Process Capability Analysis--Normal and General Non-Normal Distribution (Raw Data) - Quick Tab
Select the Quick tab of the Process Capability Analysis--Normal and General Non-Normal Distribution (Raw Data) dialog box to access the options described here.
Normal distribution
Use the options located under Normal distribution to compute capability indices based on the normal distribution and fit the normal distributions to the observed histogram.
Summary: Current variable
Click the Summary: Current variable button to produce two spreadsheets containing the standard process capability indices and process performance indices.
Available process capability indices include Cp, Cr, Cpk, Cpl, Cpu, K, and Cpm. 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, then 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 dialog box - 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 box (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 create a summary spreadsheet containing the standard process capability indices for all variables. Available process capability indices include Cp, Cr, Cpk, Cpl, Cpu, K, and Cpm.
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.
See Multiple samples (Cp, Cpk, Pp, Ppk, etc.) above for more details.
Summary histogram
Click the Summary histogram button to create 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.
The summary histogram reports both sigma estimates and includes two normal distribution fits: one using the within-sample sigma and the other using total sigma. Within-sample sigma is used to calculate capability indices (such as, Cpk) and, total sigma is used to compute process performance indices (such as Ppk).
Non-normal distribution (Pearson & Johnson curves approximation)
Use the options located under Non-normal distribution (Pearson & Johnson curves approximation) to compute capability indices based on the non-normal distributions and fit the non-normal distributions to the observed histogram.
Summary: Current variable
Click the Summary: Current variable button to display a spreadsheet with the normal and non-normal process capability indices.
If the standard 3 time Sigma limits are used for the computations, then the capability indices for the Pearson distributions fit as well as the Johnson distributions fit will be reported. The computation of these indices is described in the Overview; Clements (1989) also provides detailed step-by-step instructions of how these indices are computed.
Note: Pearson distributions vs. Johnson distributions
As described in the Overview, the capability indices based on these two methods for fitting non-normal distributions will in most cases yield very similar results.
To reiterate, one should remember that the estimated four moments (for the non-normal distribution fitting) are subject to potentially substantial sampling fluctuations (Hahn and Shapiro, 1967). Therefore, the capability indices reported here should always be interpreted with caution. Note that for distributions with extreme skewness and/or kurtosis, the capability indices based on the Johnson distributions fit will usually be more conservative (smaller) than those based on the Pearson distributions fit; for distributions with an absolute skewness that is greater than 2, only the capability estimates based on the Johnson distributions fit are reported.
All variables
Click the All variables button to display a summary spreadsheet with the non-normal (Johnson-curves) process capability indices for each variable that you have specified in your design (see also Fitting Distributions by Moments).
In the results spreadsheet, the variables will be the cases; the process capability indices along with additional statistics will be the columns. 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 the Grouping tab.
Non-normal summary histogram
Click the Non-normal summary histogram button to display a standard process analysis histogram.
Instead of a normal distribution fit, the fitted non-normal distribution curve is shown in the graph. As described in the Overview, the fitted distribution curve is computed from the respective Johnson transformation of a normal variable, and not from the tabulated values of the Pearson distributions. You can change the options and scaling for the histogram via the Options tab.
This tab contains an option to display the equivalent percentile values for the respective non-normal distribution instead of the Sigma limits for the normal distribution.
For example, instead of indicating the upper process range as 3 times Sigma, the graph may indicate the location on the x-axis of the graph that corresponds to the 99.865 percentile value (which is the equivalent to 3 times Sigma for the normal distribution). Given that the non-normal fit is appropriate, this option allows you to gain a more realistic picture of the process performance relative to the engineering specifications.