Conformity assessment: Statistical inspection of measured values

Criterion / Action

Grubb’s G and Cochran’s C statistics

If G (Grubb) and C (Cochran) are:

  • Less than or equal to their 5% critical value – accept
  • Exceeding their 5% critical value but smaller than their 1% critical value – straggler (*)
  • Exceeding their 1% critical value – “outlier” (**)

Mandel h-statistics

If a measured datum has an h-statistic:

  • Has a different character from all other data
  • Is very distinct in value from the other data
  • Depends systematically on the level

then the measurements made by that laboratory should be examined in, in particular.

Mandel k-statistics

If a datum has a k-statistic which is:

  • larger – this indicates that the lab has a worse repeatability
  • smaller, indicating that the lab may have rounded their values too much, e.g.

then the measurements made by that laboratory should be examined in, in particular.

xbarChart

Action must be taken if two consecutive results on a x-chart lie outside the warning limit.

Range (R-) Chart

Action must be taken if two consecutive results on a R-chart lie outside the warning limit.

T-test

If t <tmax of the Student t-test, the new measurements, combined older, where the new “pooled” average is calculated as:
poolmeanwhere k, j are the number of measurements: new (n) resp. old (o).

F-test

If F <Fmax of the F-test, the new measurements can be combined with the older, where the new “pooled” standard deviation is calculated as:
Spool

Process capability (mean) (standdev)

When making a process capability test based on the mean:

If M <± 15%:                    Process is accepted

When making a process capability test based on the standard deviation:

If Cpk <1.0:                       Process must be improved immediately

If Cpk is  1.0 – 1.3:            Process (just) meets specification.

If Cpk> 1.0:                       Process is accepted

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