## Chapter IV Analyse Phase

### Exploratory Data Analysis

#### Multi-vari studies

A multi-vari chart, a tool that graphical representation of patterns of variation and used to identify possible Xs or families of variation, whereas variation within subgroup, between subgroups or overtime.

#### Multi-vari charts are

• Simple and gives significant way to reduce the number of potential factors impact on primary metric.

• Quick and effective method to minimize the time and resource available for the production for identifying the primary factors of variation.

• To eliminate the large number of factors from the universe of potential factors.

**Types of variation****Positional variation**is the variation occurs when there is during the manufacturing the different item for single product.**Within individual sample:**Variation is present upon repeat measurements within the sample. In manufacturing source of variation such as, Measurement accuracy, apart from activity. In Transactional source of variation such as Line product complexity**Cyclical variation**is the variation caused by the part-part variation where variance between two consecutive units is measured. It defines the magnitude of the variation and large variation caused by various factors falls in cyclical category.**Piece to piece**: Variation occurs when the measurement of different samples collected within a short time frame .In manufacturing source of variation such as, Machine fixturing and difference in mold cavity. In transactional source of variation such as Sales office, customer difference and order editor.**Temporal variation**is the variation caused other than positional and cyclical variation.**Time to Time:**Variation is present occurs with significant amount of time between each sample. In manufacturing source of variation such as material changes, calibration drift, operator influence and tool wear. In transactional source of variation such as seasonal variation, economic shifts and Interest rate.It is measured as "units" for different process and measured in different points of the unit.

#### Simple linear correlation and regression

**Correlation analysis:**Correlation is defined as the degree of relationship between two or more variables. It is also referred to as co variation. The degree of Correlation between two variables is called simple Correlation. The degree of correlation between one variables and several others variables is called multiple Correlation.

Correlation and regression methods are to determine the associations and relationships between continuous variable gathered from same set of sampling or experimental units. Correlation measure of association between two variables is the sum of product of the deviation of each point from mean center.

Correlation used to determine the degrees of changes in variable and difference between dependent and independent variable. Also, this method allows interpreting the causality of the association. Correlation measure of association between two variables is the sum of product of the deviation of each point from mean center.

**Different type of correlation:**1. Linear Correlation

2. Non-linear Correlation

3. Doubtful Correlation

**Measure of linear correlation:**The quantitative measurements of the degree of correlation between two variables, i.e X and Y is given by a parameter called

**correlation coefficient.****Correlation coefficient is defined by the formula**r=covariance of x and y by (standard deviation of x) (standard deviation of y)

**Regression analysis**Regression method determines the nature of relationship between variables where the magnitude and change in one variable are directly responsible for changes in variable and magnitude. Regression applied into survey method and experimental method based on prior knowledge.

#### Six Sigma Data Analysis