Journal of the ICRU Vol 6 No 2 (2006) Report 76 Oxford University Press
3
doi:10.1093/jicru/ndl028
MEASUREMENT QUALITY ASSURANCE
3.1 SPECIFICATION OF MEASUREMENT QUALITY
3.2 EFFECTS OF INFLUENCE QUANTITIES ON MEASUREMENT QUALITY The consistency or stability of measurements is dependent upon maintaining the stability of ambient conditions in the laboratory. Changes in a number of parameters can affect the quality of measurements, and the parameters that can produce such effects are referred to as influence quantities.
ktp ¼
273:15 þ Ta = C Pr · ; 273:15 þ Tr = C Pa
ð3:1Þ
where Ta is the ambient air temperature, Tr is the reference temperature, e.g., 20 C, Pr is the reference atmospheric pressure of 101.325 kPa and Pa is the ambient pressure (IAEA, 2000a).
3.3 METHODS FOR THE EVALUATION OF UNCERTAINTY The Guide to the Expression of Uncertainty in Measurement (ISO, 1995) recommends the use of standard uncertainties, which are evaluated in two ways that are classified as Type A and Type B. Once numerical values have been determined for these two types of uncertainties, no further distinction is made and the values can be combined. The Type A evaluation of standard uncertainty consists of determining the uncertainty by the statistical analysis of a series of observations. In this case the standard uncertainty is the experimental standard deviation
International Commission on Radiation Units and Measurements 2006
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The assurance, or verification, of the level of quality of measurements is essentially a three-step process. First, the acceptable uncertainty must be established, usually on the basis of a published standard or national regulation. Second, a facility must have procedures in place that will lead to performance within the specified uncertainty. Third, the facility must demonstrate its capability of performing measurements within the specified uncertainty. An additional related concept that follows from the third step is a plan for remedial action when a facility fails to perform within this specified uncertainty. Measurement quality can be evaluated using a variety of techniques. Perhaps the simplest method for evaluating the quality of a measurement is the direct comparison to a national standard. For instance, a working-level ionization chamber may be periodically compared with a reference or transfer standard that has in turn been compared with a national standard. If the value measured using the chamber agrees with the value measured using the reference standard chamber to within a specified uncertainty, then the measurement quality is assured. If the difference is greater than the expanded uncertainty (see Section 5.2) the cause of this difference should be investigated and appropriate remedial action taken. Until the discrepancy is resolved, no measurements should be used or disseminated. Any such measurement disseminated, but also affected by the discrepancy, shall be identified and appropriate action taken (e.g., informing the customer).
An influence quantity may have an effect on the result of a measurement without being the object of the measurement itself. Examples of influence quantities that can affect the uncertainty in ionizing radiation measurement are shown in Table 3.1, along with the reference conditions. The effects of influence quantities on the measurement should be assessed, and, if standard test conditions are specified, care should be taken to ensure that standard test conditions are met while measurements are performed (or appropriate corrections are made). Reference conditions are normally within the range of standard test conditions; however, it is not necessary to control ambient conditions to match the reference conditions. Factors can be applied to normalize measurement results to the reference conditions. For instance, the following formula can be used to compute a correction factor that is applied to correct the response of an ionization chamber, the collecting volume of which communicates with ambient air, to reference temperature and pressure conditions:
MEASUREMENT QUALITY ASSURANCE FOR IONIZING RADIATION DOSIMETRY Table 3.1. Some examples of influence quantities, reference conditions and standard test conditions for ionization chambers used for radiation therapy calibrations (IAEA, 2000a). Influence quantities
Reference conditions
Standard test conditions
Ambient temperature Relative humidity Atmospheric pressure Stabilization time Electromagnetic fields Radioactive contamination Radiation background
20 or 22 C 50 % 101.325 kPa 30 min Negligible Negligible 1.0 mGy/h
Reference ambient temperature –2 C 45–65 %a 86–103 kPaa >15 min 1), the estimate of the quantity Q is the arithmetic mean, q, or the average of the individual observed values qj ( j ¼ 1, 2, . . ., n). n 1X qj : q ¼ n j¼1
obtained from a limited number of observations. If in such a case the value of the input quantity Q is determined as the arithmetic mean q of a small number n of independent observations, the variance of the mean can be estimated by s2 ðqÞ ¼
ð3:4Þ
s2 ðqÞ ¼
1 n1
The Type B evaluation of standard uncertainty is the evaluation of the uncertainty associated with an estimate xi of an input quantity Xi by means other than the statistical analysis of a series of observations. The standard uncertainty u(xi) can be evaluated by scientific judgment based on all available information on the possible variability of Xi. Values belonging to this category can be derived from
ð3:5Þ
j¼1
and the positive square root of this expression is termed the experimental standard deviation. The best estimate of the variance of the arithmetic mean, q, is the experimental variance of the mean given by s2 ðqÞ ¼
s2 ðqÞ : n
previous measurement data; experience with or general knowledge of the behavior and properties of relevant materials and instruments; manufacturer’s specifications; data provided in calibration and other certificates; and uncertainties assigned to reference data taken from handbooks.
ð3:6Þ
The positive square root of this expression is termed the experimental standard deviation of the mean. The standard uncertainty, uð qÞ, associated with the input estimate q is the experimental standard deviation of the mean given by uðqÞ ¼ sðqÞ:
ð3:7Þ
The proper use of the available information for a Type B evaluation of standard uncertainty of measurement calls for insight based on experience. It is a skill that can be learned with practice. A well-based Type B evaluation of standard uncertainty can be as reliable as a Type A evaluation of standard uncertainty, especially in a measurement situation where a Type A evaluation is based only on a comparatively small number of statistically independent observations. The following cases are given as illustrative examples.
It must be noted that, when the number n of repeated measurements is low (n < 10), the reliability of a Type A evaluation of standard uncertainty, as expressed by Eq. (3.7), has to be considered. If the number of observations cannot be increased, other means of evaluating the standard uncertainty have to be considered, for example, using the t-distribution (Wadsworth, 1990) for the degrees of freedom. (b) For a measurement that is well characterized and under statistical control, a combined or pooled estimate of variance s2p is given as follows: PN ni s2i 2 ð3:8Þ sp ¼ Pi¼1 N i¼1 n i
(a) If only a single value is known for the quantity Xi, e.g., a single measured value, a resultant value of a previous measurement, a reference value from the literature, or a correction value, this value will be used for xi. The standard uncertainty u(xi) associated with xi is to be adopted where it is given. Otherwise it is calculated from unequivocal uncertainty data. If data of this kind are not available, the uncertainty has to be evaluated on the basis of experience.
can be calculated, where s2i is the experimental variance of the ith series of ni independent repeated observations and has vi ¼ ni 1 degrees of freedom. The combined or pooled estimate of variance can provide a better characterization of the dispersion than the estimated standard deviation 19
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3.3.2 Type B methods to evaluate the uncertainty
(a) An estimate of the variance of the underlying probability distribution is the experimental variance s2(q) of measured values qj that is given by 2 qj q :
ð3:9Þ
The standard uncertainty is deduced from this value using Eq. (3.7).
The uncertainty of measurement associated with the estimate q is evaluated according to one of the following methods:
n X
s2p : n
MEASUREMENT QUALITY ASSURANCE FOR IONIZING RADIATION DOSIMETRY
(b) When a probability distribution can be assumed for the quantity Xi, based on theory or experience, then the appropriate expectation or expected value and the square root of the variance of this distribution should be taken as the estimate xi and the associated standard uncertainty u(xi), respectively. (c) If only upper and lower limits aþ and a can be estimated for the value of the quantity Xi and the probability is essentially unity that the value lies within the interval (e.g., manufacturer’s specifications of a measuring instrument, a temperature range, and a rounding or truncation error resulting from automated data reduction), then a probability distribution with constant probability density between these limits (a rectangular probability distribution) should be assumed for the possible variability of the input quantity Xi. According to case (b) above this leads to
u2 ð xi Þ ¼
1 ðaþ aÞ2 12
For uncorrelated input quantities, the square of the standard uncertainty associated with the output estimate y is given by u2 ð yÞ ¼
1 u ð xi Þ ¼ a 2 : 3
u2i ð yÞ,
ð3:13Þ
i¼1
Note: There are cases, seldom occurring in calibration, when the model function is strongly nonlinear or some of the sensitivity coefficients [see Eqs. (3.14) and (3.15)] vanish and higher order terms have to be included into Eq. (3.13). For a treatment of such special cases see ISO (1995). The quantity ui(y) (i ¼ 1, 2, . . . , N) is the contribution to the standard uncertainty associated with the output estimate y resulting from the standard uncertainty associated with the input estimate xi ui ð yÞ ¼ ci uðxi Þ,
ð3:10Þ
ð3:14Þ
where ci is the sensitivity coefficient associated with the input estimate xi, i.e., the partial derivative of the model function f with respect to Xi, evaluated at the input estimates xi,
ð3:11Þ
for the square of the standard uncertainty. If the difference between the limiting values is denoted by 2a, then Eq. (3.11) becomes 2
N X
ci ¼
@f @f ¼ : @xi @Xi x1 ;x2 ;...;xN
ð3:15Þ
The sensitivity coefficient ci describes the extent to which the output estimate y is influenced by variations of the input estimate xi. It can be evaluated from the model function, f, by Eq. (3.14) or by using numerical methods, i.e., by calculating the change in the output estimate y due to a change in the input estimate xi of þu(xi) and u(xi) and taking as the value of ci the resulting difference in y divided by 2u(xi). Sometimes it might be more appropriate to find the change in the output estimate y from an experiment by repeating the measurement at xi – u(xi) for example. Whereas u(xi) is always positive, the contribution ui(y) according to Eq. (3.14) is either positive or negative, depending on the sign of the sensitivity coefficient ci. The sign of ui(y) has to be taken into account in the case of correlated input quantities. If the model function f is a sum or difference of the input quantities Xi
ð3:12Þ
For example, the value of the radiation-chemical yield for the ferrous sulphate dosimeter system can be given as G ¼ 1.624 mol kg1 Gy1, and it is stated that the error in this value should not exceed 1.624 · 102 mol kg1 Gy1. It would be reasonable to assume that the true value of G lies with equal probability within the range from 1.608 to 1.640 mol kg1 Gy1, and this would represent a symmetric rectangular distribution. Following the discussion in case (b) above, the rectangular distribution is a reasonable description in probability terms of one’s inadequate knowledge about the input quantity Xi in the absence of any other information than its limits of variability. However, if it is known that values of the quantity in question near the center of the variability interval are more likely than values close to the limits, a triangular or normal distribution might be a better model. On the other hand, if values close to the limits are more likely than values near the center, a U-shaped distribution might be more appropriate.
f ðX 1 ; X 2 , . . . , X N Þ ¼
N X
pi Xi ,
ð3:16Þ
i¼1
then the output estimate according to Eq. (3.3) is given by the corresponding sum or difference of the 20
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1 xi ¼ ðaþ þ aÞ 2 for the estimated value and
3.3.3 Calculation of the standard uncertainty of the output estimate
MEASURMENT QUALITY ASSURANCE input estimates y¼
N X
correlations between input quantities could lead to an incorrect evaluation of the standard uncertainty of the measurand. The covariance associated with the estimates of two input quantities Xi and Xk can be taken to be zero or treated as insignificant under the following conditions.
ð3:17Þ
p i xi ,
i¼1
whereas the sensitivity coefficients equal pi and Eq. (3.13) converts to u2 ð y Þ ¼
N X
p2i u2 ðxi Þ:
i¼1
If the model function f is a product or quotient of the input quantities Xi N Y Xipi ;
f ðX1 ; X2 , . . . , XN Þ ¼ b
ð3:19Þ
i¼1
with b being a given constant, the output estimate again is the corresponding product or quotient of the input estimates N Y
y¼b
xpi i :
Sometimes correlations can be eliminated by a proper choice of the model function. The uncertainty analysis for a measurement (sometimes called the uncertainty budget of the measurement) should include a list of all sources of uncertainty together with the associated standard uncertainties of measurement and the methods of evaluating them. For repeated measurements, the number n of observations also has to be stated. For the sake of clarity, it is recommended to present the data relevant to this analysis in the form of a table. In this table all quantities should be referenced by a physical symbol Xi or a brief descriptor. For each of them, at least the estimate, xi, the associated standard uncertainty of measurement, u(xi), the sensitivity coefficient, ci , and the different uncertainty contributions, ui(y) , should be specified. The dimension of each of the quantities should also be stated with the numerical values given in the table. A generalized example of such an arrangement as given in Table 3.2, applicable for the case of uncorrelated input quantities, and Table 3.3 gives
ð3:20Þ
i¼1
The sensitivity coefficients equal ci ¼ piy/xi in this case, and an expression analogous to Eq. (3.16) is obtained from Eq. (3.13). If relative standard uncertainties w(y) ¼ u(y)/|y| and w(xi) ¼ u(xi)/|xi| are used, w2 ð yÞ ¼
N X
p2i w2 ðxi Þ:
ð3:21Þ
i¼1
If two input quantities Xi and Xk are correlated to some degree, i.e., if they are mutually dependent in one way or another, their covariance also has to be considered as a contribution to the uncertainty. The ISO Guide (ISO, 1995) should be consulted for this evaluation. The possibility of taking into account the effect of correlations depends on the knowledge of the measurement process and on the judgment of mutual dependence of the input quantities. In general, it should be kept in mind that neglecting
Table 3.2. Schematic representation of an ordered arrangement of the quantities, estimates, standard uncertainties, sensitivity coefficients, and uncertainty contributions used in the uncertainty analysis of a measurement with the model function Y ¼ f (X1, X2,. . ., XN). Quantity Xi
Estimate xi
Standard uncertainty u(xi)
Sensitivity coefficient ci
Contribution to the standard uncertainty ui(y)
Remark
X1 X2 : XN Y
x1 x2 : xN y
u(x1) u(x2) : u(xN) u(y)
c1 c2 : cN –
u1(y) u2(y) : uN(y) –
11 measurements Rectangular distribution : Triangular distribution u(y) is combined standard uncertainty
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(a) the input quantities Xi and Xk are independent, for example, because they have been repeatedly but not simultaneously observed in different independent experiments or because they represent resultant quantities of different evaluations that have been made independently; (b) either of the input quantities Xi and Xk can be treated as constant; and (c) investigation gives no information indicating the presence of correlation between the input quantities Xi and Xk.
ð3:18Þ
MEASUREMENT QUALITY ASSURANCE FOR IONIZING RADIATION DOSIMETRY Table 3.3. Example of an uncertainty budget of a measurement with the model function M ¼ k1k2k3IcorrkCf (see Section 2.1.1). Quantity Xi
Estimate xi
Standard uncertainty u(xi)
Sensitivity coefficient ci
Contribution to the standard uncertainty ui(y)
Remark
Icorr K Cf k1 k2 k3 M
3 nA 12 (mSv/h)/nA 1.27 1.0 1.0 1.0 45.7 mSv/h
0.07 nA 0.0 (mSv/h)/nA 0.031 0.27 0.06 0.08 13.2 mSv/h
15.2 (mSv/h)/nA 3.81 nA 36 mSv/h 45.7 mSv/h 45.7 mSv/h 45.7 mSv/h –
1.06 mSv/h 0.0 mSv/h 1.12 mSv/h 12.3 mSv/h 2.74 mSv/h 3.66 mSv/h –
11 measurements Fixed value, no uncertainty 15 measurements Correction for energy and angle Correction for nonlinearity Correction for temperature and pressure –
amounts, the conditions of the Central Limit Theorem (ISO, 1995) are met and the distribution of the output quantity is assumed to be normal. The reliability of the standard uncertainty assigned to the output estimate is determined by its effective degrees of freedom (see ISO, 1995). However, the reliability criterion is always met if none of the uncertainty contributions is obtained from a Type A evaluation based on less than 10 repeated observations. If one of these conditions (normality or sufficient reliability) is not fulfilled, the standard coverage factor k ¼ 2 can yield an expanded uncertainty corresponding to a level of confidence of less than 95 %. In these cases, in order to ensure that a value of the expanded uncertainty is quoted corresponding to the same level of confidence as in the normal case, other procedures have to be followed. The use of approximately the same level of confidence is essential whenever two results of measurement of the same quantity have to be compared, e.g., when evaluating the results of an inter-laboratory comparison or assessing compliance with a specification. Even if a normal distribution can be assumed, it might still occur that the standard uncertainty associated with the output estimate is of insufficient reliability. If, in this case, it is not expedient to increase the number n of repeated measurements or to use a Type B evaluation instead of the Type A evaluation of poor reliability, the method given in ISO, (1995) should be used (see also ISO, 2005). For the remaining cases, i.e., all cases where the assumption of a normal distribution cannot be justified, information on the actual probability distribution of the output estimate shall be used to obtain a value of the coverage factor k that corresponds to a level of confidence of approximately 95 %. For reports or calibration certificates, the complete result of the measurement consisting of the estimate y of the measurand and the associated
a specific example of an uncertainty budget. The standard uncertainty associated with the measurement result u(y) given in column 3 of the table is the square root of the sum of the squares of all the uncertainty contributions, u1(y), . . . , uN(y), in column 5. 3.3.4 Expanded uncertainty and coverage factor k Most applications for the measurement of ionizing radiation require the use of a measure of uncertainty that defines an interval about the measurement result, y, within which the value of the measurand, Y, will be found with high probability. For some applications, such as those in health and safety, an expanded uncertainty can be used to include a large fraction of values expected to represent the measurand. This interval is referred to as the expanded uncertainty of measurement, U, obtained by multiplying the standard uncertainty u(y) of the output estimate y by a coverage factor k, U ¼ k uð yÞ:
ð3:22Þ
In cases where a normal (Gaussian) distribution can be attributed to the measurand and the standard uncertainty associated with the output estimate has sufficient reliability, the coverage factor k ¼ 2 should be used. The assigned expanded uncertainty corresponds to a level of confidence of approximately 95 %. These conditions are fulfilled in the majority of cases encountered in calibration work. The assumption of a normal distribution cannot always be easily confirmed experimentally. However, in the cases where several (i.e., N 3) uncertainty components, derived from well-behaved probability distributions of independent quantities, e.g., normal distributions or rectangular distributions, contribute to the standard uncertainty associated with the output estimate by comparable 22
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The result of the measurement is M ¼ 46 (13) mSv/h, i.e., 46 mSv/h with a combined standard uncertainty, uc, of 13 mSv/h.
MEASURMENT QUALITY ASSURANCE Table 3.4. Coverage factors, k, for different effective degrees of freedom neff (EA, 1999; ISO, 1995). neff
1
2
3
4
5
6
7
8
10
20
50
1
k
13.97
4.53
3.31
2.87
2.65
2.52
2.43
2.37
2.28
2.13
2.05
2.00
The reported expanded uncertainty of measurement is stated as the standard uncertainty of measurement multiplied by the coverage factor k ¼ 2, which for a normal distribution corresponds to a level of confidence of approximately 95 %. The standard uncertainty of measurement has been determined in accordance with EA (1999) or ISO (1995).
3.4.1 Confirmation, calibration, and verification
However, in cases where the procedure of EA-4/02, EA (1999) has been followed to determine the coverage factor from the effective degrees of freedom, neff, the additional explanatory note should read as follows:
Metrological confirmation is a general term that encompasses all the operations necessary to assure that measuring equipment fulfills the requirements for intended use (ISO, 2003). This can include calibration of the equipment traceable to a primary laboratory standard and periodic verification or checks to ensure stability of response. Since comparisons with national standards are relatively infrequent, placing the same device in a specially constructed jig that ensures a reproducible geometry, and then exposing it to a radiation source with a long half-life such as 137Cs, can serve as a convenient method to perform periodic verifications. The use of a source with a long half-life tends to minimize errors that might be introduced by frequent re-calculations of the reference dose rate. Routine checks on the stability of the air-kerma response of the device can be performed every day or just before a calibration or measurement is performed. In some cases, the ingrowth of unwanted radionuclides within the reference source must be taken into account, e.g., in the use of 252Cf (ISO, 2001). Many measurements are taken as a function of time, such as the measurement of absorbed dose rate. Once the absorbed dose rate has been measured, the total dose delivered might be determined with the use of a timer. Modern electronics have significantly improved the accuracy of timers, and the uncertainty introduced by timing devices is generally quite small. However, the devices used to control the duration of an exposure to a radioactive source can introduce non-negligible uncertainties. Opening and closing a lead shutter can take a few hundred milliseconds even with a fast pneumatic
The reported expanded uncertainty of measurement is stated as the standard uncertainty of measurement multiplied by the coverage factor, which is based on a t-distribution for a coverage probability of 95.45 %. Values for k can be obtained using Table 3.4. u4 ð y Þ neff ¼ P u4 , N i i¼1 ni
ð3:23Þ
where ui(y) are the contributions to the standard uncertainty, u(y), as defined previously in Eqs. (3.13) and (3.14). The numerical value of the uncertainty of measurement should be given to two significant figures at most. The numerical value of the measurement result should in the final statement normally be rounded to the least significant figure in the value of the expanded uncertainty assigned to the measurement result. For the process of rounding, the usual rules for rounding of numbers should be used (for further details on rounding see ISO, 1992, Appendix B). However, if the rounding brings the numerical value of the uncertainty of measurement down by more than 5 %, the rounded-up value should be used.
3.4
EQUIPMENT CONTROL SYSTEM
The purpose of equipment control is to confirm the quality of measuring equipment and measurement 23
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processes. A control system, such as described in ISO 10012 (ISO, 2003), provides the methods for demonstrating that the required level of performance in the calibration and measurement of ionizing radiation has been achieved. Documented evidence of the traceability to, or consistency with, national standards is part of the metrological confirmation process. In order to ensure the proper operation of measurement and test equipment, one, or several, of the approaches described in the following sections can be employed.
expanded uncertainty U shall be given in the form (y – U) together with the value of k. To this, an explanatory note must be added, which in the general case should have the following content:
MEASUREMENT QUALITY ASSURANCE FOR IONIZING RADIATION DOSIMETRY
d¼
M2 Dt1 M1 Dt2 : M2 M1
ð3:24Þ
Consideration should be given to the frequency of routine checks or calibrations. Initially, requirements for this frequency can be set by regulations, but the first interval can also be set based on experience or recommendations from knowledgeable staff members. Some measurement equipment might require more frequent calibration or verification. Several factors need to be considered in the determination of methods used and the frequency of confirmation (see Section 5). It is expected that a calibration against a reference standard should be made in certain intervals, e.g., at least every 2 years or by comparison with other SSDLs every 5 years. Practical considerations might rule out the performance of full calibrations before each use of a dosimetric device. First of all, such devices are generally quite stable and do not require frequent calibration. In addition, the effort and expenditure associated with frequent calibrations must be weighed against the possible benefit accrued. Not to be minimized is the risk associated with frequent use of a valuable reference instrument. Each time when it is used it is possible that the device might receive some damage. An alternative approach that is often applied requires the verification frequency to depend on the results of the previous measurement. If the response of the device is found to be within specified limits, the frequency of verification can be decreased. If the response is found to be outside the specified limits, the frequency is increased. Note that these limits are expected to be well within the uncertainty limits required by legislation or accreditation. Control charts (see Section 4.1) can aid in the assessment of calibration frequency. Drifts in the response of instruments can be calculated, and the frequency of verifications can be set based on these calculations. The time between verifications can be set at 1 week, 1 month or longer. The interval can also be based on in-use time. For example, a device that is used more often might exhibit a greater drift due to wear or degradation of components. Therefore, a shorter interval between calibrations might be justified. Another approach is to focus on one critical characteristic of the measuring device. For instance,
3.4.2 Determination of lower limit of detection or minimal detectable amount The ability of a laboratory to measure small values of quantities correctly is dependent upon the level of background radiation and the variation in the background level. The lower limit of detection establishes the practical limit for the lowest value of a quantity that the laboratory can determine. There is also a difference between the amount that can be detected and the amount that can be measured. The laboratory should determine and document the lower limit of measurement for the services provided. It is particularly important for applications such as measurement of the air-kerma rate for brachytherapy sources where the signal–to-noise ratio is small and the determination of personal dose equivalent 24
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it might be appropriate to confirm frequently that the air-kerma response to photon sources such as those produced by 137Cs or 60Co is within specified limits. Other characteristics of the device such as the variation of response with the angle of incidence of the radiation can be assumed to be constant, barring any change in the components of the device. This method can represent an effective as well as a safe and efficient approach for specific instruments. Some systems, e.g., large-scale personal-dosimetry or environmental-sampling services, require that quality-system procedures be applied both to the components and to the overall system. Examples of the items that should be subject to quality control are the properties of system components such as the designs of equipment, dosimeters, sample holders, or processing and read-out equipment. The verification that system components meet their specifications is part of the quality-control procedures. Examples of system components might include dosimetric material, filters, detectors, radioactive sources, and standard reference materials (ICRU, 2003). Results of routine testing of the operation of equipment as well as any maintenance procedures performed should be documented in the quality-control records. (Dutt and Lindborg, 1994; EC, 1994). For large-scale personal-dosimetry services, checks on the dosimetric performance and stability might need to be carried out at least daily. There should also be a requirement for regular traceability exercises, with audit trails, referenced to national standards. In addition, it is important to have a system of independent tests to demonstrate compliance with regulatory requirements for the overall quality of dose or activity measurement (Ambrosi et al., 2000; van Dijk, 2000).
drive mechanism. A correction for the shutter timing error can be determined by taking two readings, M1 and M2, of a quantity such as the charge collected by an ionization chamber for two different exposure times, Dt1 and Dt2 (Attix, 1986). The shutter timing correction, d, will then be given by
MEASURMENT QUALITY ASSURANCE Table 3.5. Example of a table of correction factors for an ionization chamber. Symbol
Influence quantity
Value
Standard uncertainty
Remark
kPer kTP kH
Perturbationa Temperature/pressure Humidity
1.03 1.06 1.0
0.015 0.02 0.03
Taken from datasheet Measured temperature 27 C and pressure of 96.55 kPa No measurementb
Perturbation refers to the effect of introducing the chamber into a medium. a If the reference ionization chamber and the ionization chamber to be calibrated are of the same type and construction, the perturbation factor will have a value of 1.0. b It may be necessary to measure the humidity if its value is outside of the range of standard test conditions given in Table 3.1.
3.4.3
Corrections to measurements
Factors can be applied to the direct indication of any instrument in the laboratory, and they can be attributed to various causes. For instance, they might be related to influence quantities such as temperature or humidity, or related to the response of a particular instrument.
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The conditions under which a correction can be performed should be detailed in the quality manual. If a known systematic error can be corrected, then this correction should be carried out. Corrections should be applied consistently. All the factors should be identified and explained, and their relationship to the quantity of interest should be indicated. Values for the factors along with their associated uncertainties should also be provided. Table 3.5 gives some examples. Values for factors are to be determined using recommended procedures (ICRU, 2001), and measurements for these determinations are to be traceable to national standards.
for many radiation workers where the value of the quantity is close to zero. General guidance can be found in ISO (2000c, 2001), Currie (1968), van Dijk (1998), van Dijk and Julius (1996), Christensen and Griffith (1994), and Harvey (1998).
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doi:10.1093/jicru/ndl028
MEASUREMENT QUALITY ASSURANCE
3.1 SPECIFICATION OF MEASUREMENT QUALITY
3.2 EFFECTS OF INFLUENCE QUANTITIES ON MEASUREMENT QUALITY The consistency or stability of measurements is dependent upon maintaining the stability of ambient conditions in the laboratory. Changes in a number of parameters can affect the quality of measurements, and the parameters that can produce such effects are referred to as influence quantities.
ktp ¼
273:15 þ Ta = C Pr · ; 273:15 þ Tr = C Pa
ð3:1Þ
where Ta is the ambient air temperature, Tr is the reference temperature, e.g., 20 C, Pr is the reference atmospheric pressure of 101.325 kPa and Pa is the ambient pressure (IAEA, 2000a).
3.3 METHODS FOR THE EVALUATION OF UNCERTAINTY The Guide to the Expression of Uncertainty in Measurement (ISO, 1995) recommends the use of standard uncertainties, which are evaluated in two ways that are classified as Type A and Type B. Once numerical values have been determined for these two types of uncertainties, no further distinction is made and the values can be combined. The Type A evaluation of standard uncertainty consists of determining the uncertainty by the statistical analysis of a series of observations. In this case the standard uncertainty is the experimental standard deviation
International Commission on Radiation Units and Measurements 2006
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The assurance, or verification, of the level of quality of measurements is essentially a three-step process. First, the acceptable uncertainty must be established, usually on the basis of a published standard or national regulation. Second, a facility must have procedures in place that will lead to performance within the specified uncertainty. Third, the facility must demonstrate its capability of performing measurements within the specified uncertainty. An additional related concept that follows from the third step is a plan for remedial action when a facility fails to perform within this specified uncertainty. Measurement quality can be evaluated using a variety of techniques. Perhaps the simplest method for evaluating the quality of a measurement is the direct comparison to a national standard. For instance, a working-level ionization chamber may be periodically compared with a reference or transfer standard that has in turn been compared with a national standard. If the value measured using the chamber agrees with the value measured using the reference standard chamber to within a specified uncertainty, then the measurement quality is assured. If the difference is greater than the expanded uncertainty (see Section 5.2) the cause of this difference should be investigated and appropriate remedial action taken. Until the discrepancy is resolved, no measurements should be used or disseminated. Any such measurement disseminated, but also affected by the discrepancy, shall be identified and appropriate action taken (e.g., informing the customer).
An influence quantity may have an effect on the result of a measurement without being the object of the measurement itself. Examples of influence quantities that can affect the uncertainty in ionizing radiation measurement are shown in Table 3.1, along with the reference conditions. The effects of influence quantities on the measurement should be assessed, and, if standard test conditions are specified, care should be taken to ensure that standard test conditions are met while measurements are performed (or appropriate corrections are made). Reference conditions are normally within the range of standard test conditions; however, it is not necessary to control ambient conditions to match the reference conditions. Factors can be applied to normalize measurement results to the reference conditions. For instance, the following formula can be used to compute a correction factor that is applied to correct the response of an ionization chamber, the collecting volume of which communicates with ambient air, to reference temperature and pressure conditions:
MEASUREMENT QUALITY ASSURANCE FOR IONIZING RADIATION DOSIMETRY Table 3.1. Some examples of influence quantities, reference conditions and standard test conditions for ionization chambers used for radiation therapy calibrations (IAEA, 2000a). Influence quantities
Reference conditions
Standard test conditions
Ambient temperature Relative humidity Atmospheric pressure Stabilization time Electromagnetic fields Radioactive contamination Radiation background
20 or 22 C 50 % 101.325 kPa 30 min Negligible Negligible 1.0 mGy/h
Reference ambient temperature –2 C 45–65 %a 86–103 kPaa >15 min 1), the estimate of the quantity Q is the arithmetic mean, q, or the average of the individual observed values qj ( j ¼ 1, 2, . . ., n). n 1X qj : q ¼ n j¼1
obtained from a limited number of observations. If in such a case the value of the input quantity Q is determined as the arithmetic mean q of a small number n of independent observations, the variance of the mean can be estimated by s2 ðqÞ ¼
ð3:4Þ
s2 ðqÞ ¼
1 n1
The Type B evaluation of standard uncertainty is the evaluation of the uncertainty associated with an estimate xi of an input quantity Xi by means other than the statistical analysis of a series of observations. The standard uncertainty u(xi) can be evaluated by scientific judgment based on all available information on the possible variability of Xi. Values belonging to this category can be derived from
ð3:5Þ
j¼1
and the positive square root of this expression is termed the experimental standard deviation. The best estimate of the variance of the arithmetic mean, q, is the experimental variance of the mean given by s2 ðqÞ ¼
s2 ðqÞ : n
previous measurement data; experience with or general knowledge of the behavior and properties of relevant materials and instruments; manufacturer’s specifications; data provided in calibration and other certificates; and uncertainties assigned to reference data taken from handbooks.
ð3:6Þ
The positive square root of this expression is termed the experimental standard deviation of the mean. The standard uncertainty, uð qÞ, associated with the input estimate q is the experimental standard deviation of the mean given by uðqÞ ¼ sðqÞ:
ð3:7Þ
The proper use of the available information for a Type B evaluation of standard uncertainty of measurement calls for insight based on experience. It is a skill that can be learned with practice. A well-based Type B evaluation of standard uncertainty can be as reliable as a Type A evaluation of standard uncertainty, especially in a measurement situation where a Type A evaluation is based only on a comparatively small number of statistically independent observations. The following cases are given as illustrative examples.
It must be noted that, when the number n of repeated measurements is low (n < 10), the reliability of a Type A evaluation of standard uncertainty, as expressed by Eq. (3.7), has to be considered. If the number of observations cannot be increased, other means of evaluating the standard uncertainty have to be considered, for example, using the t-distribution (Wadsworth, 1990) for the degrees of freedom. (b) For a measurement that is well characterized and under statistical control, a combined or pooled estimate of variance s2p is given as follows: PN ni s2i 2 ð3:8Þ sp ¼ Pi¼1 N i¼1 n i
(a) If only a single value is known for the quantity Xi, e.g., a single measured value, a resultant value of a previous measurement, a reference value from the literature, or a correction value, this value will be used for xi. The standard uncertainty u(xi) associated with xi is to be adopted where it is given. Otherwise it is calculated from unequivocal uncertainty data. If data of this kind are not available, the uncertainty has to be evaluated on the basis of experience.
can be calculated, where s2i is the experimental variance of the ith series of ni independent repeated observations and has vi ¼ ni 1 degrees of freedom. The combined or pooled estimate of variance can provide a better characterization of the dispersion than the estimated standard deviation 19
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3.3.2 Type B methods to evaluate the uncertainty
(a) An estimate of the variance of the underlying probability distribution is the experimental variance s2(q) of measured values qj that is given by 2 qj q :
ð3:9Þ
The standard uncertainty is deduced from this value using Eq. (3.7).
The uncertainty of measurement associated with the estimate q is evaluated according to one of the following methods:
n X
s2p : n
MEASUREMENT QUALITY ASSURANCE FOR IONIZING RADIATION DOSIMETRY
(b) When a probability distribution can be assumed for the quantity Xi, based on theory or experience, then the appropriate expectation or expected value and the square root of the variance of this distribution should be taken as the estimate xi and the associated standard uncertainty u(xi), respectively. (c) If only upper and lower limits aþ and a can be estimated for the value of the quantity Xi and the probability is essentially unity that the value lies within the interval (e.g., manufacturer’s specifications of a measuring instrument, a temperature range, and a rounding or truncation error resulting from automated data reduction), then a probability distribution with constant probability density between these limits (a rectangular probability distribution) should be assumed for the possible variability of the input quantity Xi. According to case (b) above this leads to
u2 ð xi Þ ¼
1 ðaþ aÞ2 12
For uncorrelated input quantities, the square of the standard uncertainty associated with the output estimate y is given by u2 ð yÞ ¼
1 u ð xi Þ ¼ a 2 : 3
u2i ð yÞ,
ð3:13Þ
i¼1
Note: There are cases, seldom occurring in calibration, when the model function is strongly nonlinear or some of the sensitivity coefficients [see Eqs. (3.14) and (3.15)] vanish and higher order terms have to be included into Eq. (3.13). For a treatment of such special cases see ISO (1995). The quantity ui(y) (i ¼ 1, 2, . . . , N) is the contribution to the standard uncertainty associated with the output estimate y resulting from the standard uncertainty associated with the input estimate xi ui ð yÞ ¼ ci uðxi Þ,
ð3:10Þ
ð3:14Þ
where ci is the sensitivity coefficient associated with the input estimate xi, i.e., the partial derivative of the model function f with respect to Xi, evaluated at the input estimates xi,
ð3:11Þ
for the square of the standard uncertainty. If the difference between the limiting values is denoted by 2a, then Eq. (3.11) becomes 2
N X
ci ¼
@f @f ¼ : @xi @Xi x1 ;x2 ;...;xN
ð3:15Þ
The sensitivity coefficient ci describes the extent to which the output estimate y is influenced by variations of the input estimate xi. It can be evaluated from the model function, f, by Eq. (3.14) or by using numerical methods, i.e., by calculating the change in the output estimate y due to a change in the input estimate xi of þu(xi) and u(xi) and taking as the value of ci the resulting difference in y divided by 2u(xi). Sometimes it might be more appropriate to find the change in the output estimate y from an experiment by repeating the measurement at xi – u(xi) for example. Whereas u(xi) is always positive, the contribution ui(y) according to Eq. (3.14) is either positive or negative, depending on the sign of the sensitivity coefficient ci. The sign of ui(y) has to be taken into account in the case of correlated input quantities. If the model function f is a sum or difference of the input quantities Xi
ð3:12Þ
For example, the value of the radiation-chemical yield for the ferrous sulphate dosimeter system can be given as G ¼ 1.624 mol kg1 Gy1, and it is stated that the error in this value should not exceed 1.624 · 102 mol kg1 Gy1. It would be reasonable to assume that the true value of G lies with equal probability within the range from 1.608 to 1.640 mol kg1 Gy1, and this would represent a symmetric rectangular distribution. Following the discussion in case (b) above, the rectangular distribution is a reasonable description in probability terms of one’s inadequate knowledge about the input quantity Xi in the absence of any other information than its limits of variability. However, if it is known that values of the quantity in question near the center of the variability interval are more likely than values close to the limits, a triangular or normal distribution might be a better model. On the other hand, if values close to the limits are more likely than values near the center, a U-shaped distribution might be more appropriate.
f ðX 1 ; X 2 , . . . , X N Þ ¼
N X
pi Xi ,
ð3:16Þ
i¼1
then the output estimate according to Eq. (3.3) is given by the corresponding sum or difference of the 20
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1 xi ¼ ðaþ þ aÞ 2 for the estimated value and
3.3.3 Calculation of the standard uncertainty of the output estimate
MEASURMENT QUALITY ASSURANCE input estimates y¼
N X
correlations between input quantities could lead to an incorrect evaluation of the standard uncertainty of the measurand. The covariance associated with the estimates of two input quantities Xi and Xk can be taken to be zero or treated as insignificant under the following conditions.
ð3:17Þ
p i xi ,
i¼1
whereas the sensitivity coefficients equal pi and Eq. (3.13) converts to u2 ð y Þ ¼
N X
p2i u2 ðxi Þ:
i¼1
If the model function f is a product or quotient of the input quantities Xi N Y Xipi ;
f ðX1 ; X2 , . . . , XN Þ ¼ b
ð3:19Þ
i¼1
with b being a given constant, the output estimate again is the corresponding product or quotient of the input estimates N Y
y¼b
xpi i :
Sometimes correlations can be eliminated by a proper choice of the model function. The uncertainty analysis for a measurement (sometimes called the uncertainty budget of the measurement) should include a list of all sources of uncertainty together with the associated standard uncertainties of measurement and the methods of evaluating them. For repeated measurements, the number n of observations also has to be stated. For the sake of clarity, it is recommended to present the data relevant to this analysis in the form of a table. In this table all quantities should be referenced by a physical symbol Xi or a brief descriptor. For each of them, at least the estimate, xi, the associated standard uncertainty of measurement, u(xi), the sensitivity coefficient, ci , and the different uncertainty contributions, ui(y) , should be specified. The dimension of each of the quantities should also be stated with the numerical values given in the table. A generalized example of such an arrangement as given in Table 3.2, applicable for the case of uncorrelated input quantities, and Table 3.3 gives
ð3:20Þ
i¼1
The sensitivity coefficients equal ci ¼ piy/xi in this case, and an expression analogous to Eq. (3.16) is obtained from Eq. (3.13). If relative standard uncertainties w(y) ¼ u(y)/|y| and w(xi) ¼ u(xi)/|xi| are used, w2 ð yÞ ¼
N X
p2i w2 ðxi Þ:
ð3:21Þ
i¼1
If two input quantities Xi and Xk are correlated to some degree, i.e., if they are mutually dependent in one way or another, their covariance also has to be considered as a contribution to the uncertainty. The ISO Guide (ISO, 1995) should be consulted for this evaluation. The possibility of taking into account the effect of correlations depends on the knowledge of the measurement process and on the judgment of mutual dependence of the input quantities. In general, it should be kept in mind that neglecting
Table 3.2. Schematic representation of an ordered arrangement of the quantities, estimates, standard uncertainties, sensitivity coefficients, and uncertainty contributions used in the uncertainty analysis of a measurement with the model function Y ¼ f (X1, X2,. . ., XN). Quantity Xi
Estimate xi
Standard uncertainty u(xi)
Sensitivity coefficient ci
Contribution to the standard uncertainty ui(y)
Remark
X1 X2 : XN Y
x1 x2 : xN y
u(x1) u(x2) : u(xN) u(y)
c1 c2 : cN –
u1(y) u2(y) : uN(y) –
11 measurements Rectangular distribution : Triangular distribution u(y) is combined standard uncertainty
21
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(a) the input quantities Xi and Xk are independent, for example, because they have been repeatedly but not simultaneously observed in different independent experiments or because they represent resultant quantities of different evaluations that have been made independently; (b) either of the input quantities Xi and Xk can be treated as constant; and (c) investigation gives no information indicating the presence of correlation between the input quantities Xi and Xk.
ð3:18Þ
MEASUREMENT QUALITY ASSURANCE FOR IONIZING RADIATION DOSIMETRY Table 3.3. Example of an uncertainty budget of a measurement with the model function M ¼ k1k2k3IcorrkCf (see Section 2.1.1). Quantity Xi
Estimate xi
Standard uncertainty u(xi)
Sensitivity coefficient ci
Contribution to the standard uncertainty ui(y)
Remark
Icorr K Cf k1 k2 k3 M
3 nA 12 (mSv/h)/nA 1.27 1.0 1.0 1.0 45.7 mSv/h
0.07 nA 0.0 (mSv/h)/nA 0.031 0.27 0.06 0.08 13.2 mSv/h
15.2 (mSv/h)/nA 3.81 nA 36 mSv/h 45.7 mSv/h 45.7 mSv/h 45.7 mSv/h –
1.06 mSv/h 0.0 mSv/h 1.12 mSv/h 12.3 mSv/h 2.74 mSv/h 3.66 mSv/h –
11 measurements Fixed value, no uncertainty 15 measurements Correction for energy and angle Correction for nonlinearity Correction for temperature and pressure –
amounts, the conditions of the Central Limit Theorem (ISO, 1995) are met and the distribution of the output quantity is assumed to be normal. The reliability of the standard uncertainty assigned to the output estimate is determined by its effective degrees of freedom (see ISO, 1995). However, the reliability criterion is always met if none of the uncertainty contributions is obtained from a Type A evaluation based on less than 10 repeated observations. If one of these conditions (normality or sufficient reliability) is not fulfilled, the standard coverage factor k ¼ 2 can yield an expanded uncertainty corresponding to a level of confidence of less than 95 %. In these cases, in order to ensure that a value of the expanded uncertainty is quoted corresponding to the same level of confidence as in the normal case, other procedures have to be followed. The use of approximately the same level of confidence is essential whenever two results of measurement of the same quantity have to be compared, e.g., when evaluating the results of an inter-laboratory comparison or assessing compliance with a specification. Even if a normal distribution can be assumed, it might still occur that the standard uncertainty associated with the output estimate is of insufficient reliability. If, in this case, it is not expedient to increase the number n of repeated measurements or to use a Type B evaluation instead of the Type A evaluation of poor reliability, the method given in ISO, (1995) should be used (see also ISO, 2005). For the remaining cases, i.e., all cases where the assumption of a normal distribution cannot be justified, information on the actual probability distribution of the output estimate shall be used to obtain a value of the coverage factor k that corresponds to a level of confidence of approximately 95 %. For reports or calibration certificates, the complete result of the measurement consisting of the estimate y of the measurand and the associated
a specific example of an uncertainty budget. The standard uncertainty associated with the measurement result u(y) given in column 3 of the table is the square root of the sum of the squares of all the uncertainty contributions, u1(y), . . . , uN(y), in column 5. 3.3.4 Expanded uncertainty and coverage factor k Most applications for the measurement of ionizing radiation require the use of a measure of uncertainty that defines an interval about the measurement result, y, within which the value of the measurand, Y, will be found with high probability. For some applications, such as those in health and safety, an expanded uncertainty can be used to include a large fraction of values expected to represent the measurand. This interval is referred to as the expanded uncertainty of measurement, U, obtained by multiplying the standard uncertainty u(y) of the output estimate y by a coverage factor k, U ¼ k uð yÞ:
ð3:22Þ
In cases where a normal (Gaussian) distribution can be attributed to the measurand and the standard uncertainty associated with the output estimate has sufficient reliability, the coverage factor k ¼ 2 should be used. The assigned expanded uncertainty corresponds to a level of confidence of approximately 95 %. These conditions are fulfilled in the majority of cases encountered in calibration work. The assumption of a normal distribution cannot always be easily confirmed experimentally. However, in the cases where several (i.e., N 3) uncertainty components, derived from well-behaved probability distributions of independent quantities, e.g., normal distributions or rectangular distributions, contribute to the standard uncertainty associated with the output estimate by comparable 22
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The result of the measurement is M ¼ 46 (13) mSv/h, i.e., 46 mSv/h with a combined standard uncertainty, uc, of 13 mSv/h.
MEASURMENT QUALITY ASSURANCE Table 3.4. Coverage factors, k, for different effective degrees of freedom neff (EA, 1999; ISO, 1995). neff
1
2
3
4
5
6
7
8
10
20
50
1
k
13.97
4.53
3.31
2.87
2.65
2.52
2.43
2.37
2.28
2.13
2.05
2.00
The reported expanded uncertainty of measurement is stated as the standard uncertainty of measurement multiplied by the coverage factor k ¼ 2, which for a normal distribution corresponds to a level of confidence of approximately 95 %. The standard uncertainty of measurement has been determined in accordance with EA (1999) or ISO (1995).
3.4.1 Confirmation, calibration, and verification
However, in cases where the procedure of EA-4/02, EA (1999) has been followed to determine the coverage factor from the effective degrees of freedom, neff, the additional explanatory note should read as follows:
Metrological confirmation is a general term that encompasses all the operations necessary to assure that measuring equipment fulfills the requirements for intended use (ISO, 2003). This can include calibration of the equipment traceable to a primary laboratory standard and periodic verification or checks to ensure stability of response. Since comparisons with national standards are relatively infrequent, placing the same device in a specially constructed jig that ensures a reproducible geometry, and then exposing it to a radiation source with a long half-life such as 137Cs, can serve as a convenient method to perform periodic verifications. The use of a source with a long half-life tends to minimize errors that might be introduced by frequent re-calculations of the reference dose rate. Routine checks on the stability of the air-kerma response of the device can be performed every day or just before a calibration or measurement is performed. In some cases, the ingrowth of unwanted radionuclides within the reference source must be taken into account, e.g., in the use of 252Cf (ISO, 2001). Many measurements are taken as a function of time, such as the measurement of absorbed dose rate. Once the absorbed dose rate has been measured, the total dose delivered might be determined with the use of a timer. Modern electronics have significantly improved the accuracy of timers, and the uncertainty introduced by timing devices is generally quite small. However, the devices used to control the duration of an exposure to a radioactive source can introduce non-negligible uncertainties. Opening and closing a lead shutter can take a few hundred milliseconds even with a fast pneumatic
The reported expanded uncertainty of measurement is stated as the standard uncertainty of measurement multiplied by the coverage factor, which is based on a t-distribution for a coverage probability of 95.45 %. Values for k can be obtained using Table 3.4. u4 ð y Þ neff ¼ P u4 , N i i¼1 ni
ð3:23Þ
where ui(y) are the contributions to the standard uncertainty, u(y), as defined previously in Eqs. (3.13) and (3.14). The numerical value of the uncertainty of measurement should be given to two significant figures at most. The numerical value of the measurement result should in the final statement normally be rounded to the least significant figure in the value of the expanded uncertainty assigned to the measurement result. For the process of rounding, the usual rules for rounding of numbers should be used (for further details on rounding see ISO, 1992, Appendix B). However, if the rounding brings the numerical value of the uncertainty of measurement down by more than 5 %, the rounded-up value should be used.
3.4
EQUIPMENT CONTROL SYSTEM
The purpose of equipment control is to confirm the quality of measuring equipment and measurement 23
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processes. A control system, such as described in ISO 10012 (ISO, 2003), provides the methods for demonstrating that the required level of performance in the calibration and measurement of ionizing radiation has been achieved. Documented evidence of the traceability to, or consistency with, national standards is part of the metrological confirmation process. In order to ensure the proper operation of measurement and test equipment, one, or several, of the approaches described in the following sections can be employed.
expanded uncertainty U shall be given in the form (y – U) together with the value of k. To this, an explanatory note must be added, which in the general case should have the following content:
MEASUREMENT QUALITY ASSURANCE FOR IONIZING RADIATION DOSIMETRY
d¼
M2 Dt1 M1 Dt2 : M2 M1
ð3:24Þ
Consideration should be given to the frequency of routine checks or calibrations. Initially, requirements for this frequency can be set by regulations, but the first interval can also be set based on experience or recommendations from knowledgeable staff members. Some measurement equipment might require more frequent calibration or verification. Several factors need to be considered in the determination of methods used and the frequency of confirmation (see Section 5). It is expected that a calibration against a reference standard should be made in certain intervals, e.g., at least every 2 years or by comparison with other SSDLs every 5 years. Practical considerations might rule out the performance of full calibrations before each use of a dosimetric device. First of all, such devices are generally quite stable and do not require frequent calibration. In addition, the effort and expenditure associated with frequent calibrations must be weighed against the possible benefit accrued. Not to be minimized is the risk associated with frequent use of a valuable reference instrument. Each time when it is used it is possible that the device might receive some damage. An alternative approach that is often applied requires the verification frequency to depend on the results of the previous measurement. If the response of the device is found to be within specified limits, the frequency of verification can be decreased. If the response is found to be outside the specified limits, the frequency is increased. Note that these limits are expected to be well within the uncertainty limits required by legislation or accreditation. Control charts (see Section 4.1) can aid in the assessment of calibration frequency. Drifts in the response of instruments can be calculated, and the frequency of verifications can be set based on these calculations. The time between verifications can be set at 1 week, 1 month or longer. The interval can also be based on in-use time. For example, a device that is used more often might exhibit a greater drift due to wear or degradation of components. Therefore, a shorter interval between calibrations might be justified. Another approach is to focus on one critical characteristic of the measuring device. For instance,
3.4.2 Determination of lower limit of detection or minimal detectable amount The ability of a laboratory to measure small values of quantities correctly is dependent upon the level of background radiation and the variation in the background level. The lower limit of detection establishes the practical limit for the lowest value of a quantity that the laboratory can determine. There is also a difference between the amount that can be detected and the amount that can be measured. The laboratory should determine and document the lower limit of measurement for the services provided. It is particularly important for applications such as measurement of the air-kerma rate for brachytherapy sources where the signal–to-noise ratio is small and the determination of personal dose equivalent 24
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it might be appropriate to confirm frequently that the air-kerma response to photon sources such as those produced by 137Cs or 60Co is within specified limits. Other characteristics of the device such as the variation of response with the angle of incidence of the radiation can be assumed to be constant, barring any change in the components of the device. This method can represent an effective as well as a safe and efficient approach for specific instruments. Some systems, e.g., large-scale personal-dosimetry or environmental-sampling services, require that quality-system procedures be applied both to the components and to the overall system. Examples of the items that should be subject to quality control are the properties of system components such as the designs of equipment, dosimeters, sample holders, or processing and read-out equipment. The verification that system components meet their specifications is part of the quality-control procedures. Examples of system components might include dosimetric material, filters, detectors, radioactive sources, and standard reference materials (ICRU, 2003). Results of routine testing of the operation of equipment as well as any maintenance procedures performed should be documented in the quality-control records. (Dutt and Lindborg, 1994; EC, 1994). For large-scale personal-dosimetry services, checks on the dosimetric performance and stability might need to be carried out at least daily. There should also be a requirement for regular traceability exercises, with audit trails, referenced to national standards. In addition, it is important to have a system of independent tests to demonstrate compliance with regulatory requirements for the overall quality of dose or activity measurement (Ambrosi et al., 2000; van Dijk, 2000).
drive mechanism. A correction for the shutter timing error can be determined by taking two readings, M1 and M2, of a quantity such as the charge collected by an ionization chamber for two different exposure times, Dt1 and Dt2 (Attix, 1986). The shutter timing correction, d, will then be given by
MEASURMENT QUALITY ASSURANCE Table 3.5. Example of a table of correction factors for an ionization chamber. Symbol
Influence quantity
Value
Standard uncertainty
Remark
kPer kTP kH
Perturbationa Temperature/pressure Humidity
1.03 1.06 1.0
0.015 0.02 0.03
Taken from datasheet Measured temperature 27 C and pressure of 96.55 kPa No measurementb
Perturbation refers to the effect of introducing the chamber into a medium. a If the reference ionization chamber and the ionization chamber to be calibrated are of the same type and construction, the perturbation factor will have a value of 1.0. b It may be necessary to measure the humidity if its value is outside of the range of standard test conditions given in Table 3.1.
3.4.3
Corrections to measurements
Factors can be applied to the direct indication of any instrument in the laboratory, and they can be attributed to various causes. For instance, they might be related to influence quantities such as temperature or humidity, or related to the response of a particular instrument.
25
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The conditions under which a correction can be performed should be detailed in the quality manual. If a known systematic error can be corrected, then this correction should be carried out. Corrections should be applied consistently. All the factors should be identified and explained, and their relationship to the quantity of interest should be indicated. Values for the factors along with their associated uncertainties should also be provided. Table 3.5 gives some examples. Values for factors are to be determined using recommended procedures (ICRU, 2001), and measurements for these determinations are to be traceable to national standards.
for many radiation workers where the value of the quantity is close to zero. General guidance can be found in ISO (2000c, 2001), Currie (1968), van Dijk (1998), van Dijk and Julius (1996), Christensen and Griffith (1994), and Harvey (1998).
