Revisit the art of the estimate

We live in a precise world. Costs are tallied to fractions of a cent, time is routinely measured to femtoseconds, processors are doing 64-bit (and beyond) arithmetic. It is no wonder we sometimes confuse precision with accuracy and sensibility.

But as any analog engineer knows, they are not the same. Precision refers to how finely divided the measurement range is; accuracy specifies correctness when compared to a known standard. And you can easily have one without the other. Precise measurements with a poorly instrumented test setup or ill-conceived design will help you live the maxim: “when you don’t know where you’re going, any road will get you there.”

The reason I bring this up is that too many novices—and, sad to say, more experienced engineers and scientists—don’t know this reality, or choose to ignore it. And journalists, ever eager for the appearance of scientific validity to buttress their stories, parrot numbers with laughable precision. We get meaningless data in statements such as “Americans plan to drive 4.2% more than last year” when the underlying source of the numbers (usually a quick-and-dirty telephone survey) is very suspect—or the parameter may actually be impossible to measure in any meaningful way.

The best engineers I dealt with were always able to do a quick, upfront estimate. They call it a back-of-the-envelope calculation, a SWAG (scientific wild-ass guess), or a sanity check, it doesn’t matter. The first step any designer should do before looking at the EDA or CAD software for analysis results is ask, and answer, is this: “approximately what answer should I get here?” An estimate that falls within even a coarse 25-30% range is fine and informative. Too often, this kind of estimate is a lost art—hey, we have computers and software, and don’t need to waste time doing estimates!

What the comparison between your rough assessment and the detailed analysis does is help confirm that you haven’t put some unrealistic assumptions into your model, or used an invalid approach. If the rough walkthrough with the numbers says your project’s battery will last 100 hours, when all similar designs have the battery lasting only two hours, something is wrong somewhere or you have unknowingly designed a genuine breakthrough (possible but unlikely). And if you are excited because the SPICE analysis shows a resistor of 6.3457 megohms is the optimum amplifier load, maybe you should go back and see if you should be seeing kilohm-range values, rather than crowing about answers due to their number of significant figures.

The retiring chairman of the Federal Reserve, Alan Greenspan, is fond of looking at the reams of data he sees and then doing estimates. He knows that economic data often has significant sources of error, as well as legitimate differences in how the numbers are obtained and what they represent; it’s the nature of the situation and the complexity of economics and accounting. He often says “I’d rather be roughly right than precisely wrong.”

That’s a message all of us who deal with numbers and measurements should keep in mind every day. There’s a place for high-accuracy, high-precision measurements and analysis, but first, estimate to ensure you are in the right ballpark.

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