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Lecture 2

Lecture 2. The results of measurements. Processing and presentation of measurement results. ass . N . I . Burmas. Outline.

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Lecture 2

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  1. Lecture2 The results of measurements. Processing and presentation of measurement results. ass. N.I. Burmas

  2. Outline 1. The direct measurements. Calculation of trust limits of the error result measurements. 2. Set the type of law distribution of the resultsdirectobservations. 3. Processing results of the directunitary measurements 4. Processing results of several series of measurements. 5. Processing results indirect measurements. video - Errors in Measurement video - Propagation of Errors

  3. 1. The direct measurements. Calculation of trust limits of the error result measurements. Direct measurementsis a measurement, in which the value of directly determine the direct method (comparing the measured value with the measure or by measuring appliance, wich definedin units of measurement). 1.The withdraw with results of repeated observations of known systematic errors corrected results of observations.

  4. 1. The direct measurements. Calculation of trust limits of the error result measurements. 2.Calculation of theaverage arithmetical corrected resultsobservations, which has been the result of measurement. !!!Make sure that among of theresultsobservations are not abnormal, those are very different from other . !!!Check the normality distribution of theresultsobservations.

  5. 1. The direct measurements. Calculation of trust limits of the error result measurements. 3.Calculation of evaluationaverage square deviation of randomerrorof the average arithmetical 4. Calculation trust boundaries of random error:

  6. 1. The direct measurements. Calculation of trust limits of the error result measurements 5. Valuation of the average square deviation of possible systematic errors: 6.Valuation of the average square deviation total error ofresult measurements:

  7. 1. The direct measurements. Calculation of trust limits of the error result measurements 7. Calculation of trust limits of the errorresult measurement: coefficient whose value depends on the chosen of the trust probability and the typelaw of distribution.

  8. 2. Set the type of law distribution of the resultsdirect observations. Normality distribution is estimated on thebasis of such criterion: n>50 -the criterion ofPerson; the criterion ofMizens-Smirnov . 15<n<50 – the compoundcriterion . n<20 - the criterions of asymmetryА, kurtosisK.

  9. 1 n 4 = - - K ( x x ) 3 å i 4 = nS i 1 2. Set the type of law distribution of the resultsdirect observations. Asymmetry Kurtosis

  10. - × - 24 ( n 2 ) ( n 3 ) = D ( K ) 2 + + + × + ( n 1 ) ( n 3 ) ( n 5 ) 2. Set the type of law distribution of the resultsdirect observations. Calculated dispersion of these quantities :

  11. £ K 5 D ( K ) 2. Set the type of law distribution of the resultsdirect observations. Counting module values of asymmetry and kurtosis: If you run these dependencies, the distribution is normal.

  12. 3.Processing results of the direct unitary measurements. The causes unitary measurements: • economic • avoid damage to the sample or destruction of thesample measurement. Components of error measurement result: • errors of mean measurement; • an error of method; • an error of operator. !!!Each error may consist with possible systematic and random errors.

  13. 3.Processing results of the direct unitary measurements. All errors can be expressed: 1. Possible systematic through border ortrust limits ; 2.Random error component of trust through border                or mean square deviation . 3.Errors of the means measurement for determining metrological characteristics 4.Error method and operator of normative and technical documentation for a specific method of measurements

  14. 3.Processing results of the direct unitary measurements. The procedure of processing a single outcome measure: 1. Are the results of a single measurement. 2. Assess the possibility of systematic error of the measurementresult:A) If m is a possible systematic errors, defined its borders,thetrust limits the possible systematic errors of the measurement result are:

  15. The procedure of processing the result single measurement B)if there are m possible systematic errors given trust limits , trust limits the possible systematic errors of the measurement result are :

  16. The procedure of processing the result single measurement 3. Measure confidence limits of random error component of the result measurement. A) if the random errors are expressed through the mean square deviation, the mean square deviation of random errors result of single measurement: and trust limits of random errors result :

  17. The procedure of processing the result single measurement B)if random errors are expressed outside the trust boundaries, then trust boundary random errors of measurement results are : 4. Calculate trust limits of error of theresult measurement :

  18. 2 S 1 = F exper 2 S 2 < F F exper theor 4. Processing the results of several series of measurements. Testing significance of differences between serial dispersion of F-criterion of Fisher-Snedekor : , moreover . If , then discrepancy between the variance is insignificant

  19. - x x n n 1 2 1 2 = t a exper + 2 n n 1 2 S 4. Processing the results of several series of measurements Evaluation of differences between mean valuesand

  20. < t t a a exper theor 4. Processing the results of several series of measurements !!!If , then received results ( ) reflect the true value and all results are treated as a row with ( ) variants.

  21. 5. Processing results indirect measurements. Tom measurement (indirect) - measurement, in which the unknown value of found using calculations based on the known relationship between this value and values that are based on direct measurements. Direct problem of the theory of error - error estimation function in the error of individual arguments the function .

  22. 5. Processing results indirect measurements • Accuracy evaluation function is determined by measurement error of each argument: • How the standard deviation and variance of standard deviation and variances of individual arguments: orwith absolute errors:

  23. 5. Processing results indirect measurements • The relative standard deviation function can be expressed by the formula:

  24. 5. Processing results indirect measurements • Inverse problem theory of error - knowing limit error estimation function to estimate maximum allowable individual arguments. Let the variance function Y is a polynomial:

  25. 5. Processing results indirect measurements • The principle of equal effects: • contributions of each of the terms in variance function is equal: so you can calculate all the errors of certain arguments:

  26. Thank you for attention

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