*For a full description, see: Hellenbrand, D.; Lindemann, U.: Using the DSM to Support the Selection of Product Concepts. In: Proceedings of the 10th international Design Structure Matrix Conference – DSM’08, Stockholm – Sweden, November 11 – 12, 2008 (with friendly permission by the authors)*

## Problem Description

The conceptual design defines the basic working principles of a product; therefore, the selection of a specific concept has a great impact on all later development.

To obtain a wide field of different solutions and to handle complexity at the same time, factorization is often used: A complex system is divided into separate manageable sub-problems, which can be treated independently. The consistent combination of partial solutions leads to the overall solution (i.e. the concept).

A common method to order and systematize the different partial solutions is the use of a unidimensional ordering scheme like the morphological matrix (also called combination table). Using such a matrix, a high number of overall concepts can be created out of a small number of sub-problems and solutions. In a second step, this solution space can then be narrowed down in order to obtain an optimum concept. The utilization of a DSM to analyze interdependencies among the partial solutions can support this task in a methodical and structured way.

## Concept selection in an aviation industry project

During the conceptual design phase of a future ESTOL air plane (Extremely Short Take-Off and Landing), a morphological matrix with four partial functions and 24 partial solutions was created. Even this small matrix already leads to the high number of more than thousand theoretical concepts. Due to time and cost constrains it was not possible to analyze and evaluate all generated concepts in detail. The large number of theoretical concepts had to be reduced to a maximum of 3 promising concepts.

Therefore, the DSM was used to support the process of concept selection by consequently eliminating inconsistent concepts and identifying promising combinations:

In the beginning, all pair wise possible combinations of partial solutions were evaluated by a team of experts. The results were afterwards documented in an extended consistency matrix. Then, the consistent concepts were identified and a ranking order was calculated. Thereby, two basically different concepts, which are both very promising could be identified (see figure below).

A more detailed description of the procedure that was used and the underlying theory is given in the next paragraphs.

## System definition

The use of a morphological matrix allows for an easy creation of a high number of concepts out of a small number of partial functions and solutions. This leads to two different problems:

- It is not possible to analyze and evaluate all generated concepts in detail.
- Many of these theoretical concepts are unfeasible because the selected partial solutions are incompatible among each other.

Therefore, the number of theoretical solutions has to be reduced significantly. To fulfill this task a compatibility matrix, which incompatibilities among two different partial solutions are marked in, can be used. This enables the identification of inconsistent concepts with and their elimination from further considerations.

An example network of partial solutions and their interdependencies is shown in the figure below. An orange line indicates that two elements are incompatible. In this context, only the dependencies of partial solutions for different functions (A, B, C) are important.

## Dependencies in the system

The dependencies were first represented using a compatibility matrix, as shown on the left hand side of the figure below. It represents all pairs of inconsistent elements, thus representing the graph seen in the previous figure.

To support the task of the identification and selection of consistent overall concepts, a matrix is needed which represents all possible connections among the partial solutions. Therefore, the classic compatibility matrix is transformed into a “consistency DSM”, which represents all compatible combinations of elements (see the figure below on the right hand side). This matrix can easily be created by inverting every relationship of a given compatibility matrix. Compared to the classic compatibility matrix, the new consistency DSM can be seen as an inverted or negative image.

By using the DSM it is possible to analyze, visualize and interpret interdependencies even in very large solution fields by using computerized tools.

## Application to the generation of consistent overall concepts

**Identification of consistent concepts**

With this representation of the solution field it is possible to identify consistent overall concepts by performing a cluster analysis. A consistent and complete overall concept correlates with a completely interlinked cluster. Thereby, the size of the cluster has to meet the number of partial functions (rows in the morphological matrix). This is due to the fact that all elements contained in a solution have to be compatible to each other and that every partial problem has to be fulfilled. An example result of a cluster analysis is shown in the figure below. In total, there are seven completely interlinked clusters with a size of four in the given matrix.

Elements that are not contained in any completely interlinked cluster are eliminated from further considerations. That way, the number of theoretical solutions can be reduced significantly. The identification of clusters can be done by a computational.

The structure and interdependencies of the partial solutions can also be represented by force directed graphs. In these graphs partial solutions that are contained in many different overall solutions are arranged in the centre. Solutions with fewer connections or solutions, which are not contained in any completely interlinked cluster, can be found on the rim of the structure.

**Generation of a ranking order**

The identification of consistent solutions and elimination of partial solutions, which do not fit together, is only the first step during the process of concept selection. In general, the remaining number is still too large to be analyzed and evaluated in detail.

To identify the most promising concepts, the consistency DSM is extended by weighting factors (see next figure). These factors represent a positive or negative influence between two partial solutions. Two partial solutions, which have mutual positive influence or work perfectly together, receive a high value, poor combinations receive low factors.

To support the selection of a concept a ranking order can be calculated from the given weighting factors. The quality of a concept is represented by the sum of all the weights in a completely interlinked cluster. Concepts with a high value contain positive evaluated combinations of partial solutions; concepts with a lower sum include poor or average combinations. Based on this a ranking, consistent overall concepts can be derived easily (see figure below right).

This way of calculating a ranking out of the weights is possible because all considered clusters consist of the same number of elements and connections. Clusters that are not completely interlinked or that do not have the same number of elements in them have to be eliminated first. The generation of the ranking based on the extended compatibility matrix can then be done completely automatically.

Use Case provided by David Hellenbrand.