Chapter 3 Error

7/27/2019 Chapter 3 Error

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Week 2: chapter three

assessing and presenting experimental

data

Dr. Belal Gharaibeh

6/3/2011


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Ask your self, how good are the data?

Determine the quality of the data measured

before using it and making engineering decision

We can compare if the data are good by

comparing to theory derived results. Theory is also derived for a physical system and

it is also like data but we call it a model

(Newtons law)

Measurement should NOT be compared to a

theory to assess its quality


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We are trying to measure actual value of physical quantity beingmeasured and that is our Standard

The error is defined as the difference between the measured andtrue physical value of the quantity, we should ask, what is the errorof the data?

True value is something we can never know exactly because wehave to measure it as the first step and process of measurementwill have errors

We can estimate the possible amount of error, example: 95% ofreading from one flowmeter will have an error of less than 1 L/s, sowe say with 95% certainty (19 times of 20) that the meter has anerror of 1 L/s or less.

The reading has accuracy of 1 L/s at odds of 19 to 1. And you canfind a theory within this accuracy


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Types of error

Error = = xm-xtrue We want to minimize error in the experiment design

step, but we also need to estimate the boundon ,

This bound is in the form of:

Where u is the uncertainty estimated at odds of n:1only one measurement in n will have an error whose

magnitude is greater than u


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Specific cause of error varies from experiment to experiment

Or within the same experiment

Two general classes of error , see figures

Bias error: also called systematic errors are those

happening the same way each time ameasurement is made, a scale reads 5% high, then

every time you measure with it the reading will be

+5% higher than true value


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Precision error: also called random error are different foreach successive measurement but have an average valueof zero, for example: errors from mechanical friction orvibration may cause the reading to fluctuate about thetrue value

If enough measurements are taken then the precisionerror will be clear

Readings will cluster about the true value; therefore wecan use statistical analysis to estimate the size of the error.

Bias errors cannot be treated using statistical analysisbecause they are fixed and do not show a distribution

Bias errors are estimated by comparison of the instrumentto a more accurate standard, or by knowledge of how theinstrument was calibrated


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Classification of errors

Bias or systematic errors :

Calibration errors (most common) see figure

the most common bias errors is from calibration, calibration is theadjusting the equipment to read the measured values in the right way

zero offset error: causes all readings to be offset by a constant amount (xoffset)

scale errors: change in the slope of the output relative to the input , causes allreadings to change by a fixed percentage , see figure

Certain recurring human errors: when a human reads high values every time Certain errors caused by defective equipment: equipment sometimes have

built-in errors resulting from incorrect design, manufacturing andmaintenance. These errors are constant and can be solved by calibration ifthey dont change with time.

Loading error: the effect of the measurement procedure on the system beingtested. The measuring process changes the characteristics of both source of

the measured quantity and the measuring system. For example: the soundpressure level sensed by a microphone is not the same level if the microphoneis not in the room we want to measure the sound level for

Limitations of system resolution


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Classification of errors (continue)

Precision or random error Certain human errors: human is inconsistent in taking the

reading

Errors caused by disturbances to the equipment:

Errors caused by fluctuating experimental conditions:usually coming from outside interference like vibration ortemperature

Errors derived from not measuring the system sensitivity:the sensitivity comes from the design or the

manufacturing process of the instrument, example:instrument designed to measure constant speed will notmeasure any changes in speed you should not use it, or inthe process of making light bulbs not every bulb will be thesame exactly. Such errors are NOT a measurement errorsbut they look like precision errors from measurements and

can be estimated in similar statistical methods


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Classification of errors (continue)

Illegitimate errors, errors before or after

making measurements

Mistakes during an experiment: human is not

trained to use the instrument

Calculation errors after an experiment


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Classification of errors (continue) Errors that are sometimes bias and sometimes precision errors

Instrument backlash, friction, and hysteresis (path dependence,figure): example is the friction of a scale indicator of an instrument.The reading is low when the measured variable is increasing andreading low when the measured variable is decreasing. figure

Errors from calibration drift and variation in test or environmentalconditions: happens when the response is varying with time and

usually from the sensitivity to temperature and humidity this will bebias error

If the test time is long, errors will fluctuate during that time causingdifferent calibration errors for each time you make long tests. This isprecision error Errors from variations in procedure or definition among experiments:

when the experiment is done with more than one instrument or bydifferent people. In this case each time the test is made it has differentbias which means you have precision error from all the tests


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Terms used in rating instrument performance

Accuracy: the difference between the measured and

true values. The manufacturer will specify a maximumerror as the accuracy, what about the odds?

Precision: the difference between the instrumentsdata values during repeated measurements of thesame quantity.

Resolution: the smallest increment or change in themeasured value that can be determined from theinstrument readout scale.

Sensitivity: the change of an instrument output per

unit change in the measured quantity. Reading error: errors when reading a number from the

display scale. The display screen might round a numberor truncate numbers

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