Document b8BBzxB7KYXKNdDxzwjQQybg

/ '$ // U.S. DriJ'AKTiNJIZNT OF LABOR Occiip.uir.n.i! S.ifccy .ml lle.hrh Aiimlmtiruinn WASI.'IN'OTCN' JAU 3 1375 Mr. Sarunas S. Mingela Industrial Hygienist McCord Corpora tion 2850 West Grand Boulevard Detroit, Michigan 48202 Dear Mr Mimae1a: .4 ED 1/ /.AHI AiED ? -1. 3 Vuchmlc ai A ADD Tim m'j Lv.g V.gt.. Officer AD Mr. Edward Largent has referred your letter of November 8, 1974, wherein you ask for an explanation of the accuracy requirements for monitoring and measurement presented in Part (d)(4) of the Department of Labor 1s final Occupational Safety and Health Standard for Exposure to Vinyl Chloride (29 CFR 1910.93q,October 4, .1974), to this office for reply. Part (d)(4) details the limits of error at the 95% confidence level allowed for measurement of time weighted average exposures that fall in various ranges of concentra tion. The implied error is the cumulative error incurred in making these measurements of time weighted average exposures. The sampling strategy, samolinc mechanism, .and quantitative anaivsis orccadurgu .all - tia. vhe cumu 1 ci i-.qd orror . sampling strategy has the greatest potential influence on the accuracy of measurement cf a time weighted average exposure. A sampling strategy that calls for sampling continuously, with a personal sampler throughout the duration of exposure in the time period involved (15 minutes or 8 hours) will introduce essentially no error.. On the other hand, a sampling strategy that calls for taking a series of grab samples in the breathing zcr.e of an employee can introduce errors up to several hundred percent at the 95% confidence level. This error is due to the variability with time of the vinyl chloride concentration in the work environment. A rather sophisticated statistical treatment of the data.- is necessary to determine this component of error. iiiU V/fKVA'l liil HrI m,; ;A'1 A; rr. r, iJ l / 1i n J 7 ' ;OAt.LlG C::oior: u.. ' ! a .r* ;. ' Or Wv 0000 1 7- A . 95% confidence level refers to the frequency with which measurements must fall within specificd. limits, of error.. In this'Standard, for example, if the true 8-hour average exposure were in the range of 0.25 ppm to 0.5 ppm, then the method of measurement of this 8 hour average exposure must have an accuracy such that if a scries of measurements were made, then 95% of them would be within plus or minus 50% of the true value. The error..inherent in the sampling mechanism and the error inherent in the quantitative a.naly sis procedure are. the only components of error you need to concern yourself with if you employ full-period, continuous sampling strategy. These are best determined as 'a lump sum in a laboratory by making a large number, of measurements of prepared known concentrations of vinyl chloride in air. The plus or minus percent of error at the 95% confidence level is computed by multiplying the product of the standard deviation of a large set of measurements of a given known concentration (s) and the standard normal deviate for S5% confidence limits (1.96) by ICO and then dividing this result by the known concentration (X). In mathematical symbols: + percent of error at the 95% confidence level Tl-96) (s) (100) -f (X) . Parts (d) (2) (i), (d) (2) (ii), and (d) (3) specify the frequency with which you must determine each employee's exposures. I hope this explanation of Part (d)(4) is helpful to you. Sincerely, Barry J. White Associate .Assistant Secretary for Regional Programs vvv 00G01.T 77o INTRODUCTION The burden of proving noncompliance falls upon OSH A. Since all methods of measuremen! have inherent errors it is necessary that lhe results obtained by sampling be greater Ilian the standard in order for it to be cer tain. beyond reasonable doubt, that noncom pliance exists. This chapter applies the clas sical techniques of statistics to the specific situations which occur in environmental mea surements so as to enable decisions of noneomo'.iance to be made at stated levels of certainly. Sampling and analytical methods have er rors which are in general well known. In addition, when it is not possible to sample for I lie l ull period for which a standard is de fined, environmental variability causes vari ation, s among the individual sample results which must be considered in making decis ions at stated levels of certainty. The procedures in this chapter lead to the calculation of the 95% Lower Confidence Limit (LCL) of an occupational environmen tal sample or the arithmetic average of a group of such samples. This quantity, the LCL, must be greater than the applicable standard in order to be certain, with at least 95% confidence, that noncompliance exists. Die LCL is always lower than the sample or mean of samples. Thus, if the sample or mean of samples does not exceed the applicable standard it is not possible to be certain that mmcompliance exists and therefore no statis tical tests are necessary. Discussion of the theory underlying the various tests can be found in NIOSH TR-76. It ''hould be rioted that the standards used in the examples may not be current and refer ence should always be made to the most cur rent regulation for the appropriate standard be used in these statistical tests. 1 he statistical procedures, presented`below wj|] not detect and do not allow for analysis <>( highly inaccurate results, i.e.. systematic U.-mr.iml.iin) errors or mistakes, lhc detac5(,'n :i"d elimination of mistakes, which is pim.irily ;i technical rather than a statistical problem is covered in other chapters of the manual, In general, to assure accurate results it is necessary to have an instrument calibra tion program and a quulityj control program for laboratory analysis. Systematic errors must also be known ahead, of time whether from the instrument calibration procedure or the laboratory quality control program. If a constant systematic error is known to exist in an instrument or analytical procedure the sample mean of the daita should be cor rected before analyzing for noncompliance. Procedures for Data Analysis One or several consecutive samples taken for the entire lime period for which a stand ard is defined yields an estimate of the true average concentration of the airborne con taminant which is free from the effects of environmental variability. This type of sample is referred to as a "Full-Period Sample". A full-period sample yields an air concentration estimate with the best (narrowest) confi dence limits. Typically, a full-period sample would have to be only 10 to 35% above the standard in order to demonstrate noncompli ance with 95% confidence. The "Full-Period Sample" procedure is used; to calculate the 95% Lower Confidence Limit (LCL) for this type of sample. If several consecutive sam ples are taken for the entire time period of a standard the "Consecutive Full-Period Sam ples" procedure is used to Calculate the 95% Lower Confidence Limit (LCL) for the arith metic mean of the samples The greater the number of consecutive samipies, the less the mean of those samples has to bo above the standard in order to demonstrate noncom pliance. Thus, it is better to take two con secutive 4-hour samples than one 8-hcur sam ple and better yet to take four consecutive 2-hour samples during an $-hour period for which a standard is defined. In some cases it isn't possible lo take the samplers) for the entire period of the stand ard. if one samples for four to almost eight horns lor an 8-hour standard, the sample(s) is referred to as a "Partial Period" samplc(s). The samplers) is analyzed inuhe same manner as a full-period sample(s). but the standard VW 0000177 must be increased by a technique given at the end of the "Consecutive Full-Period Sample" procedure. Finally, if long term (greater than one hour) samples are not practical one must estimate the average air concentration by several short term or grab samples. The suit able number of grab samples is about four to seven and the mean of these samples typi cally may have to be as high as 1.8 to 2.8 times the standard in order to demonstrate noncompliance. The "Grab Samples" pro cedure is used to calculate the LCL of the arithmetic mean of these samples. Samples taken for comparison to a TWA (time weighted average) standard should be taken in a random manner over tlie period of the standard. Full-Period Sample Procedure The following procedure should be used to determine noncompiiance with either an 8 hour average, ceiling or excursion standard when only one full period sample has been collected. For an 8 hour average standard the sample must have been taken for the en tire period for which the standard is defined. The variability (standard deviation a or co efficient of variation C.V.) of the sampling and analytical methods used to collect and analyze the sample must be well known from previous measurements. The statistical test given is a one-sided comparison of means test using the t-distribution at the 95% con fidence level. Only if the LCL of the sample exceeds the standard are we at least 95% confident that the true average concentration exceeds the standard and that a condition of noncompli ance exists. LCL = x - 1.645 a where 1.645= critical standard normal devi ate for 95% confidence. a = standard deviation of sampling/analytical method which is well known from prior data. x = measurement being tested. If the coefficient of variation (C.V.) is known the LCL is computed from: LCL = x - (1.645) (C.V.) (Standard) Figure ! can be used to aid this calculation. Some coefficients of variation are available from Table 1. TABLE 1. COEFFICIENTS OF VARIATION FOR SOME SAMPLING/ANALYTICAL PROCEDURES! SAMPUNG/ANALYTICAL j Colorimetric Detector Tubes Rotameter on Personal Pumps i Charcoal Tubes (Sampling/Analyt|ica!} Asbestos (Sampling/Counting) Respirable Dust (Sampling/Weighi|ng) Gross Oust (Sampling/Weighing) i C.V. 14% 5% 10% 22% 8% 5% Consecutive Full-Period Samples Procedure The following procedure should be used to determine noncompliance with either an S hour average ceiling or excursion standard when several consecutive sa mples are taken for the entire time period for which the standard is defined. The variabilit / (standard devi ation or coefficient of variation) of the sam pling and analytical methods used to collect and analyze the samples mint be well known from previous measurements. The statistical test given is a one-sided comparison of means test using the t-distribution fidence level. Only if fhe LCL of the mean of the con secutive samples exceeds the standard arc we at least 95% confident that the true average concentration exceeds the s tandard and that a condition of noncompliance exists. LCL = x - 1.645 a/Cn),/j where x - mean of the cbnsecutive measurements. n = number of consecutive measurements. o = standard deviation of sampling/ analytical method which is well known from prior data. 1.645 = critical standard normal deviate for 95% confidence. If the coefficient of variation (C.V.) is known the LCL is computed from: LCL = x - [(L645)(C.V.)($tandard)/'(n)'/` ] Figure 1 can be used to aid this calculation. Some coefficients of variati on are available from Table f. One or a series of consecutive samples col lected over less than the period for which a standard is defined is referred to as a "Par tial Period" sumple(s). Since it is known with VVV 00l777a certainty that the concentration during the period not covered by the sample could not be less than zero, the 8 hour average standard is multiplied by the following factor to ob tain a partial period limit. The LCl is then calculated and compared to the partial period limit. (time period of the standard) Factor -i(actual time or the sampTlcT(sT)T) For an 8-hour standard typical factors would be: TOTAL TIME OF SAMPLEIS! FACTOR 8.00 hours 1.000 7.75 1.032 7.50 1.067 7.25 1.103 7.00 1.143 6.75 1.185 6.50 1.231 6.25 1.280 6.00 1.333 See Example 45 for the use of the above technique. Grab Samples Procedure The following procedure is tried to deter mine noncouipiiuncc with an 8 hour average standard from data based on short period samples collected in an unbiased manner dur ing the period of exposure. The variability (standard deviation! of the data is assumed unknown. The statistical test presented is for determining if the 95% lower confidence limit (LCL) of the arirhmerric mean (from a log-normal distribution) exceeds the standard. Only if (he LCL exceeds the standard are we at least 957o confident that the true aver age concentration exceeds the standard and that a condition of noncotnpliance exists. log to LCL = * ,' + GM factor where x = arithmetic mean of log10 trans formation of original data. s, = standard deviation of logl0 trans formation of original data. n = number of samples taken at ran dom intervals during the exposure period. t = the critical Student t-value for 95"T confidence as obtained from Table 2. GM factor = correction factor obtained from Fig. 2. NOTE: when samples are analyzed by this procedure one cannot have a zero in the data since one cannot take the log of zero. If this occurs the lowest detectable limit for the analytical method must jbe entered in the data table instead of the zero value. TABLE 2. STUDENT T-VALUES FOR 95% CONFIDENCE nt n t i rt t 2 6.314 10 1.833 18 1.740 3 2.920 4 2.353 5 2.132 11 1.812 19 1.734 12 1.796 20 1.729 13 1.782 ! 21 1.725 6 2.015 14 1.771 22 1.721 7 1.943 15 1.761 23 1.717 8 1.895 16 1.753 24 1.714 9 1.860 17 1.746 25 1.711 30 1.699 The standard deviation of the logarithms of the original data (sj) can be computed from the following equation: where: xH = logl0 of each measurement X\f = square of log10 jof each measure ment. There are commercial calculators available which are programmed to do the above cal culation lor the standard deviation. The following steps are suggested: a. Arrange the measurements in a column and take log10 of each measurement. b. If the (s,) is being calculated by the a- bove equation square each log and place in a third column. i c. Take the sum of the original concentra tions (EXI) and the sum of the logs (EXn) if necessary. d. Compute the average o the logs (Xi) and the standard deviation of thd togs ls(). e. Look up the t-valuc in Table 2 and cal culate GM-factor from Fig. 12. f. Calculate the LCL or use Fig. 2. Note that on Fig. 2 we may have to add (or sub tract) an appropriate power of 10 to x> and divide lor multiply) LCL by the cime multi ple of 10 in order to fall wijthin live range ot the scales on the monograih- See Example I for how this is done. VV\/ 000i 777C.