Identifying Models

A first step in the computations is to identify the appropriate time-dependent distribution model; once identified, the DIN and ISO standards then recommend specific computational approaches, which are discussed below.

The 8 distribution models can be identified and distinguished by performing tests for location, variability, instantaneous distributions (normal vs. non-normal), and outcoming (resulting) distribution (normal vs. non-normal). It is not necessary to compute actual tests comparing the skewness and kurtoses across samples, although this test can be performed as an option.

To determine random (r), systematic (s), and systematic-and-random ( sr) variability, Statistica follows these steps:

  1. First a linear regression model is fitted for the characteristic of interest (Y), assigning consecutive integers for each sample (1,2,.., NSamples) as X; if this correlation is significant (i.e., the slope in Y=a+b*X), then there is evidence for significant systematic variation (s).
  2. Next Statistica performs a test of lack-of-fit, to determine if the residual variance from the correlation (test for systematic variation) if significantly larger than the residual from the overall ANOVA; if so, then there is evidence for significant random variation (r).

If both tests are significant, then there is evidence for systematic and random variation ( sr); if only the ANOVA is significant (but the correlation is not), we have only random variation (r); if the lack of fit test is not significant, but the correlation is significant, then we have only systematic variation (s).