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.