Nuclear error statistics

The amt of radioactive tracer required per fuse for any desired inspection rate and accuracy can be estimated from nuclear counting statistics. An arbitrary inspection rate of one unit per sec was assumed, with the additional requirement that the charge wt be determined to 5% (std error). This accuracy is more than sufficient to detect one missing increment out of four normally used to fill delay columns... 

The Lower Limit of Detection (LLD) values required by the USNRC for nuclear power facilities are often difficult to attain even using state of the art detection systems, e.g. the required LLD for 1-131 in air is 70 fCi/m . For a gas-cooled reactor where 1-131 has never been observed in effluents, occasional false positive values occur due tos counting statistics using high resolution Ge(Ll) detectors, contamination from nuclear medicine releases and spectrum analysis systematic error. Statistically negative concentration values are often observed. These measurements must be included in the estimation of true mean values. For this and other reasons, the frequency distributions of measured values appear to be log-normal. Difficulties in stating the true means and standard deviations are discussed for these situations. 

Standard deviation error of the signal from a nuclear channel gives a handle to determine the performance of the channel. In practice, nuclear detection phenomena have statistical fluctuations arovmd their mean value [6]. The measuring instrumentation also introduces additional error due to the electronic noise. In case of some malfunction in any part of the channel (from the nuclear detector to the output stage), the standard deviation of the channel signal will exceed the nuclear error by a wide margin. Also a zero value of signal mean and standard deviation would indicate an open connection somewhere in the channel circuit. 

Errors Inherent to the Radiocarbon Dating Method. The decay of radiocarbon is radioactive, involving discrete nuclear disintegrations taking place at random dates derived from the measurement of radiocarbon levels are therefore subject to statistical errors intrinsic to the measurement, which cannot be ignored. It is because of these errors that radiocarbon dates are expressed as a time range, in the form... 

A significant source of error in nuclear orientation thermometers is due to the possible absorption of the radioactive emission in the cryostat, with a temperature increase as a consequence, low-intensity source must be used, with long counting periods to get a good statistics. 

The purely leptonic hydrogen atom, muonium, consists of a positive muon and an electron. It is the ideal atom, free of the nuclear structure effects of H, D and T and also of the difficult, reduced mass corrections of positronium. An American-Japanese group has observed the 1S-2S transition in muonium to a precision somewhat better than a part in 107. [10] Because there were very few atoms available, the statistical errors precluded an accurate measurement. The "ultimate" value of this system is very great, being limited by the natural width of the 1S-2S line of 72 kHz, set by the 2.2 nsec lifetime of the muon. 

Accidents are very rare relative to the number of near accidents and human errors. Fortunate as it may seem, this poses a real problem for complex systems with a high catastrophy potential (nuclear power plants, chemical plants, commercial aviation) few accidents means few cases to analyse and hardly any feedback to learn from. This leads to the undesirable situation of ad-hoc corrective measures after each single accident, because the database is far too small to generate statistically sensible preventi ve measures. 

I took the data for the US from 1930 to 1935 and tried to forecast oil coverage of the US market up to 1970. The predicted values, even for the saturation period, fit the statistical data better than one percent which, after all, is the minimum error that can be expected from this kind of statistics. This means that the contribution of oil to the US energy budget, e.g. in 1965, was completely predetermined 30 years before, with the only assumption that a new primary source of energy, e.g., nuclear, was not going to play a major role in the meantime. As the history of substitutions shows, however, the time a new source takes to make some inroads in the market is very long indeed—about a hundred years to become dominant, starting from scratch. 

Determination of cellular lactate production. Lactate concentration changes were evaluated on culture medium by H nuclear magnetic resonance analysis (NMR Gemini 300 spectrometer, Varian, Palo Alto, CA). Experiments were performed as already reported.6 Statistical analysis. All results were expressed as means standard error of the mean (SEM) taking into consideration at least three different experiments performed in duplicate. The means were compared by analysis of variance (ANOVA), p<0.05 was considered significant. 

Indeterminate errors really originate in the limited ability of the analyst to control or make corrections for external conditions, or the inability to recognize the appearance of factors that will result in errors. Some random errors stem from the more statistical nature of things, for example, nuclear counting errors. Sometimes, by changing conditions, some unknown error will disappear. Of course, it will be impossible to eliminate all possible random errors in an experiment, and the analyst must be content to minimize them to a tolerable or insignificant level. 

Radioanalytical measurements can have many causes of uncertainty. One of the best known is the inherent randomness of nuclear decay, radiation emission, and radiation detection, which is often referred to as counting statistics. Radiation laboratories generally recognize the existence of counting statistics and account for it when they report the uncertainty of a measurement. The component of the total uncertainty due to counting statistics is the counting uncertainty, which has traditionally been called the counting error. ... 

In the dawn of the history of nuclear science, the neutron flux density (/) of Ra-Be source was only 10 -10 n cm s The total activity produced by such neutron sources via (n,y) reaction was very low and so was the specific activity of the radionuclides. The Szilard-Chalmers process, however, could dramatically increase the specific activity the improvement could reach orders of magnitude. In the measurement of P radioactivity, which was a frequent task in early days of nuclear science, samples with low specific activity brought sometimes troublesome problems of self-absorption corrections. By the introduction of the Szilard-Chalmers process, however, this difficulty could be avoided, because the measurement could be performed within small statistical errors using a sample with high specific activity. Therefore, the Szilard-Chalmers process became one of the useful means of preparation of radioisotopes for measurement, as Szilard and Chalmers (1934b) recognized the importance of this technique in their early work. 

The Idaho Chemical Processing Plant (ICPP) soluble poison meter was developed as an instrument to monitor continuously the amount of nuclear poison entering non-geometrically safe process vessels for dissolution of spent nuclear fuel elements. The nuclear poison (gadolinium or boron) is added to the dissolver with the dissolving acid. The meter detects the poison concentration with an accuracy of il%, including errors resulting from calibration, analytical techniques, drift, and statistical... 

Fleischmann and Pons were actually the first to observe the production of helium-4 in the Pd/D system [4]. However, due to the extensive criticism of their 1989 announcement, they did not want ... to open another front for attacks on their work, and so their measurements of helium-4 were never officially reported. The first reported experiments correlating the calorimetric excess enthalpy and helium-4 production were conducted by Miles in 1990 at the Naval Weapons Center (now NAWCWD) in China Lake, California, and the helium measurements were performed under the supervision of Bush at the University of Texas [6-8]. The presence of helium-4 was observed in eight out of nine effluent gas samples collected during the presence of excess heat [7,8]. No helium-4 was observed for six out of the six samples of effluent gas for a Pd/H20 control study. Measurements were also conducted for heUum-3 in these studies, but none was detected [6]. In summary, for all experiments conducted by Miles at NAWCWD, 12 out of 12 produced no excess helium-4 when no excess heat was measured, and 18 out of 21 experiments gave a correlation between the measurements of excess heat and helium-4 [8, 18]. Three of the experiments that produced hehum-4 were conducted under double-blind rules [8, 18]. An exact statistical treatment for all experiments shows that the probability is only one in 750 000 that the China Lake set of heat and helium-4 measurements could be this well correlated due to random experimental errors [18]. Furthermore, the rate of helium-4 production was always in the appropriate range of 10 to 10 atoms per second per watt of excess power for D -I- D or other likely nuclear reactions [8,18]. 

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