Statistical Boundary
Values derived from a cumulative distribution function specify the points below which a certain percentage of observations are expected to fall. These quantile limits define the range of acceptable variation for a process or a measurement system. They provide a more stable alternative to standard deviation-based limits when the data does not follow a normal distribution.
Metrological Verification
Calibration certificates often list the percentiles of the error distribution to indicate the reliability of the instrument. When quantile limits are used, a ninety-fifth percentile limit suggests that ninety-five percent of all measurements will have an error less than or equal to the stated value. This clear threshold allows for straightforward pass-fail decisions during routine inspections.
Sample Size
Estimation of these boundaries requires a sufficient number of data points to ensure the tails of the distribution are adequately represented. If the sample is too small, the quantile limits will have a high degree of uncertainty and may change with the addition of new data. Bootstrap methods can be used to estimate the confidence intervals around the quantiles.
Tolerance Comparison
Engineers compare the calculated quantile limits to the design specifications to assess the capability of the manufacturing process.
