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Improved math

One purpose of a QFD study is to help the product development team focus on the critical or vital few rather than the trivial many design factors (Pareto principle). Few organizations have the time, budget, and resources to do all the product development activities they would like, especially in today’s fast-paced technology and lean environments. QFD recommends first focusing on the voice of the business (i and ii above) since a healthy, ongoing concern is requisite to long-term value to society, shareholders, customers, employees, and the environment. Second is focusing on the voice of the customer to understand what they are willing to buy or what QFD calls a minimally merchandisable product (MMP).

Accurate math improves confidence that the focused few are in fact critical and not trivial in order to avoid Walter Shewhart’s two types of errors – mistaking signal for noise and risk wasting resources, or mistaking noise for signal and risk missing something important. When QFD was being formulated in 1960s and 1970s Japan, handheld calculators and personal computers were uncommon and so the prioritization calculations were simplified to ordinal integer number scales such as 1-5. While these scales indicate the relative order of a set of items, they lack equality of interval or the distance between items and so appropriate mathematical operations are limited to median and mode. We know that a rating of 4 is better than a rating of 2, but is it twice as good? Maybe yes, maybe no. Ordinal scale numbers do not contain sufficient information to make that determination. Thus, mean or average is not appropriate; nor is addition, subtraction, multiplication, or division on ordinal scale values.

Personal computer availability in the 1980s simplified the use of more complex multicriteria decision making algorithms such as the analytic hierarchy process (AHP) developed by Thomas Saaty and introduced to the QFD world by Satoshi Nakui, a graduate student of Yoji Akao. Nakui first applied to AHP to improving customer needs prioritization because its forced pairwise comparison of needs and eigenvector based calculation of priorities better modeled human judgment than forced ranking or rating with ordinal scores, plus the resulting ratio-scale values were more appropriate for the other math operations in QFD matrices. The ISO 16355 standard details the steps for using AHP to prioritize customer needs as well as its expansion to other prioritizations and calculations in QFD for strategy, project selection, customer segments, quality planning, design planning, concept selection, FMEA, and elsewhere.

The customer needs from the wishbone diagram in Figure 1have been arranged in a pairwise AHP grid with the needs entered in both the rows and columns as shown in Table 1. Customers are asked to compare each need to another using a verbal scale and an associated score is entered into the grid. The verbal scale and score are:

• row and column are equally important to improve (1);
• row is moderately more important to improve than column (3);
• row is strongly more important to improve than column (5);
• row is very strongly more important to improve than column (7);
• row is extremely strongly more important to improve than column (9).

When the column is more important to improve than the row, the reciprocal fraction is entered in the appropriate cell. Notice that the diagonal where each need is compared to itself is scored as equal, and that all values below and to the left of the diagonal are reciprocals of the values above and to the right of the diagonal. These are shaded in the table and actually do not require a customer response as they can be mathematically determined. Each column is then summed and normalized, and then averaged to approximate the row priority of each need in ratio scale percentages that sum to 100%.

Effect-to-cause diagram

The customer needs priorities indicate how much value the customer puts on improving them over their current state, and indirectly how much they are willing to pay for a new product that solves their need. New product development teams can now focus their constrained resources on what matters most to the customer. Table 1 indicates that 51.6% of customer value can be improved just by helping the customer feel warm. This is about 10X more important than feel distracted and 5X more important than something to do while waiting, so improving these two needs are probably not worth any more effort than what currently exists, such as providing free Wi-Fi. Using Akao’s design approach, an effect-to-cause wishbone diagram is constructed to identify the critical-to-quality functional requirements of product design, then its systems, sub-systems, components, and raw materials, then the equipment, and finally properly training the staff to produce it.

The details to develop, produce, and commercialize a new product or service can be extensive. For many projects, existing systems, sub-systems, components, or materials may be sufficient as-is to satisfy customer needs with low priority to improve. To satisfy customer needs with a high priority to improve, only a small number of highly correlated design elements may truly call for an upgrade or innovation to beat the competition. The effect-to-cause wishbone diagram starts detailing the design and downstream details associated with only the highest priority customer needs, according to the AHP-derived ratio scale weights shown in Table 1.

Figure 2 diagrams the highest priority customer need (effect) “I want to feel warm” with causal factors related to functional requirements, materials, equipment, and staff. Causal factors interrelate as well. For example, to help the customer feel warm, the café can offer a single chocolate covered coffee bean at the time of ordering to give the customer quick metabolism boost, VR1 heat receptors on the tongue can be activated by capsaicin, the active ingredient in chili pepper, so a powdered chili flavoring in a self-serve shaker with 1.5mm diameter holes will assure customers do not over-apply. Beverage cups are served without placing the lids or sleeves so customers can momentarily perceive the heat and steam on their face and hands as they apply these themselves. Finally, the seating area can be divided into two temperature zones with appropriate HVAC and signage. 3-5 effect-to-cause wishbone diagrams can be assembled in a maximum value table as detailed in ISO 16355-5.

For more complex projects or for teams with unlimited resources, more comprehensive matrices or “houses” which accommodate hundreds of customer needs may be necessary, as detailed in ISO 16355-5 and ISO/TR 16355-8. Since these charts are time-consuming, it is recommended to get a head start with the maximum value table as soon as customer needs are prioritized and the top 3-5 customer needs identified. By definition, all the items in the maximum value table will be the top priority items on each comprehensive QFD house, so there is no wasted effort.

ISO 16355 series standards detail all these voices with supporting guidance, case studies, and supporting articles published at QFD and other symposia. Visit www.QFDI.org for more information.