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OCTOBER 2024 I PCB007 MAGAZINE 93 used in engineering and nearly 304 variables where the ratios form nondimensional num- bers. 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 noth- ing. e problem with opinions is that they are difficult to defend and explain, and when used in conjunction with producibility, they oen vary with each person. at's why the figure of merit (FOM) process is so popular. For a small amount of work by experts, it produces a scor- ing procedure that can be used and understood by all 3 . Metrics also establish a common language that links manufacturing to design. e pro- ducibility scores form a non-opinionated basis that allows a team approach, resulting in a quality, cost-competitive product. e strategy in creating these measures is known as Rayleigh's method of dimensional analysis 2 : 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 , R 2 , R 3 , …, R n , then the functional equation can be writ- ten as R = F (R 1 , R 2 , R 3 , …, R n ). 3. Express the equation as R = C R 1 a , R 2 b , R 3 c ,…, R n m , 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 equa- tion in some basic units in which the solu- tion 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). Figure 3: Example of the Reynolds Number for fluid flow in pipes. Figure 4: Critical variable for determining the flow of fluids in pipes using the Rayleigh method for dimensional analysis. Table 1: Solving the simultaneous equations from step 5