## Do We Need a Matrix for QFD?

January 21st, 2011 by Dr. Thomas M. Fehlmann

During the last years a tendency has been observed to position QFD more towards understanding customer’s needs than doing complex matrix mathemagics with insecure data and producing fuzzy evaluation profiles. It is more important saving (customer’s) time than understanding relationships between process controls and process response.

Customer’s needs can be analyzed by means of Thomas Saaty’s Analytic Hierarchical Process (AHP), prioritized with ratio scales, and assessed for consistency. This seems much quicker and more reliable than assessing the Voice of the Engineers, and then trying to understand how it transforms into something that meets Voice of the Customer’s requirements.

However, this opinion stands in contrast to the Six Sigma approach, used to define, measure, analyze, improve, and control (DMAIC) relationships between process controls and process responses. Such relationship mapping is called Transfer Function. For instance, a transfer function describes how to transform controls used by engineers into response expected by customers. If there are more than one response characteristics, and more than one control impacts the response, the QFD matrix is the natural choice for representing the transfer function.

## Transfer Functions

In Six Sigma, mapping control profiles onto process responses is the key prediction method when designing production processes with a defined response variation. Transfer functions can be measured; this is the essence of the DMAIC approach. But how should we use transfer functions if they are hard to measure, as often encountered in the Design for Six Sigma discipline?

Processes whose transfer functions are hard to measure arise in physics, astronomy, economics, and many more areas of science. For instance, measuring the blinking of stars and trying to derive from that how the universe has been created, or having to search for some particular item in the depths of the Internet, seems impossible but can be done. Both cosmologists and Google use the same mathematical theory. It is called Eigenvector Theory, part of Linear Algebra.

The idea Eigenvector theory is based on is: go to the dual space where cause and effect are inverted, and try what happens if all turns into its contrary. Then intersect the real world with the dual world; the result is the most likely stable outcome, the eigenvector of the original problem statement. This allows dealing with fuzzy data.

## Transfer Functions as Matrices

Of course this only sounds simple as an idea but can it be implemented in practice? Luckily, most of the transfer functions we encounter in business life are linear – and from a mathematical point of view linear functions can be represented as matrices. QFD matrices are approximations to the transfer function connecting different viewpoints – e.g., Voice of the Engineer to Voice of the Customer. The dual space is the transpose of the matrix, i.e., you exchange rows by the columns, i.e., rows and columns are interchanged.

The difficult step is to understand how to measure transfer functions. The Six Sigma methodology teaches how linear transfer functions can be measured: we measure the strength of relationships between controls and processes for each control/response pair – for each cell in the matrix. In QFD workshop, measurement is replaced by expert estimation; experts predict and estimate the most likely measurement result per cell. Typically, in Design for Six Sigma, production processes cannot be run for measurement purposes only, as it is possible in manufacturing. Thus QFD workshops held with the experienced people are very valuable as a replacement. If these expert judgments later can be compared to measurements later on, cell by cell, when actually executing the process, its’ even better.

Thus, matrices in QFD are the container for both process predictions and measurements, and yield much greater value than just doing AHP, or Blitz QFD. The question is whether it is worth the additional effort.

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This entry was posted on Friday, January 21st, 2011 at 5:00 pm and is filed under House of Quality, Advice, DFSS, Lean Six Sigma, Quality Function Deployment, QFD. You can follow any responses to this entry through the RSS 2.0 feed. You can also leave a response.

October 23rd, 2011 at 5:53 pm

We Need a Matrix for QFD

December 6th, 2011 at 8:20 am

i need for my colllege work

June 22nd, 2012 at 3:05 pm

Me gustaria saber mas de las matrices del QFD

March 16th, 2013 at 7:00 pm

Good night,

I’m Student of industrial engineer in Bogota, Colombia and I´m doing my degree work about QFD and its application in service companies and i need know if you have an archive in excel format for develop the struture of the QFD’s matrix. I hope your answer. Thanks.

October 7th, 2013 at 11:43 am

We Need a Matrix for QFD, I am studying.

September 16th, 2015 at 1:51 pm

For my work

October 8th, 2015 at 3:19 pm

i need a matrix of QFD because i am studyng