This document describes the applied datastructure and statistics. The current version of datastructure and statistics focus on univariate data monitoring. In later versions an expansion to multivariate data monitoring and analysis is planned.

## Univariate vs. Multivariate Statistical Monitoring and Analysis

Univariate statistical monitoring (control) and analysis is carried out based on a single variable in terms of the applicable unit of analysis. For example, if the diameter of screws is the relevant subject only the variation and trends of this variable would be subject of analysis. In process control applications only this aspect is monitored using target and controllimit settings.

Univariate analysis, monitoring and control contrasts with simultanious analysis, monitoring and control of multiple variables, taking into account the relations and perhaps correlations among different variables.

Univariate process monitoring is usually performed with the help of a control chart. The control chart was introduced by Walther a. Shewhart in the 20th of the last century with the basic intention to distingush assignable causes and common variation with the help of statistical methods. Shewhart applied this methodology first to industrial control with the intention to reduce quality cost by recognizing (new) assignable cause variation.

## Datastructure

for univariate data the following structure is used:

The UniStream (short for univariate stream) corresponds to one univariate variable. In our statistics engine a UniStream contains the supplied raw data together with at least one UniChart object. A UniChart object corresponds to a specific statistic applied to a raw data sample, e.g. the *mean* of the sample values. Currently the following four statistics are supported: mean, standard deviation (sdev), median and inter quartile range (iqr).

A UniChart object can be analyzed further:

From the above it is clear that the input to a UniChart is just a singe value e. g. a mean or a median. If this value is directly monitored in our nomenclature this is called the Shewhart sampling (after the inventor of the statistical process control). The Shewhart sampling is a must for every UniChart object. In addition EWMA (exponentially weighted moving average), CUSUM (cumulative sum) and moving range sampling types can be used.