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Tilmag's Five Steps for Solving Innovative Problems

By Paul A. Edney and Michael S. Slocum

The transformation of ideal solution elements through associations (TILMAG) is a leading method for a dominant class of issues that arise in innovation thinking.

Origins of TILMAG

TILMAG was developed by Battelle-Institut in Frankfurt am Main, Germany, and stands for “transformation idealer lösungselemente durch matrizen der assoziations und gemeinsamkeitenbildung,” the “transformation of ideal solution elements through the matrices of formation of associations and commonalities.” The full name emphasizes two key characteristics of the TILMAG process: 1) the central role of two-way tables or matrices and 2) the importance of feature comparisons and mental associations. The first characteristic links TILMAG directly to axiomatic design (AD) and Design for Six Sigma (DFSS) processes, while the latter is a reminder that TILMAG relies on synectics to stimulate creativity. Unlike brainstorming, this stimulation is highly directed and focused on the specific aspects or requirements of a problem.

The matrix nature of TILMAG is uniquely suited to the human mind. Whether or not by design, TILMAG effectively leverages the fact that the human mind is ill-equipped to retain and process more than three bits of information at any time. TILMAG naturally implements the human binary logical thought process.

The TILMAG Process

How does TILMAG work? It is a 5-step process.

  1. Define the problem: A number of tools can be used for this step: voice of customer (VOC) from DFSS, the ideal final result (IFR) from TRIZ, heuristic redefinition process (HRP), or the outputs from the customer attributes (CA-), functional requirements (FR-) or design Parameters (DP-) domains of axiomatic design (AD) are only a few.
  2. Identify the ISE: TILMAG typically begins with four to six ideal solution elements (ISEs) – features, requirements, characteristics or desired attributes that have been identified as necessary to meet the requirements or overcome the problems identified in step 1. As the “associations” part of TILMAG implies, the tool requires a minimum of two ISEs and preferably no more than six ISEs. (n ISEs will require exploring n(n-1)/2 associations, or fifteen associations for six ISEs.) If many more than six ISEs are required, they can often be regrouped into two or more loosely coupled (i.e., highly independent) subsets that can be addressed in their own TILMAG effort. This approach lends itself to divide-and-conquer ideation strategies.
  3. Build the TILMAG matrix:

    Table: TILMAG Matrix

    Ideal Solution Elements (ISE)

    ISE 1

    ISE 2

    ISE 3

    ISE 1





    ISE 2









    ISE n





    [The combination of any ISE with itself does not represent an association so the diagonal of the table is excluded. Similarly, the combination of ISEs that define cell (n,m) is identical to the combination that defines cell (m,n) (i.e., “m and n” is the same as “n and m”).]

  4. Generate solutions: Each remaining solution (cell) in the matrix is evaluated in turn, ensuring that all interactions and potential contradictions between ISEs are addressed. Depending on the dynamics of the group, on the nature of the ISEs and on the type of interaction between the ISEs, concepts and solutions can be generated with brainstorming, brainwriting or TRIZ. Any specific cell in the matrix may take a few minutes to three-quarters of an hour to analyze.
  5. Consolidate and prioritize: Finally, all concepts and ideas generated in step 4 are structured and documented. Most often, solutions are ordered into an affinity diagram (sometimes said to be “affinitized”) so that commonalities, synergies and economies in design are clear. Ideas can also be regrouped into the subsystems or subprocesses that they support or affect.

TILMAG, Systems Engineering, DFSS and Axiomatic Design

From an ideation perspective, the TILMAG process takes ISEs as inputs and outputs ideas and concepts.

In process-speak: TILMAG uses the “what”s to generate “how”s. TILMAG’s role in the transition, translation or articulation of “what” into “how” can be used to support roadmaps (e.g., systems engineering and DFSS) and cascading processes (e.g., AD, high-level TRIZ problems and QFD).

Within systems engineering, TILMAG can be deployed to articulate requirements, explore interfaces and interactions between requirements, or resolve any issues that appear in the trace matrix. TILMAG is a helpful tool in implementing the control aspects of the systems approach.

In DFSS, TILMAG integrates seamlessly into CTC (critical to customer) or CTQ (critical to quality) flowdowns, whereby customer requirements at theunclear front endare gradually translated into forms usable in development (design) and manufacturing (process or production). TILMAG also routinely moves VOC data to functional requirements followed by design parameters. While TILMAG does not offer the quantitative power of AD (and therefore cannot assess such parameters as robustness), it does provide a backbone for ideation and a focused environment to explore options, evaluate concepts based on features and requirements, and identify potential conflicts between ISEs. DFSS provides a strategy for product development. Tactically, many walk a tightrope between each phase of the process (i.e., DMADVand DMEDI); TILMAG adds considerable reliability, repeatability and reproducibility to the DFSS process.

TILMAG is complementary to axiomatic design. Each AD domain outlines needs, attributes, requirements or parameters that need be met to deliver a quality process or product to customers. Each of those items is initially a “what” in the development process. Only after the ideation process do the “what”s of a domain turn into “how”s, and those in turn become the “what”s for the next domain. In the AD zig-zagging process, TILMAG first helps generate solutions to support any of the “what”s. These concepts are then used to populate the design matrix, which in turn helps evaluate the different design concepts. The zig-zagging process then repeats at the sub-system level (and so on) until the transition from one AD domain to the next is complete. TILMAG helps stimulate the ideation process; AD then structures, evaluates and even quantifies the concepts and design.


TILMAG is particularly effective in situations in which requirements or functional requirements have been identified and need to be articulated or translated for the next step in process or product development. TILMAG is most useful in supporting such methodologies as DFSS (VOC, QFD, CTC flowdown), axiomatic design or systems engineering. TILMAG is invaluable at the front-end of these processes – when customer requirements (VOC, FR) need to be transformed to physical reality or actionable concepts.

This innovation methodology is also highly complementary when used with other ideation methodologies such as TRIZ or brainstorming. In the case of TRIZ, TILMAG allows comparisons and facilitates the identification of contradictory ISEs. With brainstorming, TILMAG helps scope and focus the creative process, increasing the quality of the generated solutions and reducing the difficulty of the problem at hand.

TILMAG is a powerful – albeit still relatively unknown – method for the ideation process.

About the Authors:

Paul A. Edney, Ph.D., is the owner of Edney Consulting. Contact Paul A. Edney at paul (at) or visit

Michael S. Slocum, Ph.D., is the principal and chief executive officer of The Inventioneering Company. Contact Michael S. Slocum at michael (at) or visit