The Psychology of Quality and More

# Matrix Diagram: How to understand it

The Quality ToolbookMatrix Diagram > How to understand it

## How to understand it

When comparing two lists, there is sometimes a simple one-to-one relationship which can be easily documented in a side-by-side table. However, when a single item from one list may be related to several items in the other list, then the side-by-side format does not work, as in Fig. 1.

Fig. 1. Relationships between lists

The Matrix Diagram allows two lists to be compared by turning the second list on its side to form a matrix. Fig. 2 shows how the relationship between two items can now be indicated in the square or cell where the row and column of the two items cross.

Fig. 2. Many-to-many relationships in a matrix

The matrix can be thought of as a special form of table where the cells contain a simple symbol or number, which is derived from a defined set of rules.

A common extension to matrices is to use different symbols in the matrix cells in order to show the strength of the relationship between pairs of items. The overall strength of the relationship between an individual item and the whole of the other list can also be determined either by visually checking the diagram or by allocating a numerical value to each symbol and summing rows and columns, as in Fig. 3.

The most common relationship symbols and their corresponding values are shown below. The non-linear relationship between the numeric symbol values indicates how a strong relationship is typically much stronger than a medium or weak relationship. Another factor that may be included in this calculation is the relative priority of each list item.

Fig. 3. Showing and summing strength of relationship

The basic matrix shown above is the most common matrix in use, and is called an L-Matrix, due to its shape. Where more than a simple comparison of two lists is required, other matrices are available, and are shown in Fig. 4. These also have descriptive letter names which indicate their shape.

Fig. 4. Different types of Matrix Diagram

A typical use of the Matrix Diagram to compare two lists is where the list on the left represents a problem (the 'what') and the list above represents a solution to that problem (the 'how'). For example, the first list details customer requirements for a product, whilst the second list shows how this is translated into design specifications. The relationship values now can be used to identify specific problems and other points of interest, for example:

• Rows with low totals indicate customer requirements which are not well met.
• Columns with low totals may indicate over-engineered or unnecessary design items.
• Columns with high totals indicate design items which are particularly important for meeting a number of customer requirements.

A constraint when using a Matrix Diagram is in the number of comparisons that may practically be made. A ten-by-ten matrix requires 100 comparisons, which needs a moderate effort to complete. However, a complex product might have hundreds of requirement details and a corresponding number of design specification elements, but a hundred-by-hundred matrix needs a prohibitive 10,000 comparisons to be made!

A practical use of the Matrix Diagram in a complex situation, is for focusing on the detail of critical, suspect or difficult parts of the problem, rather than trying to use it for the entire situation.

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