General Engineering Introduction/Error Analysis/Measurement Error

Most projects, most ideas don't work. Some don't work for economic, marketing or political reasons. Engineers are more concerned with physical failures. Science is used to figure out where physical failures are. This involves detective work.

The best engineers don't start with the expense of measuring the most accurate way possible. Technicians typically have the better equipment. The best engineers know how to determine the sources of error. This is very different than troubleshooting an existing, working system.

The goal of this section is to introduce measurement error and show why writing three bits of information down rather than one is proper engineering/scientific measurement procedure:

• the number
• the error
• the units

Error Sources

Error exists. Everywhere. It can not be avoided. Can you see this error? Can you identify the types? Do you have a strategy for dealing with each type? Can you figure out which source contributes the most to the error in the final result? Do you attempt to wrestle with these questions?

Probable Error

number of digits displayed

Manufacturers of anything know the probable error. Otherwise they could not ship it. Often the error is documented with the product.

• A monitor manufacturer knows the probable error of the dimensions and sends this to the engineer designing the shipping box.
• A resistor manufacturer knows the probable error of the resistor and puts a colored band on it indicating this. More precise resistors cost more.
• A ruler manufacturer knows the probable error in the length of the ruler, but this is much less than the probable systematic error made when using it.

Look through the documentation and the art work on the physical measurement device for error information from the manufacturer.

blow up of the most significant digit

Look at the left picture. There are three displays of the same information. The top display has 6 digits rather than 4. How are the displays below rounding?

If the instrument internally is measuring more accurately, why not display the information? Look closely at the least significant (smallest) digit in the top display. It appears to be flickering between flickering between 5 and 6. It is probably not broken. What makes you think that it is?

Here are some reasons why an instrument manufacturer would only display 4 digits:

• displaying more resolution than the instrument's systematic error is an ethical violation ...it suggests the instrument is more accurate than it really is
• displaying a number that changes constantly does not inspire confidence
• more than 4 digits intimidates people

Systematic Error

meter movement with mirror for more accurate measurement

Any measurement device can be used inappropriately. A math error, an error of when, where or what can lead to systematic errors. The fog associated with frustration is often systematic error. A working system can appear broken because it is hidden behind a combination of fogging thinking and inconsistent use of measuring equipment. Someone else, with hardly any understanding can ask a single question that causes the systematic error to disappear.

Systematic error can disappear suddenly without apparent explanation. This is not time to rejoice, but for more puzzlement. What changed? Something changed. It is now working. Systematic error can be associated with a person. Unconscious feelings, expectations, and habits can cause a person to create systematic errors. Battle this by starting over from scratch. Recreate the problem. Now repeat what you think happened to see if it starts working again.

Most equipment has quirks of detail that need to be appreciated. For example, there is a mirror behind the needle of this meter movement. The designers assumption is that you will move your head so that the needle image in the mirror is directly underneath the needle.

Random Error

Random error can not be fixed. A better word is "uncertainty." Not only has the quantum uncertainty that underlies nature been experimentally verified, it has been proven both mathematically and experimentally that we can not know more.

The problem with uncertainty is that it grows as more complex systems interact. The uncertainty or error can overwhelm the predictability of physics and chemistry. So what adds order? What makes weather if we can not predict it? What reality does biology sit on top of? Look up

• emergence
• chaos theory
• Butterfly effect
• Holographic principle or non-locality
• conjugate variables (when classic independent variables become dependent)

An introduction to engineering class typically doesn't involve the above concepts. Random error is assumed because it is a first best guess, a maximum worst case possibility, a starting point, an easy place from which to improve error analysis.

Repeated Measurement Error Reduction

Repeating the same mistake (or systematic error) over and over again is silly. Suppose someone is measuring length but is moving their body and head into a different random position each time (very unlikely to be random). Repeatedly measuring length over and over again and using statistics may reduce the error. But this is highly unlikely.

Suppose a number of different aliens (freshmen) measure length with a number of different instruments (actually same instrument used differently). (Pass out meter sticks and ask freshman to measure the width of a desk .. write down their answers and then read them out). Doing statistics on all their measurements may improve the measurement, but only if the distribution is truly random.

Suppose the systematic measuring mistakes of the freshman are studied over 10 years. Suppose the possible errors are categorized and the frequency of each is determined with high accuracy. Are there other calculus based, statistical techniques for reducing the error of a single freshman's measurement of length? Yes. Once more information about an error is well known, there are techniques to reduce the error of a single measurement. But this is beyond the scope of this class. The important point is that most error is not random. We just assume it is random as a worst case.

When to Assume Random Error

Assume random error when the fog around failure is unknown. For instance, the chemistry experiment yields different results every time it is repeated. Perhaps one or perhaps 10 systematic mistakes are being made. The random assumption is probably not true, but assuming random error as a first approximation can determine if a second experiment was better or worse.

The objective of random error assumptions is not to discover the source of systematic error, but to find a starting point to begin searching for systematic errors. The goal is to build confidence and figure out the next step and by estimating error.

Leave it to NIST to identify the truly random error and more accurate decimal places. Use Random Error at the beginning of the project because of human frailty and to quickly compute maximum error. Expect scientists to use Random Error to account for the uncertainty of nature weirdness at the end of the project.

Instrument Error

An introduction to engineering course is an introduction to the school's tools, safety protocols and stocked materials. Part of this process is learning how to use the tools appropriately. Unlike a technologists or technicians, engineers do not have classes in tools. This helps engineers use tools in a creative fashion. The goal below is not to turn this into a tool course, but to describe how to accurately measure error with them.

Most instruments are to be read with a plus and minus reading. They are not to be read over and over again as if the error is random.

Tolerance

Tolerance is space built into the design between parts. There are standards for tolerance specification and assumptions if none are mentioned. They are used by engineers to communicate technical detail to those machining or building the parts.

Allowance

Allowance is another example of how an engineer communicates to those making parts. Allowance describes the "extra" to be left in for a specific purpose either during assembly or later during the part making process.

Calibration

Certificate of Calibration and traceability back to a Hydrometer Standard

The best measuring tools will come with a certificate, a piece of paper certifying Calibration. Some will come with a sticker, some a notebook. Some never need their calibration checked in the future. Some need to be checked every year or every 6 months like an elevator. Every measurement device has it's own standards that describe how to calibrate it.

Checking calibration can be a process that is done by certified technicians in-house or may need to be shipped somewhere. The logistics of calibration can double the equipment cost and significantly delay a project if not considered beforehand.

Cheap measuring tools can come with no certificate. A $3 digital volt, current resistance meter is not going to have the same certifications as a $1000 meter. Often the material cost is very similar and the performance of the $3 device is perfect. The engineer is better off investing in the $3 device at the beginning of a project when using it the first time. Technicians and Technologists will be taught properly how to use and care for the $1000 version.

Calipers

inside calipers, used to measure inside diameters, then be removed to be measured with rule

Calipers are used where it is hard to fit a ruler. Calipers capture the measurement physically. They are stretched or compressed to measure a hard to reach place. Friction holds them in place. They are then transported to an accurate device for measuring length.

Verniers

vernier measurement

Verniers have a moving piece and fixed piece. The moving piece is moved into position and then screwed down tight. Then the vernier can be lifted off the object being measured and typically three decimal places can be read. O on the moving piece will point to the first, most significant digit. One of the lines on the moving piece will line up with a line on the fixed piece. The line on the fixed piece will give the other two digits.

A vernier works because the gradations on the moving piece are 0.9 the distance between gradations on the fixed piece.

Scales

The physical Engineer's scale has been replaced with virtual 3D software and CAD where rulers were used heavily. Today many engineers draw in 3D before dimensioning. Over dimensioning and under dimensioning are prevented by the software through error messages. Scales can be instantly changed by zooming.

However the error issue doesn't go away. The virtual rulers accumulate error and display 1.98 when they should display 2. Digital error exists within the digital ruler.

There is a certain sense of proportion that changes with scale. There is a distortion associated with any type of 3D display on paper or flat screen. For this reason architects and technicians will still invest time in these physical rulers. Most engineers do not unless the project demands it.

The best practice for measuring anything is to move one's head and body to the middle, the minimum position and the maximum position. Record all three. This is true of almost any physical world measurement involving the human eye.

There are tricks to get more accurate measurements out of almost all instruments. The human eye can be remarkably accurate. Students that have never been challenged to be accurate can create measurements very different from others. It is important as an engineer to be aware of this and to trust the technologists and technicians that learn these tricks.

Log Scales

slide ruler

A slide ruler works on the similar principal as the vernier. The line spaces are logarithmic on both the fixed and moving pieces. Looking up a number on the slide ruler is essentially looking up it's logarithm. Since multiplication turns into addition with logarithms, then the total length of the two pieces is the answer.

Slide rulers may be dead, but log scales still exist.

There was a time when an engineers tool kit contained many items similar to a slide ruler that aided measurement and calculation. Today these are puzzles and useful only when the starting point is in the physical world with an existing object to be reverse engineered.

Meter Movements

inner workings of meter movement

Meter Movements can be pegged .. that is the needle forced into one side of the meter. This will ruin the meter. The needle will sort of stick to one side. Prevent this by always selecting the largest scale and shift gradually down to smaller scales.

Some meter movements have to be zeroed. The exact process for an ohm meter is to touch the red and black wires, then twist the zero knob until the needle is on 0 ohms.

Some meters are powered when measuring some things, and unpowered when measuring others. Make sure the meter is turned off.

Make sure one's head is directly over the meter, move it left and right to get the max and min values or the plus minus error.

Digital Readouts

Digital measurements are all powered. Some meters need to warm up a crystal to a specific temperature. This can take 45 minutes. Using the meter too early can result in systematic error.

Assume digital meters have an accuracy of plus minus half of the least significant decimal place displayed. Imagine there is an undisplayed digit flickering.