Process Capability Analysis--Normal and General Non-Normal Distribution (Raw Data) - Advanced, Normal Tab

Select the Advanced, normal tab of the Process Capability Analysis--Normal and General Non-Normal Distribution (Raw Data) dialog box to access the options described here.

Summary: Current variable

Click the Summary: Current variable button to produce two spreadsheet 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 the 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 click 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. Note that the All variables button is only available if more than one variable was selected for the analysis via the Process Capability Analysis Setup--Raw Data dialog box - Raw data tab or the 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 number of steps to be used for the histogram in the plot on the Options tab. Note that 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).

Number beyond specs (estimated & observed)

Click the Number beyond specs (estimated & observed) button to create a spreadsheet that tabulates the number and percent of observed units (in the sample) that fall outside the specification limits (LSL, USL).

Also reported in this spreadsheet are the number and percentage of units that can be expected to fall outside those limits based on the normal distribution.

Descriptive statistics

Click the Descriptive statistics button to create a spreadsheet containing detailed descriptive statistics for the measures of interest.

Specifically, this spreadsheet reports the mean, median, percentiles, minimum, maximum, standard deviation, variance, skewness, and kurtosis for this variable. If you are not familiar with these descriptive statistics, refer to Basic Statistics, Nonparametrics, and Distribution Fitting. Finally the spreadsheet will also display the number of samples, sample size, and Sigma-S (R-bar/d₂).

Distribution & tests of normality

Click the Distribution & tests of normality button to create 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 & Castellan, 1988) will be computed to test the observed distribution against the normal distribution. Both the standard significance level for the Kolmogorov-Smirnov test as well as the Lilliefors probability (Lilliefors, 1967) for the respective d statistic will be computed. The Lilliefors probabilities are appropriate when the mean and standard deviation for the normal distribution was estimated from the data.

These tests are identical to those performed by the Distribution Fitting module. In short, if these tests are significant, we have reason to doubt that the variable of interest is distributed following the normal distribution. However, minor violations are of little consequence, and you should always also review the normal probability plot (see below). If the observed data show major deviations from the normal distribution, normality can usually be reestablished by using appropriate transformations of the measurements. For example, log transformations will pull in the upper tail of the distribution, square root transformations will pull in the lower tail of the distribution, etc.

You can control the scaling for distribution, that is the lower and upper limits as well as the number of categories to be used in the frequency table, on the Options tab.

Q-Q Normal distribution

Click the Q-Q Normal distribution button to produce a Q-Q plot.

This type of plot is described in the Introductory Overview (see also Hahn and Shapiro, 1967). To produce a Q-Q plot, STATISTICA will first sort the N observed data points into ascending order, so that:

x₍₁₎ <=.x₍₂₎ <= ... <=.x_(n)

These observed values are plotted against one axis of the graph; on the other axis the plot will show:

F^-1 ((i-r_adj )/(n+n_adj ))

where i is the rank of the respective observation, r_adj and n_adj are adjustment factors (<= 0.5) and F^-1 denotes the inverse of the probability integral for the respective standardized distribution (such as normal). The resulting plot is a scatterplot of the observed values against the (standardized) expected values, given the respective distribution. If the respective theoretical distribution provides a good fit to the observed data, then all data points in this plot will fall onto a straight line. Note that Statistica also computes the respective percentile values for the theoretical distribution, and places them on the scale opposite to the standardized theoretical distribution values (e.g., normal z values in case of the normal distribution).

P-P Normal distribution

Click the P-P Normal distribution button to produce a P-P plot.

This type of plot is described in the Introductory Overview (see also Hahn and Shapiro, 1967). In the P-P (probability-probability) plot, the observed cumulative distribution function is plotted against the theoretical cumulative distribution function for the same values. If the respective distribution (normal) provides a good fit to the observed data, then all data points will fall onto the diagonal in this plot.