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- 1. ME 120 Experimental Methods Accuracy, Precision, and Error in Measurement BJ Furman 17AUG05 BJ Furman SJSU MAEError in Measurement Error = ε ≡ xmeas - xtrue Error is present in every measurement Best we can do is estimate a bound on ε with some level of certainty -u ≤ ε ≤ u (n:1) where u is the uncertainty estimated at odds of n:1, or equivalently, xmeas- u ≤ xtrue ≤ xmeas+ u (n:1) Wider interval at higher odds Narrower interval at lower odds BJ Furman SJSU MAE 1
- 2. The Goal Statements of uncertainty associated with measurement results “A measurement result is complete only when accompanied by a quantitative statement of its uncertainty.” Guidelines for Evalutating and Expressing the Uncertainty of NIST Measurement Results, NIST Tech. Note 1297 1994 Edition Example • Y= y ± uc(y) 95% confidence or (n:1) odds BJ Furman SJSU MAEProbability and Odds Probability ≡ the likelihood of a particular event taking place measured with reference to all possible events. The probability of rolling ‘snake eyes’ [••] with a pair of dice is 1/36 Odds ≡ the ratio of the probability of an event to the probability that it does not happen: odds = p/(1-p) The odds of rolling snake eyes with a pair of dice is (1/36)÷(35/36) ⇒ 1 in 35 Helpful in magnifying small or large probabilities by expressing them as a ratio of whole numbers. What probability does odds of 19:1 correspond to? BJ Furman SJSU MAE 2
- 3. Important Definitions Calibration=the process of applying known values of a measurand to determine the response of a measurement system Static Calibration=calibration using a constant measurand • Ex. Weights applied to a scale Dynamic Calibration=calibration using a time-dependent measurand • Ex. Sinusoidal, step, impact Sensitivity=the change of output (measured value) per unit of input (measurand). Sensitivity is the slope of the static calibration curve at a given value of the input. BJ Furman SJSU MAECalibration, Sensitivity, and Linearity Sensor Calibration 40 35 30 Output, y units 25 K=sensitivity 20 15 10 5 0 0 5 10 15 20 25 Measurand input, x units BJ Furman SJSU MAE 3
- 4. Important Definitions , cont. Accuracy=the closeness of a measured value to the actual value being measured Repeatability (precision)=the ability of an instrument to repeat an output when measuring a given quantity under identical conditions Resolution=the smallest increment of change in the measured value that can be determined from the readout or recording instrument BJ Furman SJSU MAEAccuracy, Repeatability, and Systematic Error Accuracy Repeatability BJ Furman SJSU MAE 4
- 5. Calibration and Repeatability Sensor Calibration Repeated Several Times 40 35 30 Output, y units meas. 1 25 meas. 2 20 meas. 3 meas. 4 15 meas. 5 10 5 0 0 5 10 15 20 25 Measurand input, x units BJ Furman SJSU MAEComponents of Uncertainty Random effects (random or precision errors) Occur differently for each measurement Creates a distribution of values Arise from uncontrolled variables, e.g., _________________ Can use statistical methods to estimate the likely range that the true value lies in Systematic effects (systematic or bias errors) Occur the same way for each measurement • Ex: 1st down measurement chain – too many links • Ex: Bubble level - vial misaligned Arise from: • Calibration error • Loading error • Measurement disturbance • Aging of components in measurement equipment • Uncontrolled variables BJ Furman SJSU MAE 5
- 6. Components of Uncertainty, cont. Systematic effects, cont. In general, need more than statistical methods to determine • Can estimate using: Comparison with more accurate standards Compare with a different method of measuring the same variable Self-calibration (reversal) sometimes Inter-laboratory comparison Experience BJ Furman SJSU MAECalibration and Hysteresis Sensor Calibration with Hysteresis 35 30 25 g sin Output, y units rea 20 inc 15 ing eas ecr 10 d 5 0 0 5 10 15 20 25 Measurand input, x units BJ Furman SJSU MAE 6
- 7. References Beckwith, T. G., Marangoni, R. D., Lienhard, J. H., Mechanical Measurements, Addison-Wesley, Reading, MA, 1995. Figliola, R. S., Beasley, D. E., Theory and Design for Mechanical Measurements, 3rd ed., J. Wiley & Sons, New York, 2000. “Accuracy Specifications for Mensor Products,” Technical Note 6, Mensor Corp., www.mensor.com, September, 2002. NIST/SEMATECH e-Handbook of Statistical Methods, http://www.itl.nist.gov/div898/handbook/, September, 2002. Taylor, B. N., Kuyatt, C. E., Guidelines for Evaluating and Expressing the Uncertainty of NIST Measurement Results, NIST Technical Note 1297, 1994 edition. BJ Furman SJSU MAE 7

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