Information is presented concerning the distinction of failure data by the likelihood ratio test; detection of outliers in failure data; and properties of prior estimation techniques in Bayesian analyses.

This user's manual presents a detailed description of two FORTRAN computer codes for analyzing component failure data. The first code SAFE-R is used to analyze data giving the number of observed failures in specified component operation times, while the second code SAFE-D is to be applied to failure data giving the number of failures observed in specified numbers of component demands. The theory behind the many analyses performed by these codes is summarized in a companion report NUREG/CR-2374 'Use of Non-Conjugate Prior Distributions in Compound Failure Models.' A description of the overall program structure and detailed use of the many program commands is presented here. A sample input is given along with the resulting output.

The theory is summarized for the homogeneous Poisson and the compound gamma-Poisson probability models which can be used to analyze failure rate attribute data consisting of the number of failures in specified test times for normally operating components or systems. A computer code based on this theory is described, and instructions for its use together with a sample problem and a complete code listing are presented. For the compound model, used in a Bayesian analysis of failure rate data, values of the parameters for the prior gamma distribution, chosen a priori, are estimated from observed failure data by three methods: (1) matching the data moments to those of the prior distribution, (2) matching the data moments to those of the marginal distribution, and (3) the marginal maximum likelihood method. Many program options are available including variance estimates for the prior parameter estimators, posteriori analyses for each component, various statistical comparisons between the homogeneous and compound models, and generalized chi-square and Kolmogorov-Smirnov goodness-of-fit tests for determining how well the failure models describe the observed data.

Of considerable importance in the safety analysis of nuclear power plants are methods to estimate the probability of failure-on-demand, p, of a plant component that normally is inactive and that may fail when activated or stressed. Properties of five methods for estimating from failure-on-demand data the parameters of the beta prior distribution in a compound beta-binomial probability model are examined. Simulated failure data generated from a known beta-binomial marginal distribution are used to estimate values of the beta parameters by (1) matching moments of the prior distribution to those of the data, (2) the maximum likelihood method based on the prior distribution, (3) a weighted marginal matching moments method, (4) an unweighted marginal matching moments method, and (5) the maximum likelihood method based on the marginal distribution. For small sample sizes (N = or < 10) with data typical of low failure probability components, it was found that the simple prior matching moments method is often superior (e.g. smallest bias and mean squared error) while for larger sample sizes the marginal maximum likelihood estimators appear to be best.

A description of classical and Bayesian techniques to estimate component failure probabilities is presented. Of particular concern is the estimation, from typically sparse component failure data, of values for the parameters of the assumed beta prior distribution (used in the Bayesian analysis) and of the failure probability distribution for a particular component with an observed performance history. Three methods for the parameter estimation are described and compared, viz. (i) matching data moments to the prior distribution moments, (ii) matching data moments to marginal distribution moments, and (iii) the maximum likelihood method. Results are presented for data from standby diesel generators used in several nuclear power plants.

A method is described for the selection of the optimum size (i.e., rated power and speed) for a wind turbine generating system (WTGS) such that, for given wind speed conditions and for given demand power requirements, the annual economic savings are maximized by using the WTGS compared to purchasing all power from a utility. No storage of excess generated electricity is considered and any demand in excess of that generated by the WTGS is assumed to be supplied by the utility grid. The economic saving realized with the optimum sized WTGS is examined for various problem variables such as the degree of variability in the wind speed and in the demand load throughout the day and from season to season.

An examination of the flux magnitudes reported for a LiOD-D2O converter (thermal to 14 MeV neutrons) indicates that such a device offers little if any advantage over fission spectrum neutrons.

A method has been developed to determine a refueling pattern for light water reactors for the purpose of minimizing the radial power peaking ratio. The key points of this method are (1) the highest reactivity fuel assemblies are always placed into the peripheral region of the reactor, (2) the remainder of the assemblies are divided into two groups based on their neutronic characteristics, and are loaded into the reactor in a checkerboard pattern and (3) a loading priority sequence is generated for each group. To insure uniformity of the fuel distribution, linear programming is used for placement of the assemblies. The method is not limited by dimensional difficulties and is easily adaptable to an individual utility's current practices. Results show that this method is capable of consistently producing a satisfactory loading pattern under various refueling policies.

A device is described to convert thermal reactor neutrons to 14 MeV neutrons, via the reaction sequence 6Li(n,α)T-D(T,n)4He, in a solution of LiOD in D2O. The device's conversion efficiency was 1.93 × 10−4, i.e., for every 5200 thermal neutrons absorbed, one 14 MeV neutron was produced. Flux profiles above various threshold energies are given for the device when located in an outer ring fuel element position of the KSU TRIGA Mark II nuclear reactor. Use of the LiOD converter in fast neutron-activation analysis and CTR-materials damage studies is suggested.

Linear programming was used as the optimization technique to minimize the amount of U-235 used by an example 1160 MWe HTGR during three and six burn periods while simultaneously maximizing the production of U-233. The reactor core was divided into four concentric annular zones; an “out-in” fuel movement technique was used while the fissile loading of the core was held uniform by adjusting the power peaking constraints. The reactor was linearized by holding the neutron flux constant over each of the burn periods. The model was used to consider three cases: Case 1 consisted of three burn periods with no U-233 recycle, Case 2 consisted of six burn periods with no U-233 recycle, and Case 3 consisted of six burn periods with U-233 recycle allowed at the fourth refuelling event. The results indicate that the amount of U-233 produced in the first eight years of operation of the 1160 MWe HTGR will be sufficient to operate the same reactor with no new U-235 fuel for 3 yr hence.

A cadmium-filter, neutron-activation analysis technique was developed to analyze wheat samples for phosphorus. In this technique the gamma rays from 28Al, simultaneously produced from 31P, 28Si, 27Al, and 26Mg during a neutron irradiation, were used as the indicator for phosphorus. An “area-of-interest” unfolding technique was used in the analysis of each gamma-ray spectrum. Phosphorus concentrations varied from (1320±96) ppm to (2976±139) ppm. Concurrent analyses for magnesium content was also obtained.

From published demographic data and leukemia mortality data, the leukemia mortality rate per 100,000 populationlyr was correlated with altitude. The findings of this study indicate that the leukemia mortality rate increases with increasing altitude up to about 2000 ft elevation, but that above 2000 ft the leukemia mortality rate decreases significantly with increasing altitude. RADIATION has long been associated with an increase in the risk of contracting leukemia. While such increased risk is well established for high doses and dose rates, no positive experimental evidence has been obtained for low doses (less than a few rems) and low dose rates. The International Commission on Radiological Protection, in evaluating the consequences of radiation exposure, estimates that total leukemia risk per rad of dose is twenty cases per million persons (ICRP, 1966). A more recent study (NAS, 1972) supports this estimate of expected excess leukemia deaths resulting from a continual radiation exposure rate of 1 remlyr. I t should be noted that these studies are based on a linear extrapolation of measurable leukemia mortality rates at much higher doses and relatively high dose rates. Based on such a linear extrapolation, nothreshold model the question arises whether the variation in natural background radiation, measured primarily as a function of altitude, reflects a corresponding variation in leukemia mortality rate. The background radiation dose from all sources a t sea level has been estimated to be approximately 0.1 rad/yr with the cosmic radiation contributing about one third of this value (EISENBUD, 1963). At an altitude of 5000 ft, the background radiation dose from all sources has been estimated at approximately 0.2 rad/yr with the cosmic radiation accounting for approximately one quarter of this value. In Table 1 the estimated cosmic ray contribution to background radiation levels at various altitudes is presented. The ICRP estimate of leukemia risk provides the basis for the expected number of leukemia deaths (if one assumes that each leukemia case results in death) per 10' population per year due to the varying cosmic ray doses at the various altitudes. Therefore, as a consequence of increased cosmic ray dose with higher altitudes, one would expect about 0.14 more leukemia deaths per lo5 people/yr at 10,000 ft than at sea level. * A topographical distribution of the population of the United States during the 7yr inclusive period 1960 through 1966 (U.S. Geol. Sur.; U.S. Dept. Com., 1970) was correlated with leukemia mortality data (U.S. Dept. H.E.W.). In over 5000 geographical areas, the total of all deaths attributed to leukemia during the study period was normalized to a basis of lo5 people. The population for each area was taken as the average population as given by the 1960 and 1970 census. The normalized leukemia mortality rates were then summed €or two hundred feet increments for altitudes up to 6500 ft. Between 6500 and 7400ft, two increments each of 400ft were used. Above 7400 ft all population and leukemia mortality data were grouped in one high altitude increment with a mean elevation of approximately 8900ft. In this manner, no altitude increment contained fewer than lo5 people. The resulting plot of leukemia mortality versus altitude is shown in Fig. 1. * This increase in background radiation dose from cosmic origin per 1000 ft of increase in elevation is approximately equal to the maximum allowable dose resulting from normal radiation emissions from a nuclear power plant.