Reading time ( words)

Metrics are data and statistically backed measures. It is always expedient to base decisions on data and metrics, for example, in PCB design^{[1]}. These measures can be density, first-pass yield^{[2]} connectivity or in this context, *producibility*^{[3]}. These measures are the basis for predicting and planning a printed circuit design. But what if a metric doesn’t exist? Then you can create the next best measure, the *Figure of Merit*.

**The Figure of Merit**

When used in the design, or any process, there are four categories of measures applied to a product:

**Metrics:**Both the product and the process are measured by physical data using SPC and TQM techniques. (The Predictive Engineering Process)**Figure of Merit (FOM)**Both the product and the process are scored by linear equations developed by consensus expert opinion. (The Expert Opinion Process)*:***Opinion:**Opinion, albeit from an expert, is applied after or concurrent with design. (The Manufacturing Engineering Inspection Process)**No Opinions:**No attempt to inspect or improve the design/process is done during the specification, partitioning, or design stage. (The Over The Wall Process)

The critical parameter in the calculation of first pass yield (FPY) is the Figure of Merit—the *Complexity Index*. This is a dimensionless parameter that is what I call a pseudo-independent variable—it replaces a number of important independent variables that would be complicated if taken individually. This variable is invented, but it follows after a number of pseudo-independent variables that are essential for modern engineering, such as the *dimensionless numbers* (to be discussed in a future column near the end of the year). An example that you might remember is the Reynolds number (a measure of inertia force divided by viscous force) used in fluid flow calculations. The Reynolds number was first described quantitatively by Reynolds in 1883. Reynolds found that fluid velocity (l/t), fluid density (m/l), fluid viscosity (ml/t) and pipe diameter (l) determined the nature of pipe flow. The four variables, combined into a single dimensionless parameter. In fact, there are 154 dimensionless parameters used in engineering and nearly 304 variables whose ratios form non-dimensional numbers. Many of you might remember or work with some of these: Mach number, Stanton, Grashof, Euler, Prandtl or Knudsen. With this large body of work, there was no reason why I could not create the *Complexity Index* to represent all the critical variables in PCB fabrication.

It is always preferred to have metrics when discussing producibility. But if metrics are not available, then opinions are better than nothing. The problem with opinions is that they are difficult to defend and explain and when used in conjunction with producibility and many times they vary with each person. Attempts to remedy this problem by placing experienced manufacturing engineers in the design team have somewhat useful effects but there lies the problem that experienced manufacturing engineers take many years to educate and are needed on the factory floor. Design teams can be populated with college graduates! There just aren’t enough experienced manufacturing engineers to go around. That is why the *Figure of Merit* (FOM) process is so popular. For a small amount of work by experts it produces a scoring procedure that can be used and understood by all. With a FoM, a new college graduate in manufacturing engineering can assume the role of a much more experienced manufacturing engineer.

Metrics also establish a common language that links manufacturing to design. The "producibility scores" form a non-opinionated basis that allows a team approach that results in a quality, cost competitive product. This approach will be used to establish the design for manufacturing & assembly (DFM/A) in my next column.

The strategy in applying these measures is shown in Figure 1. The analysis process is unique to every individual and company, but certain conditions have to be met and considered if the product is going to be successful. If the score meets producibility requirements then select this approach, if not, then evaluate other opportunities and repeat the process.

**Figure 1: The Figure of Merit creation process.**

**Creating a Figure Of Merit**

Metrics are the preferred measures for design planning, but their availability for predicting producibility are limited today. Metrics also can take many months to develop and the amount of experimentation may make them costly. The measure that is much more cost effective and quicker to develop is the Figure of Merit. The Figure of Merit is the result of one or two days’ work by a group of design and manufacturing experts. The process is a nine-step procedure as follows:

- Define new measure (FOM)
- Determine why selected
- Survey customers for needs and expectations
- Brainstorm factors
- Sort ideas into groups
- Create group header definitions
- Prioritize groups
- Construct factor weighting value tables
- Create linear model for FOM

This procedure uses classical TQM techniques to brainstorm, rank and formulate an equation that will score producibility, assembly-ability or any other measure that can be used to do design planning. The two factors used in the producibility score are made up of 1) coefficient (C_{N}) and 2) factor weighting (FW_{N}).

**1. Define the new measure**

Define or identify the new measure to be developed. What property of a product would gain you the most competitive advantage? Manufacturability, DfM, Reparability, Serviceability, Testability, Reliability, Low Cost or Rapid Time-to-Market.

**2. Determine why selected**

Ensure that there is relevance to improved performance and communication if this FOM is developed. Are they part of this team? How does the new FOM improve the product?

**3. Survey customers for needs and expectations**

Who are the intended users of this FOM? Identify their needs and expectations. Collect data by surveys, interviews, or brainstorming of contributing characteristics or variables.

**4. Brainstorm factors**

Collect a team of experts that have a vested ownership of this new FOM. Invest in a facilitator to keep the activities rolling and on schedule. Giving everyone plenty of cards or Post-its, go around the team and collect ideas of what is important for this new Measure of FOM. Allow plenty of time. If the ideas stop coming, take a break and resume. Have the facilitator push for one more idea. There are no discussions or arguments during brainstorming—just ideas. Randomly lay out the cards so that all the team members can see them. Take as much room as it needs.