MATRIX DATA ANALYSIS
The objective of the technique is data reduction and identification of the hidden structure behind an observed data set. Matrix data analysis is a very effective technique to help you to discover the structure of large data sets.
Quality management technique:
Fig: Classification of quality management techniques (tree diagram)
Matrix data analysis:
· The name matrix data analysis refers to the data input to the technique which is a matrix of data consisting of a number of observations on a number of different variables.
· A typical data set of this type will be when the observations are different products and the variables are different characteristics of the products or when the observations are customers and the variables represent customer satisfaction measured in different areas.
The procedure is as follows:
1. Arrange your data in an n*p matrix. Call this matrix X.
2. Compute the matrix of squares and cross-products, X’X. Alternatively compute the matrix of variances and covariance or the correlation matrix.
3. Compute the principal components of the matrix given in 2.
4 Compute the correlations between the original variables and the principal components, the so-called loadings.
5. Use the first two principal components to give a graphical presentation of the loadings computed in 4. This presentation gives the best possible description of the original data set using only two dimensions.
The calculation of the principal components of a data set is done by solving the following equations:
Where lj is the jth characteristic root and nj is the corresponding characteristic vector. The jth principal component (yj) which is uncorrelated with all other principal components is calculated as a linear combination of the original observations as follows:
Parameters of the customer’s satisfaction:
Based on the placing of the points in the diagram it was decided to group the customer satisfaction parameters in two groups. These were:
1. Contact parameters;
2. Product parameters.