In accordance with KS Q ISO/IEC 17025 [1], testing and calibration laboratories shall verify that the entire measurement process, including facilities, equipment, personnel, and methods, meets the requirements. They shall ensure result validity by establishing a monitoring procedure, which shall in turn be planned and reviewed. Whenever appropriate, laboratories shall monitor their performance by comparing their results with those of other laboratories. This monitoring should be planned and reviewed and should include one or two of the following but not limited to: (a) participation in proficiency test (PT) and (b) participation in interlaboratory comparisons other than PT.

The laboratories accredited by the Korea Laboratory Accreditation Scheme (KOLAS) shall regularly participate in PT during the period set by the Korean Agency for Technology and Standards Notice No. 2022-0047 (KOLAS-R-007) entitled “the PT operation guidelines.” To implement KOLAS-R-007 in the national measurement system, the Korea Research Institute of Standards and Science (KRISS) directly provides PT or sometimes gives the reference value to PT in compliance with the requirements of KS Q ISO/IEC 17043 [2] and organized by the accredited PT provider of KOLAS. The PT results are used to assess the performance of the quality management system (QMS) of the accredited institute by KOLAS, and all corrective actions shall be undertaken when the PT result is assessed as “not acceptable.”

In 2021, the KRISS performed PT over the dosimetry audit service provider for the administered dose in cancer therapy and reported the results in Progress in Medical Physics [3]. In doing so, the KRISS supports the implementation of the Nuclear Safety and Security Commission Notice No. 2019-6 entitled “Technical standards for radiation safety management in the medical field” because the dosimetry audit shall be run on the basis of QMS. Furthermore, the KRISS PT is used to ensure the conformity of QMS. The PT provided by the KRISS contributes to confirming the competency of the dosimetry audit service provider and building the public confidence of the dosimetry audit itself.

PT results must be analyzed and transformed into a performance statistic for interpretation and assessment according to the defined objectives. The purpose of this step is to find the deviation of the result from the reference value to allow a comparison with performance standards. In KS Q ISO/IEC 17043, the E_n score is defined as one of the following statistical approaches:

where x is the result of the participating laboratory, y is the reference value, U_x is the expanded uncertainty of x, and U_y is the expanded uncertainty of y. The numerator of the above equation is the difference between the participant’s result and the reference value, and the denominator is the expanded uncertainty of the difference. Eq. (1) is valid only when the participant’s x is independent of the reference y and the coverage factors and effective degrees of freedom coincide. The E_n score for the case of correlation is not explicitly given in KS Q ISO/IEC 17043; however, the statistical approach follows the method described in KS Q ISO 13528 [4] and KS Q ISO/IEC Guide 98-3(GUM) [5].

According to KS Q ISO/IEC Guide 98-3, when a correlation exists between x and y, the new E_n score given in Eq. (1) becomes:

where x is the result or output estimate of a participant obtained from an appropriate function or a measurement model of the input estimates x₁, x₂, …, x_M, i.e., x=f(x₁, x₂, ..., x_M); y is the reference value or output estimate determined from a function of the input estimates y₁, y₂, ..., y_N, i.e., y=g(y₁, y₂, ..., y_N); k is the coverage factor to obtain the expanded uncertainty of (x−y); c_xi is the sensitivity coefficient of the i-th input estimate x_i given by the partial derivative (∂f/∂x_i); u_xi is the standard uncertainty of x_i; c_yj is the sensitivity coefficient of j_th input estimate y_j given by (∂g/∂y_j); u_yj is the standard uncertainty of y_j; and u_xi,yj is the estimate of the covariance between the input estimates x_i and yj. The coverage factor was determined to correspond to confidence level. Covariances appearing between input estimates xi and x_j or between y_i and y_j shall also be included in Eq. (2) for completeness.

Considering the relationship:

where f_n is the correlation coefficient given by u_xn,yn/(u_xnu_yn), we obtain the following conservative estimate of Eq. (2):

where the correlation is assumed to be over the input estimates with the subscript n.

The denominator of Eq. (4) is equal to or less than that of Eq. (2). This approach has been accepted for two decades in the uncertainty evaluations of the international dosimetry key comparison results carried out among national metrology institutes (NMIs) in the consultative committee of ionizing radiation, section I (Comité consultatif des rayonnements ionisants section I, CCRI[I]) of the General Conference on Weights and Measures (Conférence générale des poids et mesures, CGPM) [6,7]. In this study, the parameters fk2 and fj2 in references [6,7] correspond to f_n. When the condition that c_xn=c_yn and u_xn=u_yn is met, Eq. (2) is equal to Eq. (4), i.e., En=En*. When the measurement procedures used in PT are verified and validated according to KS Q ISO/IEC 17025, the related parameters are likely to satisfy the condition above.

If the input estimates are in perfect correlation, then f_n equals to 1. Perfect correlation is frequently encountered in many cases of calibration and testing. Eq. (1) underestimates the E_n score when a correlation exists between x and y. The independent terms are mostly those for the statistical uncertainties involved in the measurements in both laboratories.

When the laboratory value is traceable to other NMIs, it exhibits some systematic difference from the KRISS reference value y by an amount of

where d is the systematic difference in the laboratory value traceable to another NMI, D_NMI is the degree of equivalence (DOE) of another NMI, and D_KRISS is the DOE of the KRISS. The DOE given in mGy/Gy is the relative difference between the established standard of NMIs and the key comparison reference value. The DOE is presented with its uncertainty on the KCDB website (https://www.bipm.org/kcdb/). The relative standard uncertainty of d is then given by:

where u(d) is the standard uncertainty of d, u(D_NMI) is the standard uncertainty of the DOE of another NMI, and u(D_KRISS) is the standard uncertainty of the DOE of the KRISS. In Eq. (6), the correlation between the DOEs of another NMI and KRISS is assumed to be minor and thus ignored. When the results of a direct comparison between KRISS and another NMI are available, we need to follow the procedure in references [6,7] to obtain d instead of Eq. (5).

Eqs. (2) and (4) can be rewritten for the case of the laboratory value traceable to other NMIs as follows:

and

where we assume (x−d) is correlated with y. Eq. (2) or (4) shall be used in the case where the value of the other NMI is traceable to the KRISS.

The correlation coefficient ranges from 1 to 1 and is zero when no correlation is present. If a correlation is confirmed but the correlation coefficient is not explicitly known, then a correlation coefficient of 0.5 would be a conservative estimate. In technical report series No. 398 [8], k_Q,Q0 is given as a chamber-specific factor, and a correlation among values of k_Q,Q0 is reasonably accepted. When different values of k_Q,Q0 are involved in the KRISS PT, i.e., in the case of the absorbed dose to water from proton and electron beams, we can then use 0.5 for the correlation coefficient in the values of k_Q,Q0 as a conservative estimate during the evaluation of the new E_n score.

In this study, we describe the new E_n score in PT, which is useful particularly when a correlation exists between the participant’s value and the reference value. The new E_n score will reduce underestimation. Therefore, it will help enhance the discerning level of the participant’s performance in PT and be applicable in the PT program organized by the KRISS dosimetry team.

This research did not receive any specific grant from funding agencies in the public, commercial, or not-for-profit sectors.

The authors have nothing to disclose.

All relevant data are within the paper and its Supporting Information files.