Non-Normal Distributions - Introductory Overview
The concept of process capability is described in detail in the Process Capability Overviews.
To reiterate, when judging the quality of a (for example, production) process it is useful to estimate the proportion of items produced that fall outside a predefined acceptable specification range. For example, the so-called Cp index is computed as:
Cp = (USL-LSL)/(6*sigma)
where Sigma is the estimated process standard deviation, and USL and LSL are the upper and lower specification limits, respectively. If the distribution of the respective quality characteristic or variable (e.g., size of piston rings) is normal, and the process is perfectly centered (i.e., the mean is equal to the design center), then this index can be interpreted as the proportion of the range of the standard normal curve (the process width) that falls within the engineering specification limits. If the process is not centered, an adjusted index Cpk is used instead (see Process Capability Indices for details).
Non-Normal Distributions
The Process Analysis module will fit non-normal distributions to the observed histogram, and compute capability indices based on the respective fitted non-normal distribution (via the percentile method).
You can choose from a variety of distributions or let Statistica pick the particular distributions that best fit the data. In addition, instead of computing capability indices by fitting specific distributions, Statistica can compute capability indices based on two different general families of distributions - the Johnson distributions (Johnson, 1965; see also Hahn and Shapiro, 1967) and Pearson distributions (Johnson, Nixon, Amos, and Pearson, 1963; Gruska, Mirkhani, and Lamberson, 1989; Pearson and Hartley, 1972) - which allow you to approximate a wide variety of continuous distributions. For all distributions, you can also compute the table of expected frequencies, the expected number of observations beyond specifications, and Q-Q (quantile-quantile) and P-P (probability-probability) plots. The specific method for computing process capability indices from these distributions is described in Clements (1989).
Quantile-quantile (Q-Q) plots and probability-probability (P-P) plots
Statistica offers various methods for assessing the quality of respective fit to the observed data. In addition to the table of observed and expected frequencies for different intervals, and the Kolmogorov-Smirnov and Chi-square goodness-of-fit tests, the program provides options for computing quantile and probability plots for all distributions.
These scatterplots are constructed so that if the observed values follow the respective distribution, the points will form a straight line in the plot.