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(cs National Bureau of Standards Special Publication 506. Proceedings of the Workshop on Asbestos: Definitions and Measurements Methods held at NBS, Gaithersburg, MD, July 18-20, 1977. (Issued November 1978) STATISTICS AND THE SIGNIFICANCE OF ASBESTOS FIBER ANALYSES J. P. Leineweber Johns-Manville Research & Development Center Denver, Colorado Abstract The analysis of asbestos fibers by electron microscope methods involves many operations, each of which can affect the final results. Normal random fluctuations can be described by the Poisson distribu- tion, which applies to any truly random process. Deviations from normal statistics, sample preparation losses, identification errors, and laboratory contamination are sources of error which are difficult to quantify. Each, however, can cause variations which will be greater than predicted by the Poisson distribution. The significance of each of the sources of error are discussed together with recommendations for experimental techniques, which should minimize•the errors. Key Words: Analysis; asbestos; electron microscope; errors; fiber; statistics. Introduction The counting of asbestos fibers by the "membrane filter" method, approved by the National Institute of Occupational Safety and Health, has been studied in considerable detail [1,2,3,4]1. The procedures to be followed are specified in detait, and the precision and accuracy of the results have been analyzed by competent statisticians. The background data are based on several controlled experiments designed to describe the variations which can occur between operators in a given laboratory, as well as the variations which can occur between laboratories. Although there is considerable debate over the lower limit of fiber concentrations that can be accurately determined, the fluctuations that can occur with standard samples have been described to a reasonable degree. In recent years, there has been increasing emphasis on the quantitative determination of fiber concentrations in the environment [5,6,7]. Analysis of these samples is much more difficult because of the extremely low fiber concentrations, the very small fiber dimensions involved, and the high concentrations of extraneous materials in the sample. Traditional methods of analysis cannot be used, so the analyst must rely upon the electron microscope to resolve, identify, count, and measure the fibers. This requires the intro- duction of several additional sample preparation techniques. Furthermore, the fraction of the sample actually examined is extremely small and there is much more latitude for operator interpretation. The objective of this paper is to review the various sources of error in the counting of asbestos fibers by electron microscope methods, discuss how they might influence the results, and finally, suggest steps which might be taken to minimize these errors. 'Figures in brackets indicate the literature references at the end of this paper. 281

Electron Microscopic Fiber Analysis Procedures The techniques used to determine asbestos fiber concentrations with the electron microscope have gone through several evolutionary changes during the past decade. Although a"standard" procedure has yet to be agreed upon, all use most of the following steps (8,9]. Sample collection Deposition on Filter Ashing and refiltration . Clearing of the filter Scanning and counting Each of these steps involves manipulation of the sample in the field or in the laboratory. Errors can be introduced with each step, and, as in any sequential system, the errors will be accumulative. The following are the principal factors which can influence the accuracy and precision of the analysis. Normal statistical fluctuations Deviations from normal statistics Sample preparation losses Identification errors Laboratory contamination The significance of each of these sources of error will be discussed in more detail in the following sections together with recommendations for experimental techniques designed to minimize the errors. Normal Statistical Fluctuations - The Poisson Distribution In environmental systems such as air and water, it is reasonable to assume, as a first approximation, that the fibers are distributed in a purely random manner. Furthermore, it is also reasonable to assume that the random distribution will be maintained during the deposition of the sample on a filter. If this is the case, the variations to be expected can be described in terms of the Poisson distribution [10]. The distribution function can be represented as: f(x, m) _ mxe-m XT- where: m= the mean value of a parameter for a series of trials x = the actual value for a specific event e = the base for natural logarithms f = the probability of occurrence for a specific value. Figure 1 is a plot of the probability of occurrence for specific events for a Poisson distribution with a medn value of 10.0. The Poisson distribution is actually a limiting case of the more general binomial distribution. It has the unique characteristics that: - the variance is equal to the mean - the standard deviation is equal to the square root of the mean. For the fiber counting problem, the most significant characteristic is that the variance will be dependent on the total number of fibers counted-regardless of the number of fields that were examined to obtain the results. 282

Cos 0 0.130 " 0.120 0.110 0.100 0.090 0.060 0.070 0.060 0.050 0.040 0.030 0.020 0.010 0.000 0.0 10.0 COUNT Figure 1. Poisson distribution mean = 10. 283 20.0

C;b The consequences of the foregoing characteristics of the Poisson distribution are best illustrated by using the "two sigma" limits to define the range within which the results might be expected to fall for given total fiber counts. The "two sigma" limits are chosen on the basis of the hypothesis that about 95 percent of the results should be within two standard deviations of the mean value. Table 1 lists the "two sigma" limits for total counts ranging from 1 to 100. Figure 2 is a plot of the range (upper limit/lower limit) for various total counts. This plot shows very dramatically how large the range can be for small total counts. Only when the total fiber count is 20 or greater does the range fall to a factor close to 2. It is also significant to note that the range decreases relatively slowly for total fiber counts in excess of 20. Table 1. Two sigma limits for various fiber counts. Two Sigma Limits Total Count Lower Upper 1 0.00 3.00 2 0.00 4.83 3 • 0.00 6.46 4 0.00 8.00 5 0.53 9.47 10 3.68 16.32 20 11.06 28.94 30 19.05 40.95 40 27.35 52.65 50 35.86 64.14 60 44.51 75.49 70 53.27 86.73 80 62.11 97.89 90 71.03 108.97 100 80.00 120.00 284

cS 20.0 ,, 18.0 j 14.0 J. 12.0 10.0 8.0 1 0.0 20.0 40.0 60.0 TOTAL FIBER COUNT Figure 2. Range of 2 sigma limits. 285 80.0 100.0

The final, and most important point to be made in regard to this theoretical discus- sion is that the Poisson distribution can only be considered to be a limiting case. It represents the best that can be achieved under ideal circumstances. If the fibers are not deposited in a truly random manner, the variations will be larger than predicted. As a matter of fact, all available experimental data indicates that real world samples do not follow the Poisson distribution [11]. Although there is much more data available for optical counting, there is no reason to believe that electron microscope samples should be any better. Causes for Non-Random Distribution - Experimental Results The obvious causes for non-random distribution of fibers on a filter surface are inadequate mixing, eddy currents in the filter, and fiber clustering. With water samples, the first two of these can probably be controlled by good experimental technique. In the case of airborne samples, the operator will have little or no influence over the initial distribution and only some control over air currents which may influence the deposition. Recently, an experiment was designed to test the validity of the Poisson distribution under reasonably ideal conditions. We had available a small amount of very well charac- terized glass fiber, 1.5 micrometers in diameter and 30 micrometers long. A carefully weighed quantity, calculated to contain one million fibers, was dispersed in one liter of water. One hundred (100) mL of this dispersion was filtered on a 25 mm membrane filter. The filter was then clarified and examined by phase contrast microscopy. Figure 3 shows a typical area near the center of the filter. The distribution appears reasonably random, but there also appears to be too many fibers lying closely parallel to each other to say that the distribution is completely random. Figure 4 shows the configuration near the edge of the filter. The lower right hand corner is the region closest to the edge of the filter. Here the fibers show a tendency to align circumferentially. Next, there is a complete ring in which very few fibers are deposited. In the next few hundred micrometers, the fibers tend to be radially oriented. As we proceed toward the center of the filter, the distribution becomes more random, as was shown in the first photo in this series. Obviously, there are eddy currents near the side of the filter funnel which have strong influence on the fiber distribution. Continuing the experiment as originally designed, 1000-80 micrometer square fields were counted. The expected number of fibers per field was 2.58. The average found was 3.18. This calculates back to 1.28 million fibers per liter. An excellent correlation, considering all the possible sources of error, including the original characterization of the fibers. Figure 5 shows the actual distribution of the number of fibers per field versus the theoretical Poisson distribution for a mean of 3.18. Even in this well-controlled experi- ment, the distribution is significantly broader than predicted. 286

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Figure 4. Glass fiber dispersion. Area near edge of filter. Nominal dimensions of fibers are 1.5 x 30 micrometers. Phase contrast. 288

x 0.200 0.190 0.180 0.170 0.160 0.150 0.140 0.130 0.120 0.110 0.100 0.090 0.080 >-- 0 070 ~ . ~ 0.060 J ~ 0.050 m 0 040 ~ . m 0.030 0 ~ 0.020 m 0.010 0.000 0.0 COUNT THEORETICAL Figure 5. Actual versus theoretical fiber distribution. 289 ® ACTUAL

Table 2 shows the results of actual electron microscope counts from some typical water and air samples. The fourth water sample and the fourth air sample are of particular interest. In the water sample, 8 grid squares were counted with a mean value of 12.13. The probability of finding a grid square with only 2 fibers is calculated to be about 4 in 10,000. Likewise, in the water sample 20 grid squares were counted with a mean value of 2.9, the probability of finding 11 fibers in one grid square is 2 in 10,000. These are both good examples of serious deviations from the theoretical Poisson distribution which will lead to greater than expected uncertainties. Table 2. Typical counting results. Grid Opening Water Samples Air Samples 1 0 2 4 15 5 0 8 1 2 0 0 1 15 6 0 3 11 3 0 2 2 10 7 0 12 2 4 0 7 2 16 3 0 18 6 5 0 3 0 13 0 0 3 6 6 1 4 1 11 4 0 4 3 7 0 0 1 15 1 0 7 1 8 0 1 1 2 2 1 8 1 9 0 1 3 4 1 8 3 10 0 0 1 4 0 3 3 11 0 5 0 0 2 12 0 1 0 1 0 13 0 4 0 0 3 14 0 5 0 1 2 15 0 3 0 1 0 16 0 3 4 2 0 17 0 5 1 0 3 18 0 1 2 0 1 19 0 2 0 0 3 20 0 7 1 1 6 Figure 6 is a typical clump of fibers and other material found in a water sample. One can only speculate on whether such an agglomerate actually existed in the original sample or is an artifact caused by sample preparation. In any event, its occurrence can have serious consequences on the final results. 290