Chapter Three: Assessing and Presenting Experimental Data Dr. Belal Gharaibeh 27/9/2011 IE-JU Fall semester 2011/2012
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 (Newton’s law) – Measurement should NOT be compared to a theory to assess its quality
• We are trying to measure “actual value” of physical quantity being measured and that is our Standard • The error is defined as the difference between the measured and true physical value of the quantity, we should ask, “what is the error of the data?” • True value is something we can never know exactly because we have to measure it as the first step and process of measurement will have errors • We can estimate the possible amount of error, example: 95% of readings from one flow-meter will have an error of less than 1 L/s, so we say with 95% certainty (19 times of 20) that the meter has an error of 1 L/s or less. • The reading has accuracy of 1 L/s at odds of 19 to 1. And you can find a theory within this accuracy
Types of error • Error = ε = x m -x true • We want to minimize error in the experiment design step, but we also need to estimate the bound on ε , • This bound is in the form of: • −𝑣 ≤ 𝜁 ≤ + 𝑣 ( 𝑜 : 1) • Where ( u) is the uncertainty estimated at odds of n:1 only one measurement in ( n) will have an error whose magnitude is greater than (u) • 𝑦 𝑛 −𝑣 ≤ 𝑦 𝑢𝑠𝑣𝑓 ≤ + 𝑣 + 𝑦 𝑛 𝑜 :1
Specific causes of error • varies from experiment to experiment • Or within the same experiment • Two general classes of error , see figures 1. Bias error: also called systematic errors are those happening the same way each time a measurement is made, a scale reads 5% higher than actual, then every time you measure weight with this device the reading will be +5% higher than the true value – Bias errors cannot be treated using statistical analysis because they are fixed and do not show a distribution – Bias errors are estimated by comparison of the instrument to a more accurate standard, or by knowledge of how the instrument was calibrated
2. Precision error: also called random error are different for each successive measurement but have an average value of zero, for example: errors from mechanical friction or vibration may cause the reading to fluctuate about the true value – If enough measurements are taken then the precision error will be clear – Readings will cluster about the true value; therefore we can use statistical analysis to estimate the size of the error.
Classification of errors 1. Bias or systematic errors : – Calibration errors (most common) see figure • the most common bias errors is from calibration, calibration is adjusting the equipment to read the measured values in the right way – zero offset error: causes all readings to be offset by a constant amount (x offset ) – scale errors: change in the slope of the output relative to the input , causes all readings 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 and maintenance. These errors are constant and can be solved by calibration if they don’t change with time. – Loading error: the effect of the measurement procedure on the system being tested. The measuring process changes the characteristics of both source of the measured quantity and the measuring system. For example: the sound pressure level sensed by a microphone is not the same level if the microphone is not in the room we want to measure the sound level for – Limitations of system resolution
Classification of errors (continue) 2. 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 or temperature – 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 not measure any changes in speed and you should not use it, or in the process of making light bulbs not every bulb will be the same exactly. Such errors are NOT a measurement errors but they look like precision errors from measurements and can be estimated in similar statistical methods
Classification of errors (continue) 3. 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
Classification of errors (continue) 4. 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 and reading low when the measured variable is decreasing. figure – Errors from calibration drift and variation in test or environmental conditions: happens when the response is varying with time and usually from the sensitivity to temperature and humidity this will be bias error
Continue: mixed errors: bias and precision – If the test time is long, errors will fluctuate during that time causing different calibration errors for each time you make long tests. This is precision error – Errors from variations in procedure or definition among experiments: when the experiment is done with more than one instrument or by different people. In this case each time the test is made it has different bias which means you have precision error from all the tests
Terms used in rating instrument performance • Accuracy: the difference between the measured and true values. The manufacturer will specify a maximum error as the accuracy, what about the odds? • Precision: the difference between the instrument’s data values during repeated measurements of the same quantity. • Resolution: the smallest increment or change in the measured value that can be determined from the instrument 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 number or truncate numbers
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