Gamma Spectrometric Method Validation for the Measurements of 40 K and 137 Cs in the Milk Powder

Performance and suitability of the equipment, method or system is important for nuclear analytical laboratories. Method performance in the nuclear analytical laboratories depends on the laboratory conditions, equipment, chemical standards, operator experience, and sample matrixes. Method used in an nuclear analytical laboratory must be evaluated and tested to ensure that obtained results valid and suitable for their intended purposes. For the reliable, precise, accurate, traceable and inter-comperable measurements, method validation process can be applied to the nuclear analytical method.


Introduction
Performance and suitability of the equipment, method or system is important for nuclear analytical laboratories.Method performance in the nuclear analytical laboratories depends on the laboratory conditions, equipment, chemical standards, operator experience, and sample matrixes.Method used in an nuclear analytical laboratory must be evaluated and tested to ensure that obtained results valid and suitable for their intended purposes.For the reliable, precise, accurate, traceable and inter-comperable measurements, method validation process can be applied to the nuclear analytical method.
Method validation, with the well documentation, is a measurement procedure for the determination of the performance and suitability of the equipment, method or system for the accordance with aims, scopes and standards [1].Method validation is a necessity for laboratories which aiming for accreditation.Before routine analysis application, method which will be used in laboratory must be validated and documented by the laboratory person in accordance with the laboratory conditions.Method validation must carried on when new method developed, a parameter changed in method, method used in laboratory for the first time, validated method used in different laboratory.Validation parameters must be determined depending on the aim and the scope of the applied method.The general validation parameters are specificity, detection limit, ruggedness (reproducibility), bias (accuracy), precision (repeatability), and robustness [2].
Gamma spectrometric method is well-established radioanalytical method.Wide variety of the radionuclide, energy range, radioactivity concentration level, sample shape and sample composition of the naturally occurring and artificial radionuclides can be measured with the gamma spectrometric technique.Main purpose of the gamma spectrometric technique is to determine the radioactivity concentration and measurement uncertainty of the gamma-emitting radionuclide [3,4,5,6].
In this study, gamma spectrometric method validation of the 40 K and 137 Cs measurements in the milk powder is investigated.Each method validation parameter is evaluated and quantified.For this purpose, n-type 20% efficiency and p-type 150% efficiency HPGe detectors were used.

Material and Method
The IAEA-154 and IAEA-152 certified milk powder standards were put into analysis containers and weighed.Each container had 6x5 cm (diameter x height) dimension.The spectrometers which n-type 20% efficiency and p-type 150% efficiency HPGe detectors were used for the radioactivity measurements.Energy calibration was done by using 241 Am, 137 Cs and 60 Co standard point radioactive sources.For the determination of the background effects, an empty analysis container counted in the same counting geometry as the samples.
Standard comparison method used to determine radioactivity concentrations.For this purpose, IAEA-152 standard reference material was used as a standard.The activity concentration of 40 K was calculated by using 1460.8keV photopeak.The activity concentration of 137 Cs was determined from 661.7 keV photopeak.Minimum detectable activity (MDA) calculations were performed by using the Curie-MDA standard expression [7]: where LD is the detection limit of the system, ε is efficiency,  is the gamma emission probability, ts is measurement time, m is dried sample weight, B, n, and m are background area, gross count peak region channel number and background channel number respectively, C1 is the correction factor for nuclear decay from sample collection to the start of the measurement, C2 is the correction factor for nuclear decay during counting period, C3 is the self-attenuation correction factor, C4 is the correction factor for pulse losses due to random summing, C5 is the coincidence correction factor.

Precision/Repeatability
Precision or repeatability is closeness of the results of successive measurements carried out under the same conditions of measurement.In the precision measurements person, measuring instrument, measurement procedure, location, laboratory conditions are the same and successive measurements carrying out short period of time [8].
Repeatability is the reliability of the measurement results and is the essential parameter of the quality system, validation of the method and uncertainty budget.Additionally, precision is the random error and expressed as the standard deviation(s) or the percent relative standard deviation.

Specificity
Specificity is the distinguishability of radionuclide to be measured from other radionuclides available in the matrix.Specificity is important for the quality of the gamma spectrometric analysis results.For accurate, precise and reliable radioactivity measurement, specificity must be taken into account.
The specificity of the detection system is determined by using the IAEA-154 milk powder standard, which contains both 137 Cs and 40 K radionuclides.Gamma spectrometer has been calibrated in 30-2000 keV energy regions. 137Cs and 40 K radionuclides gammaray energies are within this energy region.There is no interference with the 137 Cs and 40 K radionuclide gamma-rays.

Bias/Accuracy
Accuracy is the closeness of the true radioactivity concentration with the result from average of the repeated measurements.Accuracy is the systematic error (bias).The relative bias between the measured value and the target value is expressed by the following equation The accuracy of the measurement can also be evaluated with Z-score.

𝑧 =
−   * (3) where As is the measured radioactivity value, Aref is reference radioactivity value.When z < 2, the quality of measurement is satisfactory.

Robustness
Experimental conditions in the laboratory may change while applying the method.Minor changes in the experimental conditions affect measurement results.These minor changes determine robustness of the method.Robustness is a degree of the sensitivity of gamma spectrometric method in the presence of minor differences in the experimental conditions.

Ruggedness/Reproducibility
Ruggedness or reproducibility is closeness of results of measurements carried out under changed conditions of measurement -reference standard, method of measurement, measuring instrument, operator, location, conditions of use, time-.Ruggedness is a measure of the method performance under changed conditions.The ruggedness or reproducibility of the method was determined by using different equipment.[8].

Limit of Detection
The detection limit is the minimum number of the counts that can be measured confidently.The detection limit is also the minimum activity that can be measured with in a confidence level.Curie-MDA standard expression was used to calculate detection limit.MDA was calculated by using the Curie-MDA standard expression in Equation 1.

Results and Discussion
Precision/Repeatability The small energy line shift for 40 K and 137 Cs may be due to the environmental effect, system stability, interaction of the high energy gamma-ray with the active volume of the detector, etc.
Generally, up to 1 keV energy line shift is acceptable and this shift is negligible.As can be seen, 137 Cs and 40 K radionuclide in the sample could easily be identified with the help of related energy line.
Although there was the small energy line shift, method was able to identify and specify intended radionuclides with their related gamma ray energies.

Robustness
In gamma spectrometric analyses, measurement conditions may change.This can be done by changing one of the measurement conditions such as analyst, detector, or laboratory.Changing of the condition affects the measurement results at some degree.In this study, different operators measured same reference material for the robustness.Three analysts were measured IAEA-154 standard twenty times.Mean, standard deviation, RSD, RSD% and Zscore values are shown in Table 4.As can be seen from the table, Z-score values of the measurements are smaller than 2. As a result, robustness condition is fulfilled.

Ruggedness/Reproducibility
The ruggedness / reproducibility of the method were determined by using different detectors.Two different HPGe detectors which had different efficiencies were used.These detectors were 20% ntype and 150% p-type reverse electrode coaxial HPGe detector.Ten consecutive measurements were carried out for each detectors and radionuclides.
Ruggedness/reproducibility results are shown at Table 5 and Table 6.Statistical f-test was applied to the obtained results.F values were found to be 0.21 and 0.23 for 137 Cs and 40 K respectively.F values were smaller than F-critic values.As a result, ruggedness/reproducibility condition was fulfilled.

Limit of Detection
There were important statistical concepts in the gamma spectrometric analysis.These concepts were critical limit (LC), upper limit (LU), detection limit (LD), and minimum detectable activity (MDA) [3].Critical limit is a decision limit.Critical limit means whether the net count significant or not.Upper limit determines statistical significance of the count.Therefore the critical limit is the threshold value of the upper limit.Detection limit is the reliability of the counts and means what is the minimum number of the counts which can be detected confidently.
where, B, A, n, and m are background area, net peak area, gross count peak region channel number and background channel number respectively [3].IAEA-154 standard milk powder sample was counted at the 20% efficiency n-type detector.Counting times were 3600 s and 58600 s.The results of the critical limit, upper limit, detection limit, and minimum detectable activity calculations are given in Table 7 and Table 8.IAEA-152 standard milk powder sample was counted at the 150% efficiency p-type detector.Counting times were 5000 s and 75000 s.The results of the critical limit, upper limit, detection limit, and minimum detectable activity calculations are given in Table 9 and Table 10.

Conclusions
Gamma spectrometric method validation of the 40 K and 137 Cs measurements in the milk powder is investigated.Specificity, detection limit, ruggedness (reproducibility), bias (accuracy), precision (repeatability), and robustness parameters were evaluated and quantified.For this purpose, n-type 20% efficiency and p-type 150% efficiency HPGe detectors were used.Homogeneity conditions ensured using IAEA-154 and IAEA-152 certified milk powder standards.In the specificity measurements, energy line shifts were measured as 0.05 and 0.15 keV for 137 Cs and 40 K respectively.Since up to 1keV shift is acceptable for the measurements, these results are reasonable.
For the precision /repeatability measurements, statistical two-tail student t-test were applied.-1.01 and 1.06 values obtained for 137 Cs and 40 K. tcrit value was 1.83, obtained values were smaller than tcrit value.Bias and Z-score values of the 137 Cs and 40 K measurements were found to be smaller than 2. 137 Cs and 40 K radioactivity concentration measurements were satisfactory.Robustness measurements were performed, Z-score values of the measurements were smaller than 2.
Ruggedness/reproducibility measurements were performed.Statistical f-test was applied obtained results.F values were 0.21 and 0.23 for 137 Cs and 40 K respectively.F values were smaller than F-critic values.Critical limit (LC), upper limit (LU), detection limit (LD), and minimum detectable activity (MDA) values for the detectors were obtained.Quality Control/Quality Assurance measurements were carried out.Count rate and the full width at half maximum (FWHM) values for 137 Cs and 40 K obtained.Count rate and FWHM values were within the 2 statistical limit.Obtained results showed that method validation parameters requirements fulfilled.
an requirement for the method validation.For the system stability measurements, Quality Control/Quality Assurance study carried out using IAEA-154 certified reference standard.Ten measurements carried out.Count rate and the full width at half maximum (FWHM) values for 137 Cs and 40 K obtained.Control charts of the count rate and FWHM are shown at Figure1, Figure2, Figure3and Figure4.Count rate and FWHM values are within the 2 statistical limit.

Figure 1 .
Figure 1.Control chart of the 137 Cs count rate

Table 1 .
Bq/kg.t-value was 1.06 which less than tcrit value.Repeatability condition is fulfilled and measurement repeatable.Statistical two-tail student t-test results of the 137 Cs and 40 K activity measurements are shown at Table 1.Statistical student two-tail t-test results of the 137 Cs and 40 K activity measurements (Bq/kg)

Table 2 .
Energy line and FWHM of the 137 Cs and 40 K

Table 3 .
Bias and Z-score values of the 137 Cs(Bq/kg) and