Characteristics of instruments
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1 Characteristics of instruments Accuracy Accuracy is a property of a complete measurement rather than a single element. Accuracy is quantified using measurement error: E = measured value true value = system output system input 1 AMEM 11 Spring 008 Dr. Sotiris L. Omirou. 1 Accuracy and Precision Accuracy: is the closeness of a measurement (or a set of observations) to the true value Higher the accuracy, lower the error Precision: is the closeness of multiple observations or repeatability of a measurement Refers to how close a set of measurement are to each other AMEM 11 Spring 008 Dr. Sotiris L. Omirou. 1
2 Accuracy versus Precision (shooting at a target) Not accurate or Precise Precise but NOT accurate Accurate and NOT Precise Accurate AND Precise 3 AMEM 11 Spring 008 Dr. Sotiris L. Omirou. 3 Percentage error The error of measuring system is expressed as a percentage of the measuring range of the equipment percentage error = indicated value true value x 100% scale value 4 AMEM 11 Spring 008 Dr. Sotiris L. Omirou. 4
3 Exercise 4 A C thermometer is found to have a constant error of 0. 0 C. Calculate the percentage error at readings of (a) 10 0 C (b) 50 0 C (c) C 5 AMEM 11 Spring 008 Dr. Sotiris L. Omirou. 5 Exercise 4 (Solution) PE 1 = 0. x 100 = % 10 PE = 0. x 100 = 0.4 % 50 PE 3 = 0. x 100 = 0. % AMEM 11 Spring 008 Dr. Sotiris L. Omirou. 6 3
4 Exercise 3 A 0 to 10 bar pressure gauge was found to have an error of ± bar when calibrated by the manufacturer Calculate (a) the percentage error of the gauge (b) the possible error for a 5 bar reading 7 AMEM 11 Spring 008 Dr. Sotiris L. Omirou. 7 Possible and Probable Errors Ex: A measuring system with 3 elements has maximum possible errors ±a%, ± b%, ± c% Maximum Possible Error = ±( a + b + c ) Probable Error = ± a + b + c 8 AMEM 11 Spring 008 Dr. Sotiris L. Omirou. 8 4
5 Exercise 5 A general measuring system has the following errors: - transducer ± % - signal conditioner ± 3% - recorder ± 4% Calculate - the maximum possible error - the probable error 9 AMEM 11 Spring 008 Dr. Sotiris L. Omirou. 9 Exercise 5 (Solution) Maximum possible error = ± ( )% = ± 9 % Probable error = ± ( ) = ± 5.4 % 10 AMEM 11 Spring 008 Dr. Sotiris L. Omirou. 10 5
6 Exercise 6 A vibration measuring system involves the use of a piezoelectric transducer, a charge amplifier and a recorder. If the maximum errors are - transducer ± 0.5% - amplifier ± 1% - recorder ± 1.5% Calculate - the maximum possible error - the probable error 11 AMEM 11 Spring 008 Dr. Sotiris L. Omirou. 11 Exercise 6 (Solution) Maximum possible error = ± ( )% = ± 3 % Probable error = ± ( ) = ± 1.87 % 1 AMEM 11 Spring 008 Dr. Sotiris L. Omirou. 1 6
7 Types of Instrument Errors Hysteresis Error Linearity Error Repeatability Error Reproducibility Error 13 AMEM 11 Spring 008 Dr. Sotiris L. Omirou. 13 Hysteresis Error Many measuring systems have the undesirable characteristic of giving a different value when the input is increasing than when it is decreasing. This is called hysteresis. Hysteresis may be the result of mechanical friction, magnetic effects, elastic deformation, or thermal effects. 14 AMEM 11 Spring 008 Dr. Sotiris L. Omirou. 14 7
8 Linearity Error Many types of measuring systems have linear input/output behavior, at least within a narrow range of inputs. The measuring systems thus follow an input/output relation like y L = a 0 + a 1 x. The data you get is the slope of the input/output relation (a( 1 ) and the zero input value (a( 0 ). For these types of measuring systems, the deviation from linear behavior can be calculated: e L = y - y L 15 AMEM 11 Spring 008 Dr. Sotiris L. Omirou. 15 Linearity error - Example Input x = 6 units Output y = 11 units y L = a 0 + a 1 x. = = 10 units 1 e L = y - y L = = 1 unit 16 AMEM 11 Spring 008 Dr. Sotiris L. Omirou. 16 8
9 Repeatability Repeatability is the variation between the measurements obtained when an operator measures the same dimension (characteristic) several times under the following conditions: the same measuring instrument; on the same parts; in the same location on the part; under the same conditions of use; over a short period of time. 17 AMEM 11 Spring 008 Dr. Sotiris L. Omirou. 17 Repeatability example If a person wants his weight to be measured, repeatability requires the measurements to give the same weight of the same person on the same weightbridge and with all the other conditions the same 18 AMEM 11 Spring 008 Dr. Sotiris L. Omirou. 18 9
10 Reproducibility Reproducibility is a measure of the ability of the instrument to give the same reading of the same measurand, if repeated under different conditions. The conditions include the effects of the method, operator, location, etc 19 AMEM 11 Spring 008 Dr. Sotiris L. Omirou. 19 Reproducibility example Assuming that the two fish above are the same, reproducibility requires the measurements to give the same length, even if the location and the people (operators) are different. 0 AMEM 11 Spring 008 Dr. Sotiris L. Omirou. 0 10
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