ISO/TS 28037:2010 直线性标定函数的确定和使用
标准编号：ISO/TS 28037:2010
中文名称：直线性标定函数的确定和使用
英文名称：Determination and use of straight-line calibration functions
发布日期：2010-09
标准范围
ISO/TS 28037:2010涉及描述两个变量X和Y之间关系的线性(即直线)校准函数，即形式为Y=a+BX的函数。尽管许多原理适用于更一般类型的校准函数，但是所描述的方法尽可能利用直线校准函数的简单形式。参数a和B的值基于测量的数据点(xi，yi)确定，i=1，.，m。考虑了与这些数据相关的不确定性性质相关的各种情况。没有假设与yi相关的误差是同方差的（具有相等的方差），当误差不可忽略时，对于xi也是如此。使用最小二乘法确定参数A和B的估计值。重点是选择最适合测量数据类型的最小二乘法，特别是反映相关不确定性的方法。讨论了与测量数据相关联的最一般类型的协方差矩阵，但详细描述了导致更简单计算的重要特殊情况。对于所考虑的所有情况，给出了验证直线校准函数的使用以及评估与参数估计相关的不确定性和协方差的方法。ISO/TS 28037:2010还描述了在给定Y的测量值及其相关标准不确定度的情况下，使用校准函数参数估计值及其相关不确定度和协方差来预测X的值及其相关标准不确定度。
ISO/TS 28037:2010 is concerned with linear, that is, straight-line, calibration functions that describe the relationship between two variables X and Y, namely, functions of the form Y = A + BX. Although many of the principles apply to more general types of calibration function, the approaches described exploit the simple form of the straight-line calibration function wherever possible.Values of the parameters A and B are determined on the basis of measured data points (xi, yi), i = 1,., m. Various cases are considered relating to the nature of the uncertainties associated with these data. No assumption is made that the errors relating to the yi are homoscedastic (having equal variance), and similarly for the xi when the errors are not negligible.Estimates of the parameters A and B are determined using least squares methods. The emphasis is on choosing the least squares method most appropriate for the type of measurement data, in particular methods that reflect the associated uncertainties. The most general type of covariance matrix associated with the measurement data is treated, but important special cases that lead to simpler calculations are described in detail.For all cases considered, methods for validating the use of the straight-line calibration functions and for evaluating the uncertainties and covariance associated with the parameter estimates are given.ISO/TS 28037:2010 also describes the use of the calibration function parameter estimates and their associated uncertainties and covariance to predict a value of X and its associated standard uncertainty given a measured value of Y and its associated standard uncertainty.
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