Calculating the Supplementary Key Figures for Information Structures S162, S164, S166

The statistics , , c p, c pk are each contained once only in the information structure. The algorithm for calculating , , c p, c pk is dependent on the respective process model.

The possible process models and the calculation procedure are as follows:

  • Model 1:

Mean value is derived from the mean value of the individual values.

Standard deviation is derived from inner dispersion.

  • Model 2:

Mean value is derived from the mean value of the individual values.

Standard deviation is derived from average dispersion.

  • Model 3:

Mean value is derived from the mean value of the mean values.

Standard deviation is derived from mean quadratic dispersion.

Depending on the model on which the calculation is based, the mean value x contains either the total mean value or the mean value of the mean values`.

The corresponding values for dispersion are the inner dispersion s in, the mean dispersion s or the mean quadratic dispersion`s q. These values are included in the subsequent calculation of c p, c pk .

The default calculation algorithm for the statistics comprises the inner dispersion s in and the total mean value . The process model can be switched at runtime and saved as a user parameter.

Calculation algorithms and source key figures:

  • n Stat No. of valid single values (2)

  • n No. of samples

Mean values:

Mean value of single valuesn i. x i. / n Stat

Mean value of mean values.x i. /n

    Total of single values (2)

      Total of mean values (2)

        Standard deviation:

        Inner dispersion

        Mean dispersions i /n

          • Mean quadratic dispersion

            Source key figures:

            • Var in Total variance of single values

              • s i Total dispersions of samples

              • åVarTotal variances of samples

              Process capability values:

              • tol un Last tolerance below

              • tol ob Last tolerance above

              • c p Process capability index (1)( tol ob - tol un ) / 6s

              • c pk Process capability index (1)( tol ob -x ) / 3sor(x - tol un ) / 3s

              Key: (1) Key figures calculated at runtime

              (2) Technical key figures (only used to calculate key figures at runtime)