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Find out between which values 95% or 99% of your parts lie, with the confidence the sample allows, and whether that range fits within the specification. Unlike the confidence interval for the mean, a tolerance interval is about individual parts: it is what is used to validate processes, release lots and set design limits. Just paste the measurements (preferably 30 or more).
Pre-sizing and estimating tool: results do not replace design, calculations or reports signed by a licensed professional, nor verification against the applicable codes and standards.
How to read: one row per sample. Normal = mean ± k × StDev, valid if the data are normal (see the Anderson-Darling P-value); nonparametric = actual values of the sorted sample, valid for any shape, with the confidence that N allows; k = how many standard deviations the interval opens on each side (larger for small samples).
Bars = sample data; curve = fitted normal; lines = tolerance limits (normal and nonparametric) and specification.
How to read: the bars count the parts in each measurement range and the curve is the fitted normal. The vertical lines mark the tolerance limits (where the requested % of parts lies) and, if entered, the specification. Good: the tolerance limits sit inside the specification. Warning: a tolerance limit goes past the specification, or the bars do not follow the curve (use the nonparametric).
Each line is an interval; the dot is the mean. Arrow = side without a bound (one-sided interval). Vertical lines = specification.
How to read: each horizontal line is one sample’s interval (normal and nonparametric), with the dot at the mean. Compare the samples with each other and with the vertical specification lines: an interval entirely inside = the process complies; an interval that crosses = some parts may fall outside. Arrows indicate the unbounded side of a one-sided interval.
Points on the line = normal data and the normal method applies. Curves or steps = use the nonparametric method.
How to read: the horizontal axis is the measurement and the vertical one the cumulative percentage of parts, on a scale where the normal distribution becomes a straight line. Points along the line = the normal method can be trusted. Points that stray at the ends, curve or step = the normal limits may be wrong exactly in the tails: prefer the nonparametric.
The larger the sample, the smaller k and the narrower the interval; with a very large N, k tends to the normal z. The dot marks your sample.
How to read: the horizontal axis is the number of parts measured (log scale) and the vertical one the k factor that multiplies the standard deviation. The curve drops fast up to about 30 to 50 parts and then flattens, approaching the z line (the value with known mean and standard deviation). The dot is your sample: if it sits on the steep part, measuring more parts narrows the interval considerably.
How to read: each row is a possible sample size. Compare the k factor and the interval width to decide how many parts to measure; the nonparametric column shows the confidence each N achieves without assuming normality.
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The confidence interval says where the process mean is; the tolerance interval says where the individual parts are. With 100 parts, the confidence interval for the mean of Machine 2 camshafts spans a few hundredths of a millimeter; the 95/95 tolerance interval spans more than 2 mm, because it must cover 95% of parts.
That the method, repeated over many samples, produces intervals that contain at least 99% of the parts 95% of the time. It is the language used in process and packaging validation: a "95/99 interval".
Because the mean and standard deviation come from a sample and may be off. k compensates for that uncertainty: for 95/95 it is 3.393 with 10 parts, 2.234 with 100, and tends to 1.960 for very large samples.
When the Anderson-Darling test rejects normality (p < 0.05) or the probability plot shows curves and steps. It holds for any distribution but needs more data: 59 parts for a one-sided 95/95 bound and 93 for a two-sided 95/95 interval.
In the nonparametric method the limits are values of the ordered sample, so the confidence cannot be set exactly: it jumps with the value chosen. The page shows the actual confidence of the interval; if it is below the requested level, the sample is small.
Enter LSL and USL. If the interval fits within them, at least the requested percentage of parts is within specification at the chosen confidence. The page also shows the largest percentage that can be guaranteed, for example "at least 99.6% within".
The exact factor (default, the same as the ISO 16269-6 and Odeh and Owen tables) solves the coverage integral; the Howe approximation, used in the NIST handbook, differs in the 3rd decimal for small samples (3.382 versus 3.393 for N = 10, 95/95). Use the exact one unless you need to reproduce an older calculation.
Important notice: Indus Metrics tools produce estimates and pre-sizing results from the data you enter and from published engineering methods. They do not replace design, calculations or reports signed by a licensed professional engineer (PE), nor verification against the applicable codes, standards and regulations, such as OSHA rules and the ASME codes. Material and fuel properties vary: check manufacturer data or your own process analyses before deciding. By using this site you agree to the Terms of Use.
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