Search for an optimum approach to the evaluation of data of varying consistency: half-live evaluations for 3H, 35S, 55Fe, 99Mo and 111In

doi:10.1016/S0969-8043(99)00217-1

Applied Radiation and Isotopes

Volume 52, Issue 3, March 2000, Pages 601-608

https://doi.org/10.1016/S0969-8043(99)00217-1 Get rights and content

Abstract

A common procedure is proposed for the evaluation of both consistent and discrepant data in which adjustments are made to the uncertainties in the measured data that are dependent on the χ² values of the data set. A computer program EV1NEW has been developed and applied to the evaluation of ³H, ³⁵S, ⁵⁵Fe, ⁹⁹Mo and ¹¹¹In half-lives to give the following values: 12.32(2) yr, 87.32(16) d, 2.732(14) yr, 2.7480(9) d and 2.8047(4) d, respectively.

Introduction

Evaluators are frequently confronted with the problem of deriving a recommended value and uncertainty from a discrepant set of data. Various evaluation procedures have been proposed and implemented over the previous thirty years. Reviews and tests of these methods have been undertaken by Rajput and MacMahon, 1992, Kafala et al., 1994.

One of the most useful methods for evaluating data is the procedure of limitation of relative statistical weights (LRSW), as defined by Zijp (1985). On the basis of this method, the computer program LWEIGHT has been developed by Browne and MacMahon (Browne, 1998), which also uses Chauvenet's criterion (De Soete et al., 1972) to reject outliers and works successfully in the evaluation of discrepant data when 1<χ²/(n−1)≤2. However, for discrepant data sets with χ²/(n−1)>2, the LWEIGHT choice of the unweighted mean (UWM) is judged to be questionable. When early measurements with large uncertainties are included in the analysis, the choice of UWM results in the assignment of equal weights to both the old inaccurate experimental data and more recent measurements with much lower uncertainties. As a consequence, the recommended UWM value is not in reasonable agreement with the more accurate experimental results. Increasing the uncertainty of the recommended UWM to encompass these results is not a satisfactory solution because the resulting large uncertainty does not reflect the achievable accuracy of modern experiments. The rejection of old experimental data leads to a weighted mean (WM) based on the subjective judgement of the evaluator (e.g. Chechev (1999) for half-life evaluations of ⁹⁰Sr, ⁹⁹Mo and ¹¹¹In).

Programs can be developed to aid in the evolution of an optimum approach to the satisfactory evaluation of data with differing consistency. Such efforts have been made by testing various statistical procedures, Student's t-test (Chechev, 1997) and a modified Bayesian approach (MBAYS) (Kafala et al., 1994) to generate more reliable uncertainties for recommended data, as well as incorporating the LRSW method as used successfully by an IAEA CRP on X-ray and Gamma-Ray Standards for Detector Calibration (1991).

Section snippets

Development of an optimum procedure to evaluate data of differing consistency

We have examined data sets of differing consistency to determine recommended half-lives for 48 radionuclides (Chechev, 1996, Chechev, 1997, Chechev, 1998). A degree of consistency was quantified by comparing the χ² value for a given data set with the quantile of χ² distribution at a significance level of 0.05 and (n−1) degrees of freedom, where n is the number of experimental data. Four types of data set can be defined in terms of the χ² value (Table 1).

Consistent data with the reduced χ²/(n

Half-life of tritium

There are a number of published measurements of the half-life of tritium (Table 3). Although three of these studies reported data with high precision (Jones, 1955, Jordan et al., 1967, Rudy and Jordan, 1977), the half-life uncertainties did not include estimates of possible systematic errors. More recent measurements permit the quantitative assessment of the minimum “external” uncertainty due to systematic effects (σ_min) which should be added to the uncertainties stated (Jones, 1955, Jordan et

Half-life of ³⁵S

There are many measurements of the ³⁵S half-life in the literature and they were all made before 1970 (Table 4). Omitting the measurements without uncertainties (Maurer, 1949, Rudstam et al., 1952), the recommended half-life could be the weighted mean of 11 values. However, these data are discrepant, with the χ² value (=66.6) exceeding (χ²)₁₀^0.05 (=18.3) by a factor of more than three. The recommended half-life has been obtained using the modified Bayesian procedure (MBAYS) to give a value of

Half-life of ¹¹¹In

Experimental values for the ¹¹¹In half-life are given in Table 5. The value measured by Gureev et al. (1972) was discarded because there was no associated uncertainty, while the data of Hoppes et al. (1982) is duplicated by Unterweger et al. (1992). Hence, only ten of the values were used to determine a recommended value, as shown in Table 5. The LRSW method (Zijp, 1985) showed that the relative weight of the data of Rutledge et al. (1986) is 91.7% and therefore the uncertainty of this value

Half-lives of ⁵⁵Fe and ⁹⁹Mo

The experimental data sets used to determine recommended half-lives for ⁵⁵Fe and ⁹⁹Mo are defined as type 4: these data are highly discrepant (χ²>10(χ²)_n−1^0.05) and the choice of statistical procedure is difficult. Nevertheless, we prefer in such cases to use a BAYS method to analyse all available experimental data if there is not sufficient grounds for rejecting some of them.

Three outliers of the 11 measurements of the ⁵⁵Fe half-life have been omitted and the evaluated value of 998(5) days

Conclusions

Bayesian procedures (BAYS and MBAYS) have been successfully adopted to analyse data sets and determine the dependence on χ² of the uncertainty of the resulting recommended value. However, this approach should not be used to assess small quantities of data or consistent data sets. Adjustments of the uncertainties of evaluated data derived from both consistent and discrepant data sets have been based on the comparison of χ² values with (χ²)_n−1^0.05 as of means of determining the final uncertainty (

Acknowledgements

The authors are grateful to Edgardo Browne and Desmond MacMahon for providing computer programs.

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Search for an optimum approach to the evaluation of data of varying consistency: half-live evaluations for 3H, 35S, 55Fe, 99Mo and 111In

Abstract

Introduction

Section snippets

Development of an optimum procedure to evaluate data of differing consistency

Half-life of tritium

Half-life of 35S

Half-life of 111In

Half-lives of 55Fe and 99Mo

Conclusions

Acknowledgements

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Nucleonics

Half-lives of radionuclides used for calibration of X-ray and γ-ray detectors

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Half-Life of 155Eu

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Search for an optimum approach to the evaluation of data of varying consistency: half-live evaluations for ³H, ³⁵S, ⁵⁵Fe, ⁹⁹Mo and ¹¹¹In

Half-life of ³⁵S

Half-life of ¹¹¹In

Half-lives of ⁵⁵Fe and ⁹⁹Mo

⁵⁵Fe

Half-Life of ¹⁵⁵Eu