Document bOxzopdgrgrLgYg9kZEKwKv76

STATISTICS IN COMPLIANCE Abstract Both in the sampling of the occupational environment and the decision making processes regarding compliance or noncompliance with mandatory exposure standards, appro priate statistical sampling plans and statistical decision criteria are utilized. Early attempts to apply statistical theory to the occupational health field are presented along with recent work by the National Institute for Occupational Safety and Health. Examples are presented of statistical sampling and decision plans promulgated as regulations by federal agencies. The differences between statistical theory for noncompliance (governmental enforcement agencies) and for compliance (employers) are discussed and practical considerations are presented. The selection of an appropriate level of risk for the statistical tests and the interaction between the pro tection levels afforded the employer and employee is discussed. Mandatory occupational health standards have been promulgated in the United States (29 CFR 1910.93) with the intent of most adequately insuring, to the extent feasible, that no em ployee will suffer material impairment of health or functional capacity. Presently, for asbestos and vinyl chloride, employers are charged with monitoring and measuring employee exposure at locations and intervals and in such a manner as may be necessary, for the protection of their employees. The employer must promptly notify any employee who has beer, or is being exposed to these toxic materials in concentrations which exceed those presexibed by the applicable occupational health standard and also must institute corrective action. Jr. addition, the National Institute for Occupational Safety and Health (NIOSH) is engaged in a joint project with the Occupa tional Safety and Health Administration {OSHA) which will ros'Tt in regulations' requiring monitoring of employee exposure to all the substances under 29 CFR 1910.93. With these mandatory health standards has come the reality of necessary governmental enforcement. Duncan^ has broadly defined enforcement as all those steps taken by a governmental agency to attain the desired level of quality. These steps for OSHA of the Department of Labor in enforcement under the Occupational Safety and Health Act of 1970 consist of administrative procedures, engineering judgement, court proceedings, and voluntary compliance programs. A simplistic legal approach toward the en forcement of these mandatory occupational health standards proceeds as follows. A sampling and analytical test method for the measurement of an employee's exposure , to a particular hazardous substance is de veloped. The test method is used to measure a particular employee's exposure. If that measurement exceeds the standard, there has been a violation of the law. This simple point of view neglects the number and dura tion of samples that were taken to estimate the employee's exposure. This approach also neglects the variability of the environment the samples were taken from and inter- and intra-laboratory variability of the analj'tical method. Finally, there is no consideration of how many samples will be required of the enforcement agency or the employer to attain a specified level of effectiveness for the sampling program. For example, if a compliance officer found an average air concentration of 105 ppm based on 5 samples at a location in a plant and the standard was 100 ppm, then bv the simple legal approach he would be obligated to issue a citation. Suppose the citation was Prepared by Nelson A. Leidel. DLCD/NIOSH, Cincinnati, Ohio, 7/74. AST 00023700 209 Statistics in Com nil an c e contested and the compliance officer was asked under cross examination if he was certain the standard had been exceeded. If he was aware of the statistics that underlie environmental sampling he would have to answer no and of course the citation would be dismissed Both the sampling of the occupational environ ment and the decision making processes re garding compliance or noncompliance with the mandatory health standards must be per formed utilizing appropriate, statistical sampling plans and statistical decision cri teria. Early proposals to apply statistical theory to the occupational health field will be presented along with recent work by NIOSH. The differences between statistical theory for noncompliance (governmental enforcement agencies) and for compliance (employers) will be discussed and statistical considerations presented. Tomlinson^) in 1957 applied the concept of sequential testing to the problem of compliance monitoring relevant to an average concentra tion standard in British coal mines. Tomlinson recognized the large within shift and shift-toshift variability of the average airborne dust concentration. Hoach^,4) introduced the con cept of utilizing the upper confidence limit on the arithmetic mean of a group of grab samples to determine the compliance status of an occupa tional environment. Roach, however, assumed a normal distribution for the samples and later work^) has shown that it is better to assume the lognormal distribution. Roach made the very important point that any sampling pro cedure, no matter how carefully performed, can only estimate the true average concentra tion that existed in the occupational environment. NIOSH first proposed the use of statistics for compliance mentioning in the carbon monoxide criteria document,^) The procedure given for grab sample, data was also based on the assumption of normally distributed data. Leidel and Busch^) of NIOSH have presented procedures for noncompliance monitoring which calculates the 95% lower confidence limit of the arithmetic average of a group of samples from the occupational environment. Both , normally and lognormally distributed data are considered. The procedures include recom mendations for the duration of samples and the optimum number of samples to be taken on a single day. The advantage of a fullperiod sample (or consecutive samples) over the mean of several grab samples is also demonstrated. There is considerable precedent in federal regulations for the inclusion and referencing of statistical methods in mandatory product and health standards. Methods have been given both for governmental enforcement and private industry compliance monitoring programs. The Consumer Product Safety Commission (CPSC) has included very specific sampling and decision plans in several of its product standards. The FF 4-72 Flammability Standard for Mattresses^ gives details for a manufacturer's compliance program and allows submission of alternate sampling plans by industry. The commission felt that these plans would protect the public against unreasonable risk and that they were reasonable, technologically practicable, and appropriate. These are goals that any sampling . and decision plan must achieve. The Commis sion accepted the concept that the enforcement agency must assume the burden of demonstrating noncompliance by showing, with a high level of statistical confidence, that noncompliance did in fact exist. The CPSC included a sequential sampling plan in its Test for Eye Irritants (16 CFR 1500.42) (see ref. 8) and a table for lot size, sample size, and failure rate for testing clacker balls in 16 CFR 1500.86 (see ref. 9). The U. S. Public Health Service has issued a Drinking Water Standard (4 2 CFR 72, Subpart J) that specified a minimum sampling frequency and a sequential decision plan. The Food and Drug Administration's eyeglass impact standards (21 CFR 3.84) state that manufactur er shall test a statistically significant number of lenses from each production batch. In the field of industrial hygiene, NIOSH re quires that manufacturers of certified gas detector tube units must maintain a quality control program based on MIL-STD-105D or 414 (42 CFR 84), The Institute's certifica tion procedures are based on these sampling plans. The Institute has also proposed that these plans be used for certification of personal protective devices (42 CFR 83) (see ref. 10), 210 AS I 00023701 Statistics in Compliance It appears that the Environmental Protection Agency (EPA) has never included or ref erenced statistical data analytical techniques in air quality or water quality regulations. However, Larsen cf EPA has discussed the ' problem in an EPA technical report. Recently Russell Train, EPA Administrator, has expressed a desire to see standard statistical techniques for determining the validity of sample results become common to environmental standard;.. ^ -0 He felt that methodology of statistical quality control charts has a place in environmental quality control. When we come to the practical application of statistical techniques to compliance moni toring, a clear distinction must be made between compliance statistics (for the em ployer) and noncompliance statistics (for the government enforcement agency). The government has to meet the substantial evidence test and has the burden of proving that a health standard has been exceeded on a particular day. This is because the health standards are either average exposure stan dards defined for an 8-hour averaging period or ceiling exposure standards which at no time shall be exceeded (29 CFR 1910.93). Leidel and Busch^) have recommended that the 55% lower confidence limit on the measured average concentration must exceed the stan dard before a decision of noncompliance is reached. This criterion is presently under consideration by OSHA and is shown in Figure 1. Each employer is require-! to furnish to each cf hir, employees a place of employee free from recognized hazards likely to cause death or serious injury. The employer must make decisions regarding his exposure measurements in such a manner that he is confident that there ir no employee whose average exposure exceeds the average ex posure standards and that no employee expo sure will at any time exceed the ceiling exposure standards. Exposure data taken on one day or over a period of many days is best discussed by Gale(13) and later by Jones |md Brief.( Figure 2 shows several possible ways that tup employe* mialyze hL, exposure data. A'typical geometric standard deviation (GSD) of 2. S was assumed for the environmental variability^'5' from which the family of lines A, B, and C were generated. Line A represents a maximum limit if the employer decided not to let the average measured exposure exceed an a/erage exposure standard of 200 ppm. However, using line A there is a 50% probability of the true average exposure exceeding 200 ppm. A proposed alternative is line B which repre sents a data line based on 30 samples where the 95% upper confidence limit (95% UCL) is set at 200 ppm. By using this line as a data boundary the employer is 95% confident that the true average exposure will not exceed a 200 ppm standard. Note that the measured mean of 30 samples must be kept at 148 ppm (about 3/4 of the standard) in order to be 9 5% confident that the standard is not exceeded by the true mean. Decisions regarding a ceiling exposure standard arc rea thed differently. Line C of Figure 2 shows a possible decision line for a ceiling exposure standard of 200 ppm. This line theoretically allows 2% of the exposures to exceed the "absolute" ceiling standard of 200 ppm. Of course this analysis assumes the exposure data perfectly fits the theoreti cal lognormal distribution. In reality, many cumulative exposure curves effectively trun cate at higher concentrations and for line C the actual number of exposures exceeding the 200 ppm ceiling standard is probably much less than the predicted 2%. However, this probability cannot be calculated. Earlier the term "95% confidence level" was introduced in reference to statistical testing. This term arises from the choice of a 5% risk level for the statistical test to be used. The clear advantage of using statistical tests for the decision process regarding exposure standards is that the maximum desired risk levels can be selected in advance and proba bility curves can be calculated. Bartlett and Provost(l6) have shown how standards, tolerances, and risk levels can be inter preted in up to five different ways. Employ ers, government inspectors, and employees can all interpret standard in different ways. The interDretations involve sample size, c nose a ri.sk levels, aim / i e jV' - criteria. AS I 00023702 211 A way of illustrating the various intt-rpn tu- *inn is thruurh thi* pf>yf>r- function (['(') r-urvr-s [<: u;i> ,'i re's'., / jg'i: v .< t, . ., itauveiy shows tilt* KP curve for a type of noncompliance test recommended by Leidei and Busch^ for government agencies. The criterion is that no citation should be issued unless the 95% lower confidence-limit (LCL) of the measured mean exceeds the standard. Can the employer state he will be wrongly cited 5% of the time? Certainly not. Only if the true average con centration in his plant is just at or slightly below the standard is there a 5% chance of an unjust citation and this probability drops to essentially zero for true average concen trations under the standard. The term "5% risk level" refers to the specific case of a 5% risk of declaring noncompliance when the true average concentrations is exactly equal to the standard. The term has no meaning anywhere else on the PF curve. An example demonstrating the use of Figure 3 involves sampling consecutively for 8 hours with three charcoal tubes. The substance involved is MEK (2-butanone) with a Federal Standard of 200 ppm average concentration. By the methods of Leidei and Busch^ a citation should not be issued until the meas ured mean of the three samples exceeded the 200 ppm standard by at least 19 ppm. Note that a measured mean is only an esti mate of the true mean. If the true mean happened to be 219 ppm there would be only a 50% chance of the employer being cited! The employee might feel that this provided him with an inadequate level of protection, However} the employer could possibly argue that the choice by the government of a 5% risk levei test does not provide him suffi cient prelection against an unjust citation if the true plant concentration is at or slightly below the standard. The employer could propose that the government use a i% risk level test and Figure 4 illustrates the effect of this proposal. The probability of a cita tion for a true case of noncompliance where the true concentration exceeds the standard decreases markedly. For the MEK example given above, where the true average air concentration was 219 ppm, the probability of the government declaring noncompliance drops to about 26% compared to 50% for the 5% risk test. Thus, when the employer's risk is decreased the protection afforded the employee is markedly decreased. 212 What is trie interaction of risk levels for an FP curve lor tne type of employer sampling plan represented by Line B of Figure 2. The employer would decide that his plant is in compliance only if the 95% upper confi dence limit (UCL) of the measured mean is below the standard. Thus, for a true noncompliance situation where the true average concentrations are slightly above the standard, there is a 5% or less chance of the employer deciding that his plant is in compliance. In conclusion, we have seen the necessity for using statistical sampling plans and decision theory both in the sampling of the occupational environment and as part of the decision making processes regarding com pliance or noncompliance with mandatory health exposure standards. The use of statistical tests means that maximum de sired risk levels can be selected in advance and the burden of the sampling program minimized. The selection of a 5% level for both compliance and noncompliance tests is appropriate in that it protects both the employer and employee against unreasonable risk. There is considerable precedent in federal regulations for the use of statistical methodology in compliance enforcement and NIOSH will continue to advocate the use of statistics in this area. ACKNOWLEDGE MENTS The suggestions and contributions of Kenneth Busch, Lorice Ede, William Kelley, and Jeremiah Lynch to this paper are gratefully acknowledged. REFERENCES 1 Duncan, A. J.: Enforcement of Govern ment Mandatory Product Standards, ASTM Standardization News. 2. (No. 4), 12-15 (1974). 2 Tomlinson, R. C.: A Simple Sequential Procedure to Test Whether Average Con ditions Achieve a Certain Standard, Applied Statistics. j6, 198-207 (1957). 3 Roach, S. A.: Testing Compliance with the ACGIH Threshold Limit Values for Respirable Dusts Evaluated by Count, Trans. ACGIH. 27-39 (1966). AS I 00023703 Statistics in Compliance Roach, S. A. , Baier, E, F. , Ayer, H. E. , and R. L. Harris: Testing Compliance with Threshold Limit Values for Respir able Dusts, AT HA J. 23, 74-82 (1967). Occupational Exposure to Carbon Monox ide, NTOSH KSM 73-1100, VIII-2 (1972). Leidel, N. A., and Busch, K. A.: Statis tical Methods for the Determination of Noncornpliance with Occupational Health Standards, N'lOSH TR-76 (to be published 1974). Federal Register, J38 (No. 110), 1509515100(June 8, 1973). 8 Federal Register, 38 (No. 187), 27019 (September 27, 1973). 11 Larsen, R. I.: A Mathematical Model for Relating Air Quality Measurements to Air Quality Standards, AP-89 (1971). 12 Train, R. E.t The Need for Sound Standards for Environmental Improve ment, remarks given before the National Conference of Standards for Environmental Improvement, Washington, D. C, , February 20, 1974. 13 Gale, H. J.: Some Examples of the Application of the Lognormal Distribution in Radiation Protection, Ann. Occup. Hyg. Ifl, 39-45 (1967). 14 Jones, A. R. , and Brief, R, S.: Evaluating Benzene Exposures, AIHA J. 32. 610-613 (1971). 9 Federal Register, 38 (No. 187), 27027 15 Ayer, H. , and Berg, J.: Time-weighted (September 27, 1973), Average vs. Maximum Personal Sample, paper presented at the 1973 American 10 Federal Register, 39. 11923 (April 1, 1974). Industrial Hygiene Conference, Boston, May 25, 1973. 16 Bartlett, R. P. , and Provost, L. P.: Tolerances in Standards and Specifica tions, Qual. Progress. 14-19 (December 1973). ASI 00023704 213 Statistics in Compliance ?J FIG. 1 - COMPLIANCE AND NON COMPLIANCE SITUATIONS FOR TW TYPES OF SAVING STRATEGIES. Oil AS I 00023705 FIS. 2 - THREE DIFFERENT CONCEPTS FOR MAKING COMPLIANCE OETtWil.'lATIOrtS PROBAflJL.ITVI Of GQVERHf'EHT OlCLARJ(G PLANT Ifl NONCOfiPLIAXCE FIG. 3 - POO FUNCTION <Pf) CURVE FOR A IEST OF WKaWlIMCE AT THE 51 RISK LEVEL. FIG. A - POWER FUNCTION (PF) CURVE FOR A TEST OF IBNCOniANCE AT THE II RISK LEVEL. FIG. S - POKER FUNCTION (PF) CURVE FOR A TEST OF CtmiMCE AT THE 51 RISK LEVEL. ASI 00023706 215 CHAPTER 05B "T'/T) O Basdoj tj U L r? Crv^ rL.j.,LnJ *OfO-j)r^`<'{vViy)ut INTRODUCTION Chapter II discusses the considerations that mzy !;cd to the decision that there is suffi cient likelihood that a health standard is being violated to justify the collection of samples. When this decision is made it is necessary to devise a sampllns strategy for the particular situation which will permit a decision regarding noncompliance to be made as efficiently as possible. In the sense of a health standard, noncompliance means that the standard was exceeded for certain for the period appropriate to the standard on the occasion of the inspection. DECISION PROCESS The development of an appropriate sam pling strategy for a given situation requires decision* involving the following three factors: a. Location of the samples b. Period of the samples c. Number f samples These decisions are made within several con straints including the way the standard is defined, the particular work situation and the capabilities of the sampling and analytical methods. Selection of the exact sampling strategy within the range available for each of the factors should be made so as to optimize the likelihood of finding noncompliance if it exists with maximum efficiency in terms of field and laboratory effort. Thiir strategy takes into account the sam ple collection and analytical errors which are inevitable in any environmental measurement and the sampling error which will occur when random measuremen's of a varying environ ment arc made. ir. statistical terms a null hypothesis that the establishment is in com pliance is assumed. Samples axe the,; collected and the data analyzed to see if it is possible to reject this hypothesis with appropriate certainty. For this situation, the following concepts apply (See Fig. 1) The Type I error, which is a measure of any uncertainly that ; . !>?> in hit exist, should be kept as small as possible so that we are certain that noncompliance de cisions are correct. However, for a given en vironmental condition and measurement sys tem, the effect of reducing the Type I error is to increase the Type II error, that is, to increase the likelihood of not finding noncompliance when noncompliance does actu ally exist. For almost all industrial hygiene measurements Type II errors arc greater than Type I errors. For example, if the Type I error is held to 5%, the Type II error could be as large as 30% in some situations; re ducing the Type I error In this instance to 1% could result in a Type II error of a* much as 80%. Thus the Type I error must not be made unreasonably small since this resulta in a very large Type II error with consequent lack of protection to , the employee. The somewhat complicated statistical method* in Chapter VI have been chosen for the purpoae of minimizing Type II error for a given Type I error. In the selection of sampling strategy, it is important to use those methods, such as full period samples, which result in as low as pos sible Type II error so as to increase the likeli hood that compliance does exist when noncompliance is not found. LOCATION OF SAMPLES For most types of standards, with certain exceptions noted below, the location of the sample must be such as to yield a reliable estimate of the exposure of an employee. Personal Samples Direct exposure measurement ia most ef ficiently accomplished by attaching the sam- EVENT Cofpplltrc# Ho/y-ecmpHtnct C&nfittonc* NO anon FIND1NO NofXomfiUsnc* TYPE i axon TYPI II RftROU MO fftftOR Figure 1 217 II1-1 AS I 00023707 CHAPTER III--SAMPLING STRATEGY plmg device directly to the employee using a* * - * ' * ' * ' ) 4 , Ol ueiitxrsie t4it. w::h the sample are rare, it is important for the CSHO to keep the employee wearing the sampling device under sufficient observation to insure the validity of the sample. If tampering is sus pected the sample should be rejected. Hand Held Samples For certain substances there are at present no collection techniques which permit the use of personal samplers. In this case it is necessary to adopt the second alternative of following the employee as closely as possible holding the sample device inlet as close to the employee** breathing zone as possible. General Air Samples Those samples taken in the general work place at a fixed location somewhat independ ent of the movements of the employees are called general air samples and are permissible only when one of the following conditions is met. a. When it is reasonable to assume that essentially the same exposure exists 3t the sampling location as in the employee's breath ing zone. This may be the case, for example, when employees arc moving freely through out a workplace which contains many diffuse lources of air contaminant emission. b. When the standard is defined in terms of a general air concentration instead of the exposure of the employee. c. In certain special cases where additional material is needed for analtyica! purposes, luch as for the determination of percent quartz in the same atmosphere to which the employee is exposed. ): these cases, the em ployee's exposure is not determined by the fixed location sample but rather by a personal or breathing zone sample. The general sam ple is u;;.i only for tne purpose of determin ing the nature of the containment to which the employee ip exposed. It is important in this instance to be certain that the atmos phere in which the general air sampler is lo cated is the same atmosphere to which the employee is exposed. d. When a number of general air samplers can be located in such an array as to permit the calculation of an employee's exposure given the locations and times of movement of the employee whose exposure is bring EVf'lOYEE ELECTION The selection of the employee whose ex posure is to be measured is based on the initial concept that the object of the in spection is to determine as efficiently as pos sible if a state of noncompliance exists. For that reason the exposure of the employee who, based on the judgment of the industrial hygienist, is presumed to have the maximum risk in each exposure situation, is measured. When a number of exposure situations exist, resulting from different processes or emissions requiring different controls, a maxi mum risk employee should be selected for each situation in which noncompliance is likely. The exposure of other employees may also be pleasured so as to eliminate the possi bility that the maximum risk assumption was in error. It is not, however, necessary or ef ficient to measure the exposure of employees who are known to have lower exposures than those employees at maximum risk. Occasionally, the employee being sampled leaves the area of exposure for another area in which it is presumed that there is a low (or no) exposure. In this event several ap proaches could be taken. First, the sampler may be left on for the whole period including lunch or any other low exposure period since this will not affect the validity of the 8-hour average and it may happen that some expos ure occurred during this period. Alternatively the sampler may be removed during any peri od of assumed low exposure and then the average for the 8-hour period may be calcu lated assuming zero exposure during the un sampled period. EIGHT-HOUR AVERAGE STANDARDS The majority of the standards in the regu lations are for the average exposure of a worker over an 8-hour period. These stand ards are referred to as TWAs' although the time weighted average method of calculation may not be the preferred method of determining the 8-hour average. Full Period Single Sample When it is possible within the constraints of inspection time and sampling method available to collect a single sample represen- 218 M-2 ASX 00023708 CHAPTER lll~SAMPLING STRATEGY tativc of the employee's exposure over the full period for which the standard is defined, this sample is referred to as a full period sin* gle sample. It has the advantage that the en vironmental variance occurring during the sample period docs not influence the accu racy of the data since the sample is a direct measure of the entire period appropriate to the standard. A disadvantage is (hat it is more time consuming sim.e it is necessary to begin sampling at the beginning of a shift and continue to the end. Also, separate sam ples are necessary for the measurement of peaks. In general, the measurement (sampling and analytical) error associated with the sam pling method is known and as a consequence it is possible to obtain valid confidence limits in the result ofa single sample. If the measure ment error is not known, it may be necessary to devise a means of collecting simultaneous samples of the exposure of a single employee. Example; A personal sampling pump with a respirable dust sampling head is at lathed to an employee at the start of his shift at 7:00 a.m., turned off from 11:30 a.m to 12:00 p, m (lunch) and turned on again from 12:00 p.m. to 4:30 p.m. The sample col lected constitues a full period sample for the determination of quartz exposure. Full Period Consecutive Sample Even when it is not possible to collect a single sample over the full period for which the standard is defined, it may be possible to collect a series of consecutive samples which completely cover the entire period. The average of these samples weighted in pro portion to the sample period yield a result which is equiavlent to the full period single sample. The accuracy of such a result may be even greater than for a full period sample since rire collection of more than one con secutive sample has 'he result of reducing the effective sampling and analytical error. As in the case oi full period single samples the measurement error is generally known. When it is not, it may be determined by some simultaneous vamplinc Example. A rjunal samples are collet ted <>n an asbestos worker as follows: SAMPLE NO. 1 2 3 .4 5 - TIME 7:00 a.m. (Start of jhift)-8:00 a.m. 8:00 a.m.- 9:30 a.m. 9:30 a.m.-11:00 a.m. 11:00 a.m.- 1:00 p.m. (turned off and covered for 30 min. during tunch) 1:00 p.m.- 3:30 p.m. The time weighted average of (he results of these samples is a full period consecutive sample for asbestos. Partial Period Samples When time does not permit sampling over the full period for which the standard is de fined, it may be possible to make a determinrtion of noncompliance based on a partial period sample if the standard (See Chapter VI) is adjusted by a factor (Fig. 2). This factor is calculated from the certain know ledge that the concentration during the peri od not covered by the sample could not be less than zero. Thus, for an 8-hour standard of l mg/m3, a sample which yielded a result which indicated that 2 mg/mJ was certainly exceeded over a 4-hour sampling period would indicate noncompliance. Example: Collection of a personal sample for lead exposure was started at 9:00 a.m. and continued until the end of the shift at 3:00 p.m. The equivalent 6-hour standard for comparison with the mean of the result is ob tained by multiplying the 8-hour standard by the factor from Table 1. Grab Samples In some cases it is impossible, due to limi tations in such measurement methods as sound level meters or detector tubes, to collect either a single or a series of consecu tive samples whose duration approximates the period for which the . standard is defined. It is still possible to determine noncompli ance based on some number of short period Grab Samples taken in a random or unbiased fashion during the period appropriate to the <far !r.' Wt <- i tits-, m 'hod h applied the measurement system random error need not be known. However, since this method is subject to a large Type II error it is necessary b I pU I !k * r i II1-3 219 i ASI 00023709 CHAPTER III--SAMPLING STRATEGY that the standard ne exceeded by a consider able amount in order to make a decision that noncornpliar.ee exists. Since the duration of such giXib samples is unrelated to the period of the standard, some choice of sampling period is possible. The minimum sampling duration given in Chapter V is determined by the sensitivity ol the analytical method. Simple durations longer than minimum yield little advantage since a sample as much as 10 times as long as tne minimum sample would reduce the variance by less than 30 percent. This is, of course, assuming that it is not possible to take samples long enough to ap ply the full period consecutive or partial period sampling schemes. As the number of samples collected in this procedure increase, the ratio of the average of the samples to the standard, required to arrive at a decision of noncompliance, decreases. These ratios are shown in Fig. 3. As can be seen, consider able improvement is obtained by taking at least four samples but rather little additional improvement is accomplished beyond seven or eight samples. Therefore, in general, the optimum number of short period samples is between four and seven. Below four samples the sample average must be so far above the standard as to result in an unnecessarily con servative judgment of noncompliance where as above seven samples the small decrease in variability obtained is not normally justified when compared to the time and effort re quired to obtain and analyze additional sam ples. This leads to a statistical criterion which economizes on sampling for a given degree of contidenee. Grab samples should be collected over the period for wrack the standard is defined at random intervals. This is accomplished by dividing the diy into periods equal to the sample duration and selecting, from this s, r.edule of possible sampling occasions, the intervals ?l wh>;h the four to seven u;` what ever number of samples are tu be collected, by some random process as, for example, a table of random numbers. Results from random sampling by this method are valid even when cycles or trends occur during the period of the standard. It is valid to sample at equal intervals, for example, once every half-hour or every hour, if there is reason to believe that tire mean concentration in the workplace is constant, that is, that the con taminant levels m the workplace vary ran domly about a constant mean and that fluctu ations are of short duration relative to the duration of the sample. When this assumption cannot be made the random sample period selection process should be used. If it is not possible to collect samples at random inter vals over the entire work day, the result cal culated from the grab sample procedure may be interpreted as in the case of the par tial period sample. Alternatively professional judgment regarding the concentrations oc curring in the unsampled portion of the day could be applied. Example: It is necessary to evaluate pos sible noncompliance with the standard for phosgene using detector tubes. Each detector tube sample takes five minutes to collect. It is Intended to collect 10 samples out of the possible 96 samples in the eight-hour period. a. The starting random number of 70 (col IS, row 26) is selected from the table of ran dom numbers (Table I) by making a pencil mark on the page without looking. b. The following 10 numbers were selected by reading vertically down and excluding all numbers of 96 and any duplicates. 70, 22, 34, 75, 67. 25. 74, 73. 31. 96. c. Number the 5-minute intervals during the eight-hour period 1-96 and sample during the periods with the 10 numbers selected. The mean of these 10 results may be ana lyzed by the procedure for grab samples given in Chapter VI. Time Weighted Sampling In certain instances, where the process has a very definite cycle of a period longer than the sampling period and it is possible to make the assumption with certainty that the air contaminant concentrations are varying with the cycle and only random variations are occurring within- phases of the cycle, it is possible to apply the following formula to the determination to the ,8-hour average. ,,_C,T, + C2T2 -C,,T,, 8 where Tn = time period of a phase of the cycle (Note XT,, = 8 hours; C,, = mean concentration of the con taminant during time period T,,. 220 AS I 00023710 ill-4 CHAPTER 111--SAMPLING STRATEGY In the application of thi1; formula it is neces sary to treat each consecutive time period T,, as the period for which tire standard is denned. The procedures !. 2, 3 or 4 as ap propriate may then be used in each period Tn to determine the concentrations Cn. That is, if only short period samples were possible and four 2-hour phases were defined by the process, then some number, preferably be tween 4 and 7, short samples could be taken during each of these 2-hours phases to deter mine the concentration during each phase and its associated lower confidence limits. The formula could then be used to determine -hour average concentration from these val ues and statistical procedures which are be yond the scope of this manual could be used to calculate the lower confidence limit of this 8-hour average. The practical application of this time-weighted sampling procedure is much more complicated than the use of either procedures 1, 2 or 3 and only rarely is it an improvement upon the procedure described in 4 above: Example. A plastic casting operating is observed to have the following schedule: TIME PHASE 7:00 a.m.- 9:00 s.im. 9:00 a.m,-10:30 a.m. 10:30 a.m.-11:00 a.m. 11:0Q a,rr\ H:30 a.m. 11:30 a.m,- 1:30 p.m. 1:30 p.m.* 3:00 p.m. 3:00 p.m.- 3:30 p.m. Mixing Casting Cleanup Lunch Mixing Casting Cleanup If it is possible to assume that the nonrandom variations tn the concentrations of allyl glycidyl ether occur only from phase to phase, then the TWA method may be used. a. Collect four grab samples randomly dur ing each phase (mixing, casting, cleanup) for a total of 21 samples. b. Calculate the mean of each phase. c. C'Jculate the average concentration for the eight-hour period from d. Special statistical procedures, nor given here, are required to after:;.me the .toeer <.on- Jm. n,f . p r C 11 Li riot ,hjt th,S conjideme limit will be much smaller than that obtained by taking a smaller number of samples at random over the whole eight-hour period. A much tighter lower confidence limit could be obtained if it were possible to take longer samples and use either the full or par tial period strategies. SHORT PERIOD STANDARDS For some standards a short period limit of usually less than one hour is defined. These standards include the ceiling limits, certain standards for which both an 8-hour average and an excursion or short-term limit is defined and certain peak limits for which no time period is defined. In order to insure uni formity in the determination of noncompli ance in the case of those standards for which no sampling period is defined, the minimum sampling time as given in Chapter V should be used. In all cases the interpretation of a short period standard is that noncompliance exists when the standard has been exceeded for the period for which it is defined or some longer period, when both short and long period standards are defined for a given substance, a sampling strategy should be adopted which allows for the evaluation of both. The selection of the location at which the sample should be collected for short-period limits is the same as for 8-hour average limits in that the exposure of the employee must be measured either directly or indirectly unless the standard is set in terms of general work place concentration, and the employee whose exposure is measured should be selected from among the maximum risk employees. In addi tion to these criteria for selection of the loca tion, the sample should be collected at a time when the maximum exposure is presumed to occur. Since short period limits are rarely defined for periods of more than 30 minutes, the pro cedures described under Full Period Single Sample and Full Period Consecutive Sample for 8-hour average standards may almost always be used and the Partial Period Sample and Grab Sample techniques are rarely if ever necessary. The time weighted average pro cedure described under Time Weighted Sam pling is nut applicable. AST 00023711 1II-5 221 CHAPTER 1II--SAMPLING STRATEGY TABLE 1 SHORT TABLE OB RANDOM NUMBERS 05 57 23 06 25 23 08 66 16 11 75 2S 81 56 14 62 82 45 65 80 36 02 76 55 63 >j > 78 16 06 Cl ! 12 4 6 <V> 50 73 67 39 r-r, ,"*7 00 51 02 07 16 75 12 SO 41 16 23 71 15 03 i 04 87 29 01 20 46 72 05 SO 15 27 47 15 76 51 0 67 05 80 t: <4^ 42 67 98 41 67 44 28 71 4 5 08 19 47 76 30 26 72 33 69 92 51 95 23 26 85 76 05 3 03 84 22 62 S3 27 4S S3 09 19 1 90 20 20 50 87 74 93 51 62 10 23 30 CO 46 18 41 23 74 73 51 72 90 40 S'7 93 41 20 89 48 93 27 33 81 33 83 82 94 S2 54 75 91 9S 03 40 64 89 29 99 46 3 5 69 91 50 73 75 92 90 56 82 93 24 79 5 53 77 7 8 05 62 f>7 48 82 71 00 73 21 65 65 S3 45 S2 44 78 93 22 78 09 <5 3 3 23 32 0! 09 46 35 43 66 37 15 35 04 SS 79 S3 53 19 13 91 59 81 81 87 20 60 57 43 21 41 84 22 7 n 77 99 SI S3 30 4 6 15 SO 26 51 73 66 34 99 40 60 67 91 44 83 43 25 56 33 28 80 99 53 oh- A1 56 19 80 76 32 53 95 07 53 09 61 98 6 50 76 93 86 35 68 4 5 37 S3 47 44 92 57 66 59 64 16 48 39 26 94 54 66 40 65 73 3S 3S 23 35 10 95 16 01 10 01 59 71 55 59 24 88 31 41 00 73 13 80' 62 55 n 50 29 17 73 97 04 :o 39 20 22 71 11 43 00 15 10 12 35 09 11 00 89 05 23 54 33 S7 ?2 92 04 49 73 95 57 53 57 OS 93 09 69 87 83 07 45 39 50 37 85 41 4S 67 79 44 57 40 29 10 34 58 63 51 18 07 41 02 39 79 14 40 63 10 01 61 03 97 71 72 43 27 36 24 59 88 82 87 26 31 11 44 28 58 99 47 83 21 35 22 88 90 24 83 43 07 41 56 SS 1! 14 77 75 48 68 08 90 89 63 87 00 06 18 63 21 91 S3 98 37 42 27 11 SO 51 13 13 03 42 91 14 51 22 15 48 67 52 09 40 34 SO 85 74 20 94 21 49 SS 51 69 99 85 43 7 6 55 81 36 11 88 68 32 43 03 14 78 05 34 94 67 48 87 11 84 00 85 93 56 43 99 21 74 84 13 56 41 90 96 30 04 19 63 73 S3 18 S4 82 71 23 66 33 19 25 65 17 90 84 24 91 75 36 14 83 86 22 70 86 89 31 47 28 24 88 49 23 69 78 62 23 45 53 38 78 65 87 44 91 93 91 62 76 09 20 45 62 31 06 70 92 73 27 83 57 15 64 40 57 56 54 42 35 40 93 55 82 08 78 87 31 49 87 12 27 41 07 91 72 64 63 42 06 66 82 71 28 36 45 31 99 01 03 35 76 69 37 22 23 46 10 75 83 62 94 44 65 46 3 65 71 69 20 89 12 15 56 81 70 41 S3 67 21 56 93 42 52 53 14 86 24 70 25 28 23 23 56 24 03 86 11 06 46 10 23 77 56 18 37 01 32 20 13 70 79 20 85 77 89 23 17 77 15 52 ** A< IS 30 35 12 75 37 07 47 79 CO 75 24 15 31 63 25 93 27 66 19 53 52 49 98 45 12 12 06 00 32 72 08 71 01 73 46 39 60 37 58 22 25 20 84 30 02 03 62 68 58 38 04 06 89 94 55 22 48 46 72 .50 14 24 47 67 84 37 32 84 82 64 97 13 69 86 20 09 80 46 75 69 24 98 90 70 29 34 25 33 23 12 69 90 50 38 93 84 32 28 96 03 65 70 90 12 01 86 77 13 21 31 6$ 11 S4 65 48 75 26 94 51 40 51 53 36 39 77 69 06 25 07 51 40 94 05 80 61 34 2S 46 28 11 48 4S 94 so 65 06 63 71 06 19 35 05 32 58 53 78 02 85 80 29 67 27 44 07 67 23 20 28 22 62 97 59 62 13 41 72 70 71 07 33 75 83 11 00 33 63 15 84 34 23 50 16 65 12 81 56 43 54 14 63 37 74 97 69 53 SO 37 45 2 09 95 S3 IS 59 35 22 91 78 04 97 C3 80 20 01 33 93 13 92 30 72 13 12 55 32 87 59 32 ^3 65 40 17 92 57 rt<7 63 33 79 18 23 53 56 56 07 47 ->** ' 1 13 16 1 0 .rJ A, 57 71 40 49 95 25 55 35 95 57 25 25 77 05 38 05 62 57 77 97 94 83 67 50 68 74 58 17 oi,oi. 33 01 04 33 49 38 47 57 61 37 15 39 43 87 00 09 03 63 53 n At. A if 27 MJ 86 53 39 34 S3 87 04 35 80 69 52 74 99 18 52 01 85 77 9 7 61 42 65 05 72 27 28 IS 09 85 24 59 46 03 91 55 33 62 51 71 47 37 33 ?i *8 73 90 4 V 41 3S *1 /* 32 03 03 j-j 26 72 85 23 22 30 70 51 53 93 23 54 80 41 C_ 20 7 A 2 ! 57 57 00 47 20 10 87 2 45 72 03 51 75 23 33 38 56 77 97 05 A^ O4 12 1 r' OS 02 13 7< 55 :s 21 53 63 41 77 15 07 39 87 11 13 25 62 19 30 33 77 60 29 09 25 03 42 23 07 15 40 67 5S 29 58 75 &4 OS 19 54 31 16 53 54 13 39 19 25 01 97 73 71 61 73 03 21 02 93 SS 63 76 74 23 ca 98 84 08 3 75 16 85 64 04 93 SS 63 03 84 15 41 57 84 45 11 70 13 17 CO 47 80 10 13 00 35 <7 17 03 79 C3 32 c5 13 <2 95 48 27 37 93 53 81 94 44 72 06 95 42 31 17 29 61 03 21 91 23 76 72 4 93 26 23 66 54 SS 83 95 14 82 57 17 99 16 23 99 222 III-6 AS 1 00023712 C'riA*-' t Hi C/.f.-r>L!f-:G STRATEGY 1 '7 J +1 J 1 --J 1 1 1 j 1 FIGURE 2 NUMBER OF SAMPLES TOTAL SAMPLE TIME/HOURS III-7 AS I 00023713 223