Lecture 04: Errors During the Measurement Process
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Gross errors are caused by mistake in using instruments or meters, calculating measurement and recording data results. The best example of these errors is a person or operator reading pressure gage 1.01N/m2 as 1.10N/m2. This may be the reason for gross errors in the reported data, and such errors may end up in the calculation of the final results, thus deviating results.
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Lecture 04: Errors During the Measurement Process
- 1. Instrumentation & Measurements Engr. Taimoor Muzaffar Gondal [email protected] Faculty of Engineering & Technology The Superior University Lahore Spring-2022 Lecture-04 4/6/2022 LECTURE 04 1 Errors During the Measurement Process
- 2. In this lecture 1 • Types of Errors in Instrumentation and Measurements 2 • Reduction of Systematic Errors 3 • Quantification of Systematic Errors 4 • Aggregation of measurement System Errors 4/6/2022 LECTURE 04 2
- 3. A. Types of Errors in Instrumentation and Measurements 4/6/2022 LECTURE 04 3 Gross Errors Blunders Measurement Errors Random Errors Systematic Error Instrumental Errors Environmental Errors Observational Errors Theoretical Errors
- 4. 1. Gross Errors Gross errors are caused by mistake in using instruments or meters, calculating measurement and recording data results. The best example of these errors is a person or operator reading pressure gage 1.01N/m2 as 1.10N/m2. This may be the reason for gross errors in the reported data, and such errors may end up in calculation of the final results, thus deviating results. 4/6/2022 LECTURE 04 4
- 5. 2. Blunders Blunders are final source of errors, and these errors are caused by faulty recording or due to a wrong value while recording a measurement or misreading a scale or forgetting a digit while reading a scale. These blunders should stick out like sore thumbs if one person checks the work of another person. It should not be comprised in the analysis of data. 4/6/2022 LECTURE 04 5
- 6. 3. Measurement Errors The measurement error is the result of the variation of a measurement of the true value. Measurement error consists of a random error and systematic error. The best example of the measurement error is, if electronic scales are loaded with 1kg standard weight and the reading is 10002 grams, then The measurement error is = (1002 grams-1000 grams) = 2 grams 4/6/2022 LECTURE 04 6
- 7. 3.1: Systematic Errors The Systematic errors that occur due to fault in the measuring device are known as systematic errors. Usually, they are called as Zero Error: a positive or negative error. These errors can be detached by correcting the measurement device. 4/6/2022 LECTURE 04 7
- 8. 3.1.1. Instrumental Errors Instrumental errors occur due to wrong construction of the measuring instruments. These errors may occur due to hysteresis or friction. These types of errors include loading effect and misuse of the instruments. In order to reduce the gross errors in measurement, different correction factors must be applied and in the extreme condition instrument must be recalibrated carefully. 4/6/2022 LECTURE 04 8
- 9. 3.1.2. Environmental Errors The environmental errors occur due to some external conditions of the instrument. External conditions mainly include pressure, temperature, humidity or due to magnetic fields. In order to reduce the environmental errors Try to maintain the humidity and temperature constant in the laboratory by making some arrangements. Ensure that there shall not be any external electrostatic or magnetic field around the instrument. 4/6/2022 LECTURE 04 9
- 10. 3.1.3. Observational Errors 4/6/2022 LECTURE 04 10 These types of errors occurs due to wrong observations or reading in the instruments particularly in case of energy meter reading. The wrong observations may be due to PARALLAX (Eye Displacement Angle). In order to reduce the PARALLAX error highly accurate meters are needed: meters provided with mirror scales.
- 11. 3.1.4. Theoretical Errors Theoretical errors are caused by simplification of the model system. For example, a theory states that the temperature of the system surrounding will not change the readings taken when it does. Then this factor will begin a source of error in measurement. 4/6/2022 LECTURE 04 11
- 12. 3.2. Random Errors Random errors are caused by the sudden change in experimental conditions and noise and tiredness in the working persons. These errors are either positive or negative. An example of the random errors is during changes in humidity, unexpected change in temperature and fluctuation in voltage. These errors may be reduced by taking the average of many readings. 4/6/2022 LECTURE 04 12
- 13. Errors in Electrical Circuits 4/6/2022 LECTURE 04 13
- 15. B. Reduction of systematic errors 4/6/2022 LECTURE 04 15 CAREFUL INSTRUMENT DESIGN METHOD OF OPPOSING INPUTS HIGH-GAIN FEEDBACK CALIBRATION MANUAL CORRECTION OF OUTPUT READING INTELLIGENT INSTRUMENTS
- 16. About Feedback System 4/6/2022 LECTURE 04 16 Open Loop System: Close Loop System:
- 17. C. Quantification of systematic errors Unfortunately, it is not always possible to quantify exact values of a systematic error, particularly if measurements are subject to unpredictable environmental conditions. The usual course of action is to assume mid-point environmental conditions and specify the maximum measurement error as +x% or –x% of the output reading to allow for the maximum expected deviation in environmental conditions away from this mid-point. Data sheets supplied by instrument manufacturers usually quantify systematic errors in this way. 4/6/2022 LECTURE 04 17
- 18. D. More on Random errors Random errors in measurements are caused by unpredictable variations in the measurement system. Therefore, random errors can largely be eliminated by calculating the average of several repeated measurements. The degree of confidence in the calculated mean/median values can be quantified by calculating the standard deviation or variance of the data 4/6/2022 LECTURE 04 18
- 19. D.1: Statistical analysis of measurements subject to random errors Mean and median values Standard deviation and variance 4/6/2022 LECTURE 04 19
- 20. D.2: Standard deviation and variance 4/6/2022 LECTURE 04 20 Gaussian distribution Standard Gaussian tables Standard error of the mean Estimation of random error in a single measurement Distribution of manufacturing tolerances Goodness of fit to a Gaussian distribution Rogue data points Special case when the number of measurements is small
- 21. More about Statistical Analysis 4/6/2022 LECTURE 04 21
- 22. D.3: Aggregation of errors from separate measurement system components 4/6/2022 LECTURE 04 22 Error in a sum Error in a difference Error in a product Error in a quotient
- 23. End of Lecture-04 4/6/2022 LECTURE 04 23