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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.
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.
Bars = sample data; curve = fitted normal; lines = tolerance limits (normal and nonparametric) and specification.
Each line is an interval; the dot is the mean. Arrow = side without a bound (one-sided interval). Vertical lines = specification.
Points on the line = normal data and the normal method applies. Curves or steps = use the nonparametric method.
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.
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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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