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Interval for Values

The interval for values represent a range containing almost all of the individual values.  Methods are given below for calculating the interval for individual values for a worst-case tolerance, a statistical tolerance and a process tolerance.
Worst-Case Tolerance:  Worst-case tolerances are themselves intervals for individual values.  Therefore the interval for values is equal to the worst-cast tolerance.
Statistical Tolerance:  The interval for individual values is frequently specified as the target plus or some number of standard deviations.  Commonly 3 or 4.5 standard deviations is used.  If 3 standard deviations is used, 99.7% of the individual values are expected to fall within this interval.  If 4.5 standard deviations is used, all but 6.8 units per million are expected to fall within this interval.  VarTran allows the number of standard deviations to be specified using the Number of Standard Deviations for Intervals for Values menu item on the Options menu.  The default is 4.5 standard deviations.
Process Tolerance:  The interval for individual values is from the minimum average minus 4.5 standard deviations to the maximum average plus 4.5 standard deviations.  As before, VarTran allows the number of standard deviations to be changed using the Number of Standard Deviations for Intervals for Values menu item on the Options menu.  When 4.5 standard deviations is used, meeting the process tolerance ensures no more than 3.4 units per million are outside the interval for values.  This level of defects is called Six Sigma Quality.
When displaying intervals for values, VarTran always specifies the number of standard deviations that was use.  For example, VarTran might refer to the +/-4.5 SD interval for values.