|
The Substance Behind the Equation...
Many of you know of my fondness for Dr. Richard Feynman. For those who do not recognize the name, Richard Feynman, a physicist, was best known for his contributions to the development of quantum electrodynamics. Feynman, jointly with Julian Schwinger and Sin-Itiro Tomonaga, received the Nobel Price in Physics in 1965.Much later he was in the public eye due to his participation in the technical failure assessment of the Space Shuttle Challenger's explosion in 1986. During a televised hearing, Feynman demonstrated that the material used in the shuttle's O-rings became less resilient in cold weather by compressing a sample of the material in a clamp and immersing it in ice-cold water. The commission ultimately determined that the disaster was caused by the primary O-ring not properly sealing in unusually cold weather at Cape Canaveral.
Feynman was an extremely capable mathematician, but transcended pure mathematics in a very human way. In his book, Genius: The Life and Science of Richard Feynman, James Gleick wrote, "Feynman seemed to possess a frightening ease with the substance behind the equations, like Albert Einstein at the same age, like the Soviet physicist Lev Landau-but few others."
I want to focus on the phrase "the substance behind the equation". This "substance" is a very big deal. In the measurement of things during product and process development, you will find two sets of books being kept: metrics associated with quality (typically attribute variable data) and metrics of physical law-based data (always continuous variable data). The "substance" behind the equations is what Feynman called "the character of physical law". This article is about the difference between using quality vs. physics-based metric systems. You need both to do a complete job of proving you are ready for product launch but physics MUST come before quality! Physics must come first, then you can deal with fulfilling quality objectives. You cannot run a product development project correctly if you get that backwards. Try it now yourself: "Hey everyone on the Project - lets focus on quality first and once we have used quality metrics to achieve it then let's check it against the laws of physics and chemistry to see if it all works harmoniously!" It's irrational - backwards. Here is why...
The Order of Development: First understand what makes it work - then tune performance to meet desired goals!
The reason things work is because they obey the laws of physics; quality has nothing to do with it. There are only two laws that must be obeyed to ever hope of satisfying our customers: the law of conservation of mass and the law of conservation of energy. This is THE LAW. The time it takes to develop a product must not break the speed limit imposed by following the metrics of learning progress in light of THE LAW. Physical laws are always able to be expressed by equations: some form of Y = f(Xs).
There are no immutable laws of quality
By contrast, there are no immutable laws of quality. Quality standards, tolerances and targets, are typically subjective to human preference but in some cases are objectively regulated as standards for human safety. There are no quality equations that directly link to physical law and their specific equations. Try to write an equation that physically and directly links Bernoulli's Equation of fluid flow to Defects per Unit! You can't do it! The best we can do is to write an equation, a Capability ratio called Cp = [(USL-LSL)/6(std. dev.)] that does link Specification Limits (USL-LSL) to measures of fluid flow variation (std. deviation) when the mean of fluid flow is tuned to a desired target. Now if you write a special form of Bernoulli's Equation across a boundary of interest and importance to a customer, set the equation up to allow the continuous variables within and across the equation to be run through a Monte Carlo simulator, say 1000 times, then we can calculate sample statistics of a mean and standard deviation of a flow rate.
The true character of physical law exposes itself to us by way of this conservation of energy and mass equation along with the two continuous variable-based statistical parameters (mean & std. dev.) we need to build the Capability ratio, Cp. Most Monte Carlo simulation software packages can use this information to forecast a count of defects, that is, flow rates that come out larger or smaller than the allowable range in between the specification limits. In fact, if we run the simulation 1,000,000 times we can forecast the Defects per Million Opportunities (DPMO). We must know the substance of Bernoulli's equation intimately, setting it up correctly and specifically for our design. This comes first. Then we must obtain a realistic sample of continuous variable functional data. Once we have this information we can use a form of regression called Analysis of Variance (ANOVA) to separate signal from noise. The end result is an empirical model that can be compared to our analytical model. Feynman was noted for stating "if the analytical model does not agree with the empirical model, then our analytical model was wrong!". The key thing is to underwrite the substance of the math by experimental confirmation.
If you ignore measurement of X-Y behavior and performance in light of immutable physical laws you will waste time chasing ghosts! The ghosts generated by running experiments where you accidentally or intentionally count or measure quality attribute data (Quality Ys) while purposefully changing physics-based Xs. It can even get more complicated than that! If you change what I call "little xs"; basic, contributory factors that can be varied at their lowest and simplest level of design characterization, then you can miss the more important parametric contributions made by "Big Xs" that really express and govern the application of true laws of physics that make Physics-based Ys change in very continuous and real ways.
Here are some examples of Quality Ys and Physics Y's to illustrate the difference:
Quality Ys:
Yield (% of acceptable outcomes)
Go-NoGo counts (# of items that Pass vs. # of items that Fail)
Defects per Unit (DPU - # of defects found in a completed product or assembly)
Defects per Million Opportunities to have a Defect (DPMO - typically the # of defects in a part or material in light of the opportunity of making a defect over 1 million attempts to get it in spec.)
Number of defects
Faults
Reliability (time-based failure events)
Voids
Appearance
Pass/fail
Fraction defective
% Non-Conforming
Physics-based Ys:
Force (vector)
Acceleration (vector)
Displacement (vector)
Pressure (scalar)
Velocity (vector)
Hardness (scalar)
Time (scalar)
Functions are continuous and give us deep insight into parametric relationships that can enable us to adjust performance (mean & std. dev. of the function) to meet quality objectives.
Attribute Quality characteristics are not continuous variables. They convey a picture of a step function between what is acceptable and the step down of discrete counts of what is not acceptable, as the plot below illustrates...
This picture is not nearly as useful as the continuous variable plot of the function that actually governs quality. Adjustable functions allow us to dial in performance to meet quality standards. You need both illustrations but you have to start with understanding the parametric and statistical functional behavior before you can manage quality outcomes. The "substance" of the equation that shows us how a design or process actually works is expressed in the continuous variable plot.
If we take the time and effort to set up our modeling, simulation and designed experiments in this context, we will explore the character of physical law. Then we can see if our concept and its physical instantiation, the adjustable, modular proto-type, can be controlled to meet our quality standards. A real control plan has the functional plot underwriting the integrity of the quality plot. We need this insight to define operating windows and where to set up tolerance boundaries and the best location to place the mean of our functional performance in light of its standard deviation.
In the next several articles, we will explore deeper issues regarding math modeling, simulations, proto-typing and the design of experiments to close the loop on our understanding the "substance" behind both analytical and empirical equations. Remember - obey The Law!
| 
