Process Capability Analysis Distribution (Raw Data) - Quick Tab

Select the Quick tab of the Process Capability Analysis Distribution (Raw Data) dialog box to access the options described here.

Summary: Current variable

Click the Summary: Current variable button to display two spreadsheets containing the standard process capability indices and process performance indices. Available process capability indices include Cp, Cr, Cpk, Cpl, Cpu, and K. Available process performance indices include Pp, Pr, Ppk, Ppl, and Ppu. These indices are reviewed in Process Capability Indices and Process Performance vs. Process Capability Introductory Overview.

Note: Multiple samples (Cp, Cpk, Pp, Ppk, etc.)

If the input data consist of multiple samples, and you specified a grouping variable with sample identifiers,Statistica estimates the within-sample Sigma based on ranges, standard deviations, or variances, depending on your selection on the Process Capability Analysis Setup Raw Data: Grouping tab. This estimate of Sigma is used to compute the capability indices when you select the Summary button on the Process Capability Analysis Normal and General Non-Normal Distribution dialog (for Raw Data). The standard deviation for all cases (total variation) is used to compute the performance indices, which will be displayed in a second spreadsheet; the standard deviation for all observations is also used in all other options available on this dialog. Refer to the Introductory Overview for additional details (see also the ASQC/AIAG reference manual; ASQC/AIAG, 1991, page 80). 

All variables

Click the All variables button to display a summary spreadsheet containing the standard process capability indices for all selected variables. Available process capability indices include Cp, Cr, Cpk, Cpl, Cpu, K, and Cpm. Note that the All variables button is only available if more than one variable is selected for the analysis via the Process Capability Analysis Setup Raw Data - Raw data tab or Grouping tab. These indices are reviewed in the Introductory Overview. The spreadsheet will contain these indices computed via the percentile method for the respective theoretical non-normal distribution

The Introductory Overview discusses how capability indices can be computed for non-normal distributions, using the percentile method (see also process capability indices). In short, instead of using as the practical process range the Sigma limits pertaining to the normal distribution, the equivalent percentile values for the respective non-normal distribution are used.

Summary histogram

Click the Summary histogram button to display the standard summary plot for the process capability study. You can specify the minimum, maximum, and the number of steps to be used for the histogram in the plot on the Options tab.

Descriptive stats and parameter estimates

Click the Descriptive stats and parameter estimates button to display a spreadsheet with 1) detailed descriptive statistics for the measure of interest, 2) the parameter estimates for the respective non-normal distribution, and 3) the estimate of Sigma from the within-sample variances, if a grouping variable was specified to indicate that the input data consists of multiple samples.

Frequency distribution & goodness of fit

Click the Frequency distribution & goodness of fit button to display a spreadsheet containing the frequency distribution for the variable of interest. Also, the Chi-square test and the Kolmogorov-Smirnov one-sample test (see Siegel and Castellan, 1988) will be computed to test the observed distribution against the respective theoretical non-normal distribution. Note that the probability level reported for the Kolmogorov-Smirnov d statistic assumes that the parameter estimates for the respective distribution were known a priori, which is usually not the case. Thus, these p-values should be interpreted with caution.

If the goodness-of-fit tests are significant, you have reason to doubt that the variable of interest is distributed following the respective theoretical distribution. However, minor violations are of little consequence, and you should always also review the Q-Q and P-P plots.

LSL = lower threshold

Many of the available non-normal distributions are bounded by a lower threshold, and the Beta distribution is bounded on both sides (see the Introductory Overview for valid value and parameter ranges for each distribution). When computing the potential capability indices Cp and its inverse Cr (capability ratio), it is often desirable to treat the natural lower (and upper bounds) as the limits for the engineering tolerances; however, note that the Cpl, Cpu, and Cpk (demonstrated excellence) indices are still computed using the actual current engineering tolerances (for an illustration and example of these computations, see Ford Motor Company Ltd and GEDAS, 1991, page 8).