Process Capability Analysis Setup--Raw Data - Distribution Tab

With a spreadsheet open, click on the Statistics tab on the ribbon.

Select the Process Analysis icon.

Select the Distribution tab of the Process Capability Analysis Setup--Raw Data dialog box to access the options described here.

Distribution

The Distribution group box contains the options described below.

    1. Select any one of the distributions, or click the Fit all distributions button (see below) to review the goodness-of-fit for all available distributions.
    1. Fit all distributions (compute parameters and K-S d) a or Grouping tab, to produce spreadsheet(s) (one for each selected variable) with the results of fitting all available distributions, including the general non-normal distribution (Johnson curves, fitting by moments; see the Introductory Overview).

      The spreadsheet(s) will be sorted according to the Kolmogorov-Smirnov d statistic.

  • The first row will show the distribution with the smallest d statistic (for example, those that produced the best fit),
  • The second row will show the distribution with the second smallest d statistic, and so on.
    Note: the p-values reported in the spreadsheets for the Kolmogorov-Smirnov tests are based on the tabulated values (see Massey, 1951; see also Siegel and Castellan, 1988). Thus, they are only valid if the parameter estimates are known a priori (they typically are not) and should be interpreted with caution.

    To compute Lilliefors probabilities for the normal distribution, refer to the Normal and General Non-Normal Distribution (Raw Data) dialog - Summary Results tab.

Beta

Select the Beta option button to specify the Beta distribution.

Exponential

Select the Exponential option button to specify the Exponential distribution.

Extreme value (Type I, Gumbel)

Select the Extreme value (Type I, Gumbel) option button to specify the Extreme value distribution (Type I, Gumbel).

Gamma

Select the Gamma option button to specify the Gamma distribution.

Log-Normal

Select the Log-Normal option button to specify the Log-normal distribution.

Normal and general non-normal (Pearson and Johnson fitting)

Select the Normal and general non-normal (Pearson and Johnson fitting) option button to specify the Normal and general non-normal (Pearson and Johnson fitting by moments).

Percentile fit

By default, the Johnson distribution is fitted by moments (for details see Hahn and Shapiro, 1967, pages 199-220; and Hill, Hill, and Holder, 1976).  Select this checkbox to estimate the parameters of the Johnson distribution via the percentile based method outlined in Chou, Polansky, and Mason (1998).

Rayleigh

Select the Rayleigh option button to specify the Rayleigh Distribution.

Weibull

Select the Weibull option button to specify the Weibull distribution.

By default, Statistica will fit the normal distribution to the data, and you can review the results (such as Q-Q plot, P-P plots, capability indices, histograms, etc.) of fitting a general non-normal distribution by moments (see the Introductory Overview).

If you click the Fit all distributions button (see above), a spreadsheet is created (for each variable) with the parameter estimates and Kolmogorov-Smirnov d tests for all available distributions (including the general non-normal). The p-values reported in that spreadsheet for the Kolmogorov-Smirnov tests are based on the tabulated values ( see Massey, 1951; and Siegel and Castellan, 1988). Thus, they are only valid if the parameter estimates are known a priori (which they typically are not), and they should be interpreted with caution. (To compute Lilliefors probabilities for the normal distribution, refer to the Process Capability Results dialog box topic.)

Offset (threshold/location) and Scale parameter

Some distributions have particular valid value ranges (such as for Weibull the observed values must be greater than zero; see the Non-Normal Distributions Overview). For those distributions, you can specify a lower threshold (location) value and, in the case of the Beta distribution, a Sigma value. The threshold (location) values will be subtracted from the observed values before the respective distribution is fitted. In the case of the Beta distribution, the observed values are rescaled as:

(x-location)/sigma

Because the valid range for the Beta distribution is 0 < x < 1, when fitting that distribution be sure to specify a Sigma value so that the rescaled values fall into the 0/1 interval. For details concerning all available distributions, refer to the Non-Normal Distributions Overview.

Also see: Process Capability Analysis Percentile Fit Option to Estimate Johnson Distribution