The impact of linear algebra on QFD

Purpose - This paper introduces a new method to calculate a QFD matrix.Design methodology approach - One of the most prominent tools in QFD is the matrix. Matrices represent cause-effect relationships. Matrices are well-known in mathematics for representing linear mappings between vector spaces. Vectors, the elements of a vector space, represent the customer's needs profile or a product profile. Linear mappings define relationships between vector spaces. QFD matrices are constructed from cause-effect relationships. Thus, they represent a linear mapping from the solution space (technical requirements, or "hows" in a house of quality) into the goal space (customer needs or "whats").Findings - A solution for a QFD matrix (e.g. a set of technical requirements) is an optimum profile that best approximates the goal topics (e.g. customer needs). The traditional way of calculating solution profiles from a QFD matrix is the first step but does not yield the optimum solution. The convergence factor is the natural metric for optimization. Moreover, one can also use the cause-effect matrices to translate measurements. Thus one can compare planned goal profiles with actual outcome.Originality value - The new mathematical approach to QFD was presented at the QFD Conference in Orlando, Florida in 2003, but has not yet been published in an international journal.