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Natural tolerance
Indicates the variability inherent in the measurements. It is determined using different
methods, depending on the characteristic type:
Bilateral or single limit characteristic
Natural Tolerance = 6*S
where S is the standard deviation of the measurements
Unilateral characteristic
with upper limit: Natural Tolerance = Minimum between (6*S) and (3*S + X)
with lower limit: Natural Tolerance = Minimum between (6*S) and (3*S - X)
Where:
S is the standard deviation of the measurements
X is the mean value of the measurements
In the case of the unilateral characteristics formula it is assumed that the natural
limit is 0. If the mean value X is closer to this 3*S limit, it means that, for this part of
the measurement, 3*S cannot be considered as dispersion, because, as the limit
is insuperable, the maximum dispersion value will be equivalent to the mean value.
Estimated process sigma (Sigma Hat)
When sample measurements are used to evaluate a process, instead of using the
standard deviation S to find its inherent variability, we use a formula and a series
of tables to estimate the process dispersion, taking into account the fact that the
measure-ments were obtained through a sampling method. The index calculated
in this way is known as Sigma Hat (σ). This dispersion index is based exclusively
on the variability within the samples, and does not take into account any variabi-
lity between different samples that may have been taken at significantly different
periods. There are two formulas that can be used for estimating this dispersion:
the first is based on the Range of each sample, while the second is based on the
Standard Deviation of each sample.
Formula based on the sample ranges. In the above formulas, Ri represents the
range of the i
th
sample, Nc is the number of samples taken, and d2 refers to the
values in column of the same name in the tables found in the appendix, in the row
corresponding to number of measurements in the sample used.
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