Getting From A to B: Assessing Error Range From Input to Result

As a general rule, a mechanical measure cannot be written without a precision. When a study does not contain an error range estimation or analysis, and when mechanical design engineers don’t pay attention to such details, it’s a warning sign that risks are probably not well understood or handled.

In our practice, we are more aware than anyone of how small details can have a large impact on results, how quantities go on accumulating and the painful fact that we will never reach the perfect solution but rather converge towards an optimal one.

We know we are at a point A and we want to reach point B through a path AB. As engineers, we are aware that we will never reach B, but rather approach it. We are also aware that we are not actually at A, but within the hazy surroundings of A. Therefore, to assess our situation accurately, for any measures or quantities A and B, we say: “We are around A within the values contained in area A and we will go along the path AB to the surroundings of B.”


Now that we’ve cleared the importance of assessing the range of the values, and therefore the error range, the next dilemma is the quantification of the gap.

What precision to choose for the hazy surroundings of the value A?

What about complex operations of the path to B, particularly when they involve random or black box operations?

What is the range of precision with which to assess B?

Assessing B
In our metaphor, B is the end result of one input value A being carried through path AB. It’s also the first quantity we will assess. Most practices start with the requirement to define the required input data.

Let’s suppose we have to have to produce some beams intended for steel construction. The precision of the metalworking machinery is 0.01mm/0.0005inches. There is therefore no need to input a requirement of 10-4mm precision. But, if the beams are intended for the aeronautics industry, the machinery used will be much more precise, possibly up to 10-6 mm precision. Therefore, the precision requirement should be provided accordingly.

In this example, two major factors are taken into account:

  • The precision and accuracy of the manufacturing machines.
  • The industry we’re working in.

If we know the precision of the manufacturing machines, we basically saved ourselves the hassle of computing many overly accurate quantities. Therefore, we can easily zero in our precision and narrow our error range at point B. The outcome’s range is uncovered for us.

Assess A
When it comes to A, the two factors to consider are:

  • The measuring tool.
  • The type of data.

After all, there is no use to write an input value we can’t check on consistent grounds with a calibrated mechanism. We can’t measure 143.2433 °C as input data if we don’t have a measuring device that can provide this level of precision. If we can’t verify a measurement consistently and report the value with the practical precision, we take the value along with its accuracy and precision.

The type of data refers to its nature: a temperature, a length, an angle, an acidity, etc. For every data type, a set of rules should be taken into account. For example, with acidity, the indicators being specified might depend greatly on environmental conditions, so such conditions should be listed as well.

Assess path AB
Assessing the path from A to B can prove delicate since it might contain functions with closed off behavior or formulas that can’t be assessed except by other formulas. Luckily, the path can be reviewed itself. We can get an estimated view of how the path from A to B will look if we have some specific points to plug in.

Here is a simple presentation of what the path could look like:


While theoretically we can segment and analyze every dent and curve on our path, in reality we are constrained by time. Therefore, smoothing of our path has to be performed in a clever way. There is no quick fix solution and the mechanical design engineer has to be flexible and logically asses the various different scenarios:

Scenario 1: You start walking the road with a rough error range (perhaps the one resulting from the maxima and minima of the curve), then narrow it as you apprach B.

Scenario 2: You take an error range and lead the way with it until you reach B. Then, you iteratively narrow the error range and walk the path all over again.

Each way has its pros and cons and there is no best way that will work in every case. Each engineer must take into account the standard practices of his project, his industry requirements, and the resources available and arrive at an acceptable solution.



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