Approximate one-sided tolerance limits in random effects model and in some mixed models and comparisons

Setting Alarm Thresholds in Measurements with Systematic and Random Errors

For statistical evaluations that involve within-group and between-group variance components (denoted σ W 2 and σ B 2 , respectively), there is sometimes a need to monitor for a shift in the mean of time-ordered data. Uncertainty in the estimates σ ^ W 2 and σ ^ B 2 should be accounted for when setting alarm thresholds to check for a mean shift as both σ W 2 and σ B 2 must be estimated. One-way random effects analysis of variance (ANOVA) is the main tool for analysing such grouped data. Nearly all of the ANOVA applications assume that both the within-group and between-group components are normally distributed. However, depending on the application, the within-group and/or between-group probability distributions might not be well approximated by a normal distribution. This review paper uses the same example throughout to illustrate the possible approaches to setting alarm limits in grouped data, depending on what is assumed about the within-group and between-group probability distributions. The example involves measurement data, for which systematic errors are assumed to remain constant within a group, and to change between groups. The false alarm probability depends on the assumed measurement error model and its within-group and between-group error variances, which are estimated while using historical data, usually with ample within-group data, but with a small number of groups (three to 10 typically). This paper illustrates the parametric, semi-parametric, and non-parametric options to setting alarm thresholds in such grouped data.

A simple method for assessing occupational exposure via the one-way random effects model

A one-way random effects model is postulated for the log-transformed shift-long personal exposure measurements, where the random effect in the model represents an effect due to the worker. Simple closed-form confidence intervals are proposed for the relevant parameters of interest using the method of variance estimates recovery (MOVER). The performance of the confidence bounds is evaluated and compared with those based on the generalized confidence interval approach. Comparison studies indicate that the proposed MOVER confidence bounds are better than the generalized confidence bounds for the overall mean exposure and an upper percentile of the exposure distribution. The proposed methods are illustrated using a few examples involving industrial hygiene data.

Respirable crystalline silica exposures during asphalt pavement milling at eleven highway construction sites

Asphalt pavement milling machines use a rotating cutter drum to remove the deteriorated road surface for recycling. The removal of the road surface has the potential to release respirable crystalline silica, to which workers can be exposed. This article describes an evaluation of respirable crystalline silica exposures to the operator and ground worker from two different half-lane and larger asphalt pavement milling machines that had ventilation dust controls and water-sprays designed and installed by the manufacturers. Manufacturer A completed milling for 11 days at 4 highway construction sites in Wisconsin, and Manufacturer B completed milling for 10 days at 7 highway construction sites in Indiana. To evaluate the dust controls, full-shift personal breathing zone air samples were collected from an operator and ground worker during the course of normal employee work activities of asphalt pavement milling at 11 different sites. Forty-two personal breathing zone air samples were collected over 21 days (sampling on an operator and ground worker each day). All samples were below 50 µg/m(3) for respirable crystalline silica, the National Institute for Occupational Safety and Health recommended exposure limit. The geometric mean personal breathing zone air sample was 6.2 µg/m(3) for the operator and 6.1 µg/m(3) for the ground worker for the Manufacturer A milling machine. The geometric mean personal breathing zone air sample was 4.2 µg/m(3) for the operator and 9.0 µg/m(3) for the ground worker for the Manufacturer B milling machine. In addition, upper 95% confidence limits for the mean exposure for each occupation were well below 50 µg/m(3) for both studies. The silica content in the bulk asphalt material being milled ranged from 7-23% silica for roads milled by Manufacturer A and from 5-12% silica for roads milled by Manufacturer B. The results indicate that engineering controls consisting of ventilation controls in combination with water-sprays are capable of controlling occupational exposures to respirable crystalline silica generated by asphalt pavement milling machines on highway construction sites.