Gary H. Ganser

An Accurate Substitution Method for Analyzing Censored Data

When analyzing censored datasets, where one or more measurements are below the limit of detection (LOD), the maximum likelihood estimation (MLE) method is often considered the gold standard for estimating the GM and GSD of the underlying exposure profile. A new and relatively simple substitution method, called β -substitution, is presented and compared with the MLE method and the common substitution methods (LOD/2 and LOD/√2 substitution) when analyzing a left-censored dataset with either single or multiple censoring points. A computer program was used to generate censored exposure datasets for various combinations of true geometric standard deviation (1.2 to 4), percent censoring (1% to 50%), and sample size (5 to 19 and 20 to 100). Each method was used to estimate four parameters of the lognormal distribution: (1) the geometric mean, GM; (2) geometric standard deviation, GSD; (3) 95th percentile, and (4) Mean for the censored datasets. When estimating the GM and GSD, the bias and root mean square error (rMSE) for the β -substitution method closely matched those for the MLE method, differing by only a small amount, which decreased with increasing sample size. When estimating the Mean and 95th percentile the β -substitution method bias results closely matched or bettered those for the MLE method. In addition, the overall imprecision, as indicated by the rMSE, was similar to that of the MLE method when estimating the GM, GSD, 95th percentile, and Mean. The bias for the common substitution methods was highly variable, depending strongly on the range of GSD values. The β-substitution method produced results comparable to the MLE method and is considerably easier to calculate, making it an attractive alternative. In terms of bias it is clearly superior to the commonly used LOD/2 and LOD/√2 substitution methods. The rMSE results for the two substitution methods were often comparable to rMSE results for the MLE method, but the substitution methods were often considerably biased.

Simple Procedures for Calculating Confidence Intervals around the Sample Mean and Exceedance Fraction Derived from Lognormally Distributed Data

Abstract The determination that a work environment is acceptable or unacceptable is often based upon the calculation of the mean exposure and/or exceedance fraction [i.e., the fraction of measurements expected to exceed an occupational exposure limit (OEL)] for an employee or exposure group. The purpose of this article is to introduce simplified procedures for calculating accurate estimates of the 95 percent lower confidence limit (LCL) and 95 percent upper confidence limit (UCL) for (1) the sample arithmetic mean and (2) the sample exceedance fraction for lognormally distributed exposure data. The procedure for the arithmetic mean is adapted from Lands procedure for calculating exact confidence intervals around the mean of lognormally distributed data. The procedure for the exceedance fraction is based on the Odeh and Owen confidence limits for a proportion in one tail of the normal distribution. Both procedures are graphically based and require no hard-to-find references. The two 95 percent confidence ...

Nonlinear periodic waves in a two-phase flow model

A partial differential equation is presented as a model for a two-phase flow. A nonlinear analysis is done using perturbation theory formally yielding periodic traveling wave solutions. In light of previous work these solutions, under certain restrictions, are interpreted as linearly unstable waves which have equilibrated.

Numerical solution of a hyperbolic system of conservation laws with source term arising in a fluidized bed model

Abstract A model a gas fluidized bed is considered which leads to a hyperbolic system of conservation laws with a source term. The system is solved numerically by a second-order operator splitting technique based on a Roe approximate Riemann solver. Numerical experiments demonstrate the ability of the model to reproduce qualitatively the slugging phenomenon in the case when the bed is subject to a relatively large gas flux.

Oscillatory traveling waves in a hyperbolic model of a fluidized bed

Abstract A class of admissible solutions to a hyperbolic system of equations modeling a gas fluidized bed is constructed. The solutions are traveling waves composed of smooth transitions joined by admissible shocks. The existence of these solutions depends on the presence of stable and unstable regimes for the linearized system. These regimes are due to particle inertia and particle phase pressure and do not exist in the simpler kinematic models which omit these effects. Included are oscillatory and slug-like solutions previously conjectured to exist only in systems with particle viscosity.

Correcting Diacetyl Concentrations from Air Samples Collected with NIOSH Method 2557

Diacetyl (2,3-butanedione), a diketone chemical used to impart a buttery taste in many flavoring mixtures, has been associated with bronchiolitis obliterans in several industrial settings. For workplace evaluations in 2000–2006, National Institute for Occupational Safety and Health (NIOSH) investigators used NIOSH Method 2557, a sampling and analytical method for airborne diacetyl utilizing carbon molecular sieve sorbent tubes. The method was subsequently suspected to progressively underestimate diacetyl concentrations with increasing sampling site humidity. Since underestimation of worker exposure may lead to overestimation of respiratory health risk in quantitative exposure-effect analyses, correction of the diacetyl concentrations previously reported with Method 2557 is essential. We studied the effects of humidity and sample storage duration on recovery of diacetyl from experimental air samples taken from a dynamically generated controlled test atmosphere that allowed control of diacetyl concentration, temperature, relative humidity, sampling duration, and sampling flow rate. Samples were analyzed with Method 2557, and results were compared with theoretical test atmosphere diacetyl concentration. After fitting nonlinear models to the experimental data, we found that absolute humidity, diacetyl concentration, and days of sample storage prior to extraction affected diacetyl recovery as did sampling flow rate to a much smaller extent. We derived a mathematical correction procedure to more accurately estimate historical workplace diacetyl concentration based on laboratory-reported concentrations of diacetyl using Method 2557, and sample site temperature and relative humidity (to calculate absolute humidity), as well as days of sample storage prior to extraction in the laboratory. With this correction procedure, quantitative risk assessment for diacetyl can proceed using corrected exposure levels for air samples previously collected and analyzed using NIOSH Method 2557 for airborne diacetyl.

A numerical study of nonlinear waves arising in a one-dimensional model of a fluidized bed

Abstract A third-order nonlinear problem, which under certain circumstances approximates the flow in a 1-dimensional fluidized bed, is solved numerically. A Petrov-Galerkin finite element method, with piecewise linear trial functions and cubic spline test functions, is used for the discretization in space. If product approximation is applied to the numerical representation of the nonlinear terms, then the scheme is fourth-order in space in the finite difference sense. Second-order backward differentiation is used for the time stepping. It is found that, while certain values of the time step may produce stable results, a reduction in the time step introduces instability. This is confirmed by a von Neumann stability analysis of a simplified case and is also shown to be reasonable in view of the continuous problem which contains stable and unstable modes. A set of numerical experiments is presented.

Corrigenda - Models for nearly every occasion: Part II - Two box models

In volume 14, issue 1 of Journal of Occupational and Environmental Hygiene, an incorrect equation is shown in “Models for Nearly Every Occasion: Part II - Two Box Models”, by Gary H. Ganser and Pau...

Models for nearly every occasion: Part III – One box decreasing emission models

ABSTRACT New one box “well-mixed room” decreasing emission (DE) models are introduced that allow for local exhaust or local exhaust with filtered return, as well the recirculation of a filtered (or cleaned) portion of the general room ventilation. For each control device scenario, a steady state and transient model is presented. The transient equations predict the concentration at any time t after the application of a known mass of a volatile substance to a surface, and can be used to predict the task exposure profile, the average task exposure, as well as peak and short-term exposures. The steady state equations can be used to predict the “average concentration per application” that is reached whenever the substance is repeatedly applied. Whenever the beginning and end concentrations are expected to be zero (or near zero) the steady state equations can also be used to predict the average concentration for a single task with multiple applications during the task, or even a series of such tasks. The transient equations should be used whenever these criteria cannot be met. A structured calibration procedure is proposed that utilizes a mass balance approach. Depending upon the DE model selected, one or more calibration measurements are collected. Using rearranged versions of the steady state equations, estimates of the model variables—e.g., the mass of the substance applied during each application, local exhaust capture efficiency, and the various cleaning or filtration efficiencies—can be calculated. A new procedure is proposed for estimating the emission rate constant.