A **Matrix Diagram** is a table that allows sets of data to be compared in order to make better decisions. It displays the existence and strength of relationship between pairs of items of two or more sets. The relationship is then indicated by a number or symbol in each cell where the two items intersect in the matrix. A matrix diagram can be used as part of other decision making tools. Cause and Effect Matrix and Quality Function Deployment are examples of tools that use the matrix diagram.

A matrix diagram is used to help identify and understand the relationship between variables. This connection between variables can be useful in decision making, problem solving and process improvement efforts. It is often used to understand the relationship between two lists where the first represents problems and the second represents possible solutions to those problems. It can also be used when the second list is generated as a result of the first list, for example, to generate design specifications that best meet the required operating conditions.

Matrix diagrams can be useful in a wide range of applications including: searching of possible problem causes, matching requirements with specifications, comparing the significance of alternative solutions, identifying opportunities for improvement, and assigning responsibilities based on appropriate personnel competencies.

For example, and as part of a quality function deployment (QFD) analysis, a design team may select the most effective design features that meet customer requirements. In this example, the first set will be the customer requirements while the second set will be the design features. Other examples may include:

- A marketing team selects the most effective sales tools to increase sales.
- A restaurant team selects the most effective work processes that improves customer experience.
- A quality team selects the most effective inspection methods to discover product defects.
- A manufacturing team selects the possible causes which affect materials consumption in a production line.

A matrix diagram has a number of types, each has many applications. The most basic and the most used one is the **L-Shaped matrix diagram** where you only compare two sets of data. In an L-shaped matrix, a two-dimensional table is used to represent the diagram. The items of the first set are listed in the left hand column while the items of the second set are listed in the top row of the table. Numbers or symbols are then indicated in the cells to show the strength of the relationship between each pair of items. Weighting can also be used for prioritization and ranking. Other information can be displayed including: the totals and the overall strength of the relationship.

Other shapes are available to compare more than two lists including: the **T-Shaped**, **X-Shaped**, and **Y-Shaped** matrices.

#### Building a Matrix Diagram

The following steps describe how to build and use an L-matrix diagram:

- Clearly explain to the team the purpose for building the matrix diagram.
- Select and collect the two sets of data that need to be compared.
- Agree on the symbols and their values.
- Construct a two-dimensional table.
- Insert the first set of data on the left hand column and the second one on top row of the table.
- Work through the matrix and discuss the relationships between every pair of items.
- Place the appropriate symbol at the intersecting cell of the matrix.
- Give weighted scores to show relative importance of items.
- Calculate the final weighted scores for each item.
- Review the completed matrix with your team in order to make the best decision for your situation.

#### Example – How to Make a Better Cup of Tea

The following is a simple example of an L-shaped matrix diagram that shows the cause and effect relationship between two sets of data.

#### Example – Allocation Human Resources to Multiple Projects

A program manager decided to use a matrix diagram to help him allocating human resources to multiple improvement projects. This is an example of a T-shaped matrix diagram which allows two sets of data to be compared with a third one.