Victor E. McGee

A practical method of estimating standard error of age in the fission track dating method

Abstract A first-order approximation formula for the propagation of error in the fission track age equation is given by P A = C[P 2 s +P 2 i +P 2 φ −2rP s P i ] 1 2 , where PA, Ps, Pi and Pφ are the percentage error of age, of spontaneous track density, of induced track density, and of neutron dose, respectively, and C is a constant. The correlation, r, between spontaneous are induced track densities is a crucial element in the error analysis, acting generally to improve the standard error of age. In addition, the correlation parameter r is instrumental is specifying the level of neutron dose, a controlled variable, which will minimize the standard error of age. The results from the approximation equation agree closely with the results from an independent statistical model for the propagation of errors in the fission-track dating method.

Statistical treatment of experimental errors in the fission track dating method

The major stochastic elements in the fission track dating method are (i) the number of spontaneous fission tracks (Ns) in a sample, and (ii) the number of induced tracks (Ni) observed when the sample is irradiated with neutrons. The foundations for the statistical uncertainty in these measures are of two kinds: (i) there exists a definite probability of uranium fission by means of natural decay and by neutron activation, and (ii) within a crystal the distribution of uranium is not uniform and perhaps follows something like a Poisson law. In any event, the natural logarithm of the ratio (Ns/Ni) is proportional to age. A plausible statistical fission track dating model should, therefore, start by considering the joint distribution of Ns and Ni. In this paper a joint bivariate normal model is described which allows the rigorous definition of the probability distributions of Ns, Ni, the ratio Ns/Ni, and age itself. A general computer program (FISSION) has been developed to perform all the necessary computations. By accounting for the correlation between Nsand Ni, the statistical model here ascribes smaller standard errors to Ns/Ni (and therefore age) than do previous methods. In addition, the error associated with neutron flux is a significant factor in the age relationships and has been incorporated into the model.

Simulated fissioning of uranium and testing of the fission-track dating method

Abstract A computer program (FTD-SIM) faithfully simulates the fissioning of 238U with time and 235U with neutron dose. The simulation is based on first principles of physics where the fissioning of 238U with the flux of time is described by N s = λ f 238 U t and the fissioning of 235U with the fluence of neutrons is described by Ni = σ235Uφ. The Poisson law is used to set the stochastic variation of fissioning within the uranium population. The life history of a given crystal can thus be traced under an infinite variety of age and irradiation conditions. A single dating attempt or up to 500 dating attempts on a given crystal population can be simulated by specifying the age of the crystal population, the size and variation in the areas to be counted, the amount and distribution of uranium, the neutron dose to be used and its variation, and the desired ratio of 238U to 235U. A variety of probability distributions can be applied to uranium and counting-area. The Price and Walker age equation is used to estimate age. The output of FTD-SIM includes the tabulated results of each individual dating attempt (sample) on demand and/or the summary statistics and histograms for multiple dating attempts (samples) including the sampling age. An analysis of the results from FTD-SIM shows that: (1) The external detector method is intrinsically more precise than the population method. (2) For the external detector method a correlation between spontaneous track count, Ns, and induced track count, Ni, results when the population of grains has a stochastic uranium content and/or when the counting areas between grains are stochastic. For the population method no correlation can exist. (3) In the external detector method the sampling distribution of age is independent of the number of grains counted. In the population method the sampling distribution of age is highly dependent on the number of grains counted. (4) Grains with zero-track counts, either in Ns or Ni, are in integral part of fissioning theory and under certain circumstances must be included in any estimate of age. (5) In estimating standard error of age the standard error of Ns and Ni and φ must be accurately estimated and propagated through the age equation. Several statistical models are presently available to do so.

Periodic production scheduling at a fastener manufacturer

Abstract This paper presents the application of periodic production scheduling at a metal-fastener manufacturing company. The problem was initially presented as a mandate to reduce finished goods inventory by 33%. Preliminary investigations, however, revealed that any effort to reduce finished goods inventory necessarily involved two major endeavors: 1. (1) significant improvements to forecasting and 2. (2) a periodic production scheduling system (PPS). The forecasting system provided the input to the PPS system. The PPS required initial procedures for sorting parts into families, which, as far as possible, shared the same setup patterns, engineering specifications, raw material requirements, etc. The PPS itself was developed on a spreadsheet, and the output from this package fed into an interactive PC package. In addition to graphic presentation of production scheduling, the PC software package also provided manpower implications of specific PPS plans for tooling and supervision during runs, on the basis of the periodic schedule. The paper concludes with lessons learned from attempts to finalize implementation.

Statistical forecasting in a hospital clinical laboratory.

Three forecasting methodologies were applied to monthly laboratory test count data in order to arrive at a best procedure for forecasting ahead to cover the next fiscal year. The purpose of the forecasting was, first, to aid in reimbursement and income decisions and, second, to assist in operations management decisions within the laboratory itself. The Box-Jenkins ARIMA models were found to be superior in all cases, and forecasts for individual test counts (as opposed to packages of tests billed as a unit) were improved if forecasts for inpatients and outpatients were done separately and then aggregated. With 2 years of experience to go on, the annual forecast error stands at around 4.5%.

NOTE ON AN "ELASTIC" MULTIDIMENSIONAL SCALING PROCEDURE

A new orientation and a hybrid technique of multidimensional scaling are introduced in the interests of rational theoretical underpinnings and efficient numerical computation.

Japanese Foreign Direct Investment and Dominant Factors for Selection of Locations in the U.S.

Abstract When Japanese companies locate a facility in a state of the U.S., what critical variables have played a dominant role is the focus in this paper. After considering data for the year 1988 comprising of more than 1000 Foreign Direct Investments (FDIs) by Japanese and other major investing countries in the U.S., four main variables were found to be significantly related to the location of Japanese FDIs. However, it turned out that only two out of those four variables were significant for companies from other major investing countries.

The OWL: software support for a model of argumentation

The OWL is an “idea cruncher” designed to assist in constructing, analyzing, and comparing debates and arguments. The design philosophy of OWL and the pragmatics of representing argument structures are explained, and applications are presented in three different areas: a 2-year open forum on state revenue issues, an analysis of the cohesiveness of a published argument, and a personalized learning system. The presentation concludes with a prognosis and a discussion of future plans.

Invariance of Personal Characteristics of Voice over Two Vowel Sounds

19 adult male voices were analyzed acoustically over two vowel sounds—/ee/ as in “heed” and /aw/ as in “hawed.” It was found that the individual differences observed on the utterances of /ee/ were preserved very closely (invariant) on the utterances of /aw/. Frequencies between 1000 cps and 2300 cps appeared not to play any part in producing this invariance.