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Happy’s Tech Talk #34: Producibility and Other Pseudo-metrics

As an engineer, I thrive on data, and one of my favorite forms is metrics. However, the one metric that has always challenged me is producibility. I define this as more than just passing a DRC in CAM, but the entire envelope of “simplicity of design,” “suitability for test,” and many more. Yet, producibility seemed to be different for different engineers and we had no clear way to establish and define producibility other than opinion. When I worked at HP, the company invested in a methodology called design for manufacturing and assembly using the GE/Hitachi Methodology and Dewhurst-Boothroyd software¹. Finally, I had a methodology that created a producibility score.

Metrics
Metrics are data and statistically backed measures, such as wiring demand (Wd)². These measures can be density, first pass yield (FPY)², connectivity, or in this context, producibility. These metrics are the basis for predicting and planning a printed circuit design. CAD files and drawings do not always provide the necessary data as illustrated in the Escher drawing (Figure 1) produced on a notable 3D mechanical CAD software. When used in the design and manufacturing engineering process, there are four levels of measures applied to a product:

• Metrics: Both the product and the process are measured by physical data using SPC and TQM techniques (Predictive engineering process)
• Figure of merit: Both the product and the process are scored by linear equations developed by consensus expert opinion (Expert opinion process)
• Opinion: Opinion, albeit from an expert, is applied after or concurrent with design (Manufacturing engineering inspection process)
• No Opinions: No attempt to inspect or improve the design is done during the specification, partitioning, or design stage (Over the wall process)

The critical parameter in the calculation of FPY (Figure 2) was the metric called complexity index. This is a dimensionless parameter that I call a pseudo-independent variable: It replaces a number of important independent variables that would be complicated to take individually. This variable is invented, but it follows several pseudo-independent variables that are essential for modern engineering: the dimensionless numbers.

For example, you might remember the Reynolds Number², a measure of inertia force divided by viscous force (Figure 3) used in fluid flow calculations. The Reynolds Number was first described quantitatively 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 are combined into a single dimensionless parameter. In fact, there are 154 dimensionless parameters used in engineering and nearly 304 variables where the ratios form nondimensional numbers. You might remember or work with some of these: Mach Number, Stanton, Gasthof, 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. 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, they often vary with each person. That’s 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 all³.

Metrics also establish a common language that links manufacturing to design. The producibility scores form a non-opinionated basis that allows a team approach, resulting in a quality, cost-competitive product.

The strategy in creating these measures is known as Rayleigh’s method of dimensional analysis²:

1. Identify the independent variables that are likely to affect the dependent variable.
2. If R is a variable that depends upon the independent variables R_¹, R₂, R₃, …, R_n, then the functional equation can be written as R = F(R_¹, R₂, R₃, …, R_n).
3. Express the equation as R = C R₁^a, R₂^b, R₃^c,…, Rnm, where C is the dimensionless constant and a, b, c, …, m are arbitrary exponents:  Y = d^a, v^b, ρ^c, µ^d.
4. Express each of the quantities in the equation in some basic units in which the solution is required: Pipe diameter: d (in); fluid velocity: v (in/sec); fluid density: ρ (lb/in); fluid viscosity: µ (lb-in/sec).
5. By using dimensional homogeneity, obtain a set of simultaneous equations involving the exponents a, b, c …, m.
6. Solve these equations to obtain the value of the exponents a, b, c … m. (See Table 1).
7. Substitute the values of exponents in the main equation, and form the non-dimensional parameters by grouping the variables with the exponents: dpv/µ.

The Reynolds Number can now be used as the pseudo-independent variable to produce the famous Moody diagram for friction loss in fluids flowing through pipes (Figure 5).

Example
The Reynolds Number is just one of 154 dimensionless parameters used in engineering. Figure 6 shows 77 of the 154 DPs and also highlights the Mach Number which is not velocity but the inertia force/elastic force of a moving body.

Summary

Hopefully, this Tech Talk has introduced you to some new PCB metrics and/or FOMs. It is important to understand where your organization fits into the Five Stages of Metrics:

1. Age of Anarchy (60%): Where anything goes (over-the-wall approach).
2. Age of Folklore (25%): Where wisdom is passed from one generation to another over pizza and beer (an attempt is made).
3. Age of Methodology (10%): The way DFM/A is to be engineered is documented and is actually done that way (using a figure of merit).
4. Age of Metrics (4%): Both the product and the manufacturing processes are measured in standardized ways.
5. Age of Engineering (1%): Producibility is achieved through continuous quality improvements for both design and manufacturing, much like it is in enlightened management.

References

1. Chapter 10, 24 Essential Skills for Engineers, by Happy Holden.
2. Chapter 19, 24 Essential Skills for Engineers, by Happy Holden.
3. Chapter 9, 24 Essential Skills for Engineers, by Happy Holden.

Happy Holden has worked in printed circuit technology since 1970 with Hewlett-Packard, NanYa Westwood, Merix, Foxconn, and Gentex. He is currently a contributing technical editor with I-Connect007, and the author of Automation and Advanced Procedures in PCB Fabrication, and 24 Essential Skills for Engineers. 

This column originally appeared in the October 2024 issue of PCB007 Magazine.