Measurement uncertainty evaluation method and examples for component inspection

0 Introduction
    Measurement uncertainty is a parameter associated with the measurement result, which characterizes the dispersion of the value reasonably assigned to the measured value. It is an assessment of the degree of uncertainty of the measurement result after comprehensive consideration of various influencing factors including measurement error.
    For testing laboratories, conducting measurement uncertainty assessment is an important means to improve the quality of test results and measure the impact of various factors in the test process. It is also a necessary capability to adapt to the development trend of testing laboratories. This article introduces the measurement uncertainty assessment method, analyzes the sources of uncertainty in component testing and examples of uncertainty assessment based on this.

1 Requirements for measurement uncertainty assessment of component testing laboratories
    For laboratories that need to be accredited by accreditation bodies, the accreditation basis uses ISO/IEC17025:2005 "General Requirements for the Competence of Testing and Calibration Laboratories" or criteria based on this. It stipulates the laboratories with testing properties: "5.4.6.2 The testing laboratory shall have and apply procedures for measuring uncertainty. In some cases, the nature of the test method will prevent rigorous metrological and statistically valid calculation of the measurement uncertainty. In this case, the laboratory should at least strive to identify all components of the uncertainty and make reasonable judgments, and ensure that the results are reported in a way that does not create a false impression of uncertainty. Reasonable assessments should be based on an understanding of the characteristics of the method and the measurement range, and use data such as past experience and confirmation." It can be seen that due to the different types of tests, accurate uncertainty assessments are difficult in many cases. Laboratories should give uncertainty as much as possible based on existing sources of information, including experience, so that the risks of the test results in use can be controlled. Therefore, take the provisions in the CNAS (China Accreditation Service for Conformity Assessment) rule CNAS-CL07:2011 "Requirements for Measurement Uncertainty" as an example: "8.2 The testing laboratory should have the ability to evaluate the measurement uncertainty for each measurement result with numerical requirements. When the uncertainty is related to the validity or application of the test result, or when the user requires it, or when the uncertainty affects the compliance with the specification limit, when it is specified in the test method and when CNAS requires it (such as the application instructions of the accreditation criteria in special fields), the test report must provide the uncertainty of the measurement result." For testing laboratories, unlike the provisions that calibration laboratories must provide uncertainty, they are only required to have the ability to evaluate uncertainty, and are allowed to evaluate the uncertainty of the results when specifically needed.
    For component testing laboratories, since the purpose of testing is to make qualitative conclusions about the tested parts, and the customers generally do not have uncertainty requirements, most of the uncertainty is only a principled method, and there are relatively few examples of evaluation. However, even if it is only used to determine whether the device meets the upper and lower limits of the parameters, the evaluation of uncertainty is still very valuable and worth actively practicing to improve the quality of test results and to evaluate the risks of new test methods when giving results.
    For example, when a component is tested and accepted, the qualified range of a parameter is [x, z]. If the measurement uncertainty U is known, then the tightened acceptance range is [x+U, zU]. This will obviously reduce the risk of acceptance, and this measure is supported by IEC policy. The problem of test result limit often encountered in actual work has also been reasonably solved.

2 Measurement uncertainty assessment method
    The measurement uncertainty assessment method is mainly based on JJF1059~1999 "Evaluation and Expression of Measurement Uncertainty". The requirements and guidelines issued by the accreditation body also point to and reference this standard. The main steps in assessing measurement uncertainty are:
2.1 Identify the sources
    of uncertainty. Components of measurement uncertainty may come from: incomplete definition of the measured quantity; imperfect methods for achieving the definition of the measured quantity; insufficient representativeness of sampling; incomplete understanding of the environmental impact of the measurement or imperfect measurement and control of environmental conditions; perceived deviations in the readings of analog instruments; insufficient resolution or discrimination of the measuring instrument; inaccurate values ​​assigned to the measurement standard or reference material; inaccurate constants and other parameters used in data calculations; similarity and assumptions in measurement methods and measurement procedures; and variations in repeated observations of the measured quantity under seemingly identical conditions.
2.2 Establish a mathematical model
    (1) Determine the functional relationship between the measured quantity Y and the input quantities X1…Xn.
    (2) The input quantities X1…Xn include estimated values ​​(measured readings) and externally introduced values ​​(such as correction factors obtained by measurement and uncertainties provided by certificates).
    (3) Components that are difficult to quantify and cannot be clearly presented in the functional relationship are ignored in the function and treated as uncertainties. According to the specific characteristics of the measurement, some input values ​​can be correction factors (optimal value is 0) or correction coefficients (optimal value is 1).
2.3 Evaluation and calculation of standard uncertainty components
    (1) Evaluation of type A uncertainty components - Evaluation of the observation series by statistical analysis. (The classification of type A and type B is to point out the difference in evaluation methods. The components of type A standard uncertainty are obtained by calculating a series of repeated observations, while those of type B are evaluated based on relevant information, that is, obtained through an assumed probability density function)
    1) Perform n independent measurements of equal precision on the input quantity Xi, and the measurement results obtained are X1, X2...Xn as their average values, that is:
   
    2) The evaluation of type A measurement uncertainty is generally carried out by pre-evaluating the test system and representative samples used for daily testing and calibration.
    3) When performing type A uncertainty evaluation, the number of sufficient measurements should be sufficient, generally not less than 6 times.
    (2) Evaluation of type B uncertainty components - When the estimated input quantity Xi is not obtained by repeated observations, its standard deviation can be evaluated using relevant information or data on Xi. The information source can come from: calibration certificate, manufacturer's manual, standard for testing, reference data in the reference manual, previously measured data, relevant material properties, etc.
    1) If the data gives the expanded uncertainty u(Xi) and coverage factor K of Xi, the standard uncertainty of Xi is
   
    where K is the coverage factor. When the distribution form of Xi cannot be determined, according to the provisions of the standard, K is selected as 2, which is equivalent to a coverage probability of about 95%; generally, when the expanded uncertainty is given, the coverage factor is also given. If the given expanded uncertainty is up(Xi) (p is the coverage probability), then its Kp is related to the distribution of Xi. When considering it according to the normal distribution, such as p=0.95, it can be found in the table that Kp=1.960. [page]

    2) If the data gives the possible value distribution interval of Xi with half width a (usually the absolute value of the allowable error limit):
   
    At this time, K is related to the probability distribution of Xi in this interval, and the corresponding distributions (non-normal) have inclusion factors of:

   
    (3) The standard uncertainty component ui(y) of y caused by the standard uncertainty u(Xi) of the input quantity is:
   
    where is the sensitivity coefficient, which is equal to the change in y caused by a unit change in the input quantity Xi, and can be obtained from a mathematical model or from actual measurement. It reflects the sensitivity of the standard uncertainty of the input quantity to the uncertainty of the output quantity.
    (4) Calculation of the combined standard uncertainty uc(y)
   
    In actual work, if the input quantities are uncorrelated, or some input quantities are correlated, but their correlation coefficient is small (weak correlation), that is, r(Xi,Xj)=0, it can be simplified to: In

    this case, the square root method is used to calculate the combined uncertainty, that is, square each standard uncertainty component, sum it up, and then take the root.
    (5) Calculation of the expanded uncertainty u
    1) The uncertainty usually provided is the expanded uncertainty under a specific inclusion probability. At this time, it is necessary to estimate the distribution form of the uncertainty component. When there are many uncertainties and their sizes are close, and their distribution form cannot be determined, K=2 is taken according to the provisions of the standard. The inclusion probability of the approximate normal distribution is about 95%, that is, U=Kuc(y)=2uc(y).
    2) If the probability distribution form of the majority or dominant component in the combined uncertainty can be determined, the K value needs to be determined according to its distribution form.

3 Examples of measurement uncertainty assessment in component testing
3.1 Test process information
    (1) The test equipment is the digital circuit automatic test system J750.
    Voltage measurement capability: range 5V, resolution 0.625mV; measurement voltage accuracy ±0.1%+3mV.
    (2) Test parameters and test results: Under repeatability conditions (26.4℃, 54%), the Voh parameter (Ioh=3mA) of the standard sample 54LS245 was measured, and the 6 results are as follows:

    The average value is Ave = 2.93477V

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3.2 Analysis of sources of test uncertainty
    (1) Inherent uncertainty of test equipment: voltage measurement resolution, voltage measurement accuracy.
    (2) Environmental conditions. For component testing, the environmental conditions can be controlled at a specific temperature and humidity in the laboratory, and the uncertainty introduced by this can be ignored.
    (3) Measurement method and detection process. For more complex component testing processes, the uncertainty cannot be analyzed due to various technical factors such as assumptions and approximate calculations, and it takes multiple tests to quantitatively describe it; for the simple process of adding current and measuring pressure in this example, the introduced uncertainty can be ignored. (
    4) Residual parameters of tooling auxiliary devices such as test fixtures and leads. For such self-made or temporarily added devices, the measurement of their residual parameters is a more complicated process, which depends on many factors such as their medium, shape, length, and is also related to the test speed and test object. The fixture configured by the equipment manufacturer is used in this example, and its residual value is already included in the error range of the system. The uncertainty introduced by this factor is ignored here.
    (5) Uncertainty caused by measurement repeatability. It can be obtained through experimental methods of multiple measurements. The repeated tests in this example are 6 times.
    (6) Uncertainty caused by personnel quality. The measurement of this example is realized by automatic test equipment, and the operation process complies with the requirements of the regulations. The uncertainty introduced by this factor can be ignored.
3.3 Calculation process of uncertainty evaluation
    (1) Mathematical model
    Y=Voh
    (2) Uncertainty introduced by repeated measurements.
    Class A evaluation, use Bessel formula to calculate the uncertainty introduced by repeated measurements:
   
    (6) Expanded uncertainty.
    U=K×uc=0.0068V(k=2)
    (7) Voh=2.9348V measured by standard sample 54LS245 on J750, uncertainty is 0.0068V.

4 Conclusion
    When the factors affecting the measurement results are controlled, the sources of uncertainty are mainly the dispersion of repeated tests and the deviation of the equipment itself. The evaluation of measurement uncertainty is not complicated. When the sample used in this example is used as a blind sample to compare the measurement results obtained in different laboratories, it shows that the measurement results are satisfactory. The calculation method of the comparison result value:
   
    includes the calculation using the expanded measurement uncertainty. Therefore, conducting an assessment of measurement uncertainty is also a necessary task to evaluate the rationality of testing methods and processes and to evaluate inter-laboratory comparison test results.