and it is probably the most expensive statistical mistake in manufacturing.
A large p-value means the test could not demonstrate a difference. That happens when there is no difference — and equally when you measured six parts and the test had no power to see one. Absence of evidence is being read as evidence of absence.
Showing that two things are the same requires its own test, and it requires something the data cannot give you: a statement of how much difference is small enough to ignore. That margin is an engineering decision. Two MPa on a tensile spec may be irrelevant; on a safety-critical dimension it may not be. Once you state it, the two one-sided test procedure (TOST) asks the right question: does the difference stay inside your margin?
The clearest way to read the result is not the p-value but the interval. If the whole interval for the difference sits inside ±margin, the two are equivalent. If it sits entirely outside, they are genuinely different. And if it straddles the margin, the honest answer is that you cannot say either way — which usually means you need more measurements, not a different conclusion. SenSight reports all three outcomes separately, because that third one is the one people skip.
Try it in the app
Try: SPC tab, Decision Tools at the bottom. Start with the sampling plan — enter your lot size and read the OC curve before you trust any inspection rule you inherited.