The Assessment of Uncertainty in Radiological Calibration and Testing

Transcription

1 No. 49 Measurement Good Practice Guide The Assessment o Uncertainty in Radiological alibration and Testing Vic Lewis National Physical Laboratory Mike Woods National Physical Laboratory/IRM Peter Burgess UKAEA Stuart Green RRPPS, Birmingham John Simpson RWE NUKEM Ltd Jon Wardle DRMS, Aldermaston

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3 The Assessment o Uncertainty in Radiological alibration and Testing Vic Lewis National Physical Laboratory / onsultant Mike Woods National Physical Laboratory / IRM Peter Burgess UKAEA, Harwell Stuart Green RRPPS, Birmingham John Simpson RWE NUKEM, Winrith Jon Wardle DRMS, Aldermaston Abstract A brie summary o the principles o the treatment and expression o uncertainty is given. The evaluation o uncertainty in several key areas o radiological measurement is illustrated by examples showing the application o those principles to photon dosimetry, neutron area survey monitoring and radioactive surace contamination monitoring.

4 rown opyright 005 Reproduced by permission o the ontroller o HMSO ISSN: February 005 National Physical Laboratory Teddington, Middlesex, United Kingdom TW11 0LW Website: Acknowledgements This guide has been produced by a working group o the Ionising Radiation Metrology Forum (IRMF). The IRMF is organised by the National Physical Laboratory and supported under the National Measurement System Programme in Ionising Radiation Metrology, which is unded by the Department o Trade and Industry. Past and present members o the working group include - Peter Burgess UKAEA Stuart Green RRPPS, Edgbaston Richard Hedley AWE, Aldermaston Vic Lewis National Physical Laboratory / onsultant John Pople BAE Systems Marine John Simpson RWE NUKEM Ltd, Winrith Roger Stillman United Kingdom Accreditation Service Jon Wardle DRMS, AWE, Aldermaston Mike Woods National Physical Laboratory / IRM The authors are grateul to David Smith, Bob Burns and Roger Worrall or advice; to Graham Bass and Andy Weeks or providing examples o uncertainty budgets; and to various members o the IRMF or their comments and interest.

5 Foreword The need or an internationally-accepted procedure or the treatment and reporting o uncertainties in measurement has been recognised or some time. In 1981 the omité International des Poids et Mesures (IPM) approved outline recommendations rom national standards laboratories and the ISO was asked to develop a guide applicable to all levels o metrology. A working group (ISO/TAG4/WG3) was set up and, as a result, the ISO Guide to the Expression o Uncertainty in Measurement [1] was published in Prior to this time, a working group o the United Kingdom Accreditation Service (UKAS) produced the NAMAS publication B085, The Expression o Uncertainty in Radiological Measurements [], although this contained no advice speciic to radiological measurements. UKAS published M 3003, The Expression o Uncertainty and onidence in Measurement [3] in This is consistent with the ISO Guide and contains examples o the application o the theory or several ields o measurement but excluding radiological measurements. Recognising the need to revise the guidance set out in B085 to bring it in line with the ISO Guide and M 3003, the Ionising Radiations Metrology Forum (IRMF) set up a working group in 1996 to advise UKAS on how best to revise B085. However, with the decision by UKAS to withdraw B085 altogether, it was decided to produce the present good practice guide, whose main purpose is to augment existing guidance in M 3003 with examples or several areas o radiological measurement. It is not intended to describe all possible sources o uncertainty in these areas; nor is it intended to tell users which ones they must put into their uncertainty budgets. Nor is this document intended either to be a guide on how to make measurements. The values used in the examples are or illustrative purposes only; each laboratory must evaluate the values applicable to the conditions concerned. For convenience, a brie summary o the theory is given in the present publication. This is based on publication M 3003, which, along with the ISO Guide, is strongly recommended as urther reading or detailed background inormation and or coverage o additional topics. The examples in this guide are based partly on experience gained with the IRMF comparisons o calibrations in the areas o gamma dose monitoring, neutron area survey monitoring and surace contamination monitoring. These exercises have underlined the need or a consistent approach to the treatment o uncertainties in those areas. The ormat o the examples in this guide ollows that o the examples in M In accordance with IRMF policy, it is intended to ormally review this guide within ive years o publication. The IRMF will appoint a working group to carry this out. In the meantime, readers may send any comments or corrections to the Secretary, IRMF, at the National Physical Laboratory. These will be considered and incorporated i appropriate.

6 The deinitive version o the guide is the version maintained on the IRMF website (part o the NPL website). Any changes, as a result o comments and corrections notiied to NPL since the document was irst published are shown in red within the text and are also listed at the end o the website version. The IRMF consists o representatives o a wide range o UK organisations involved in the measurement o ionising radiation. One o the major aims o the Forum is the promotion o good measurement practice through the production o guidance material based on what is currently considered by practitioners in this ield to be good practice. A urther activity is the organisation o measurement comparisons in the UK.

7 The Assessment o Uncertainty in Radiological alibration and Testing Glossary ontents 1 Treatment o Uncertainties Basic oncepts Type A Uncertainties Type B Uncertainties ombination o Uncertainties ombined standard uncertainty Expanded uncertainty overage actor or non-ideal situations Dominant component Expression o Uncertainty Signiicant digits Summary o Steps Involved in Deriving an Uncertainty... 5 Photon Monitoring alibration o a Photon Beam Measurement o air kerma using a secondary standard Uncertainty components or measurement o air kerma alibration o beam monitor Uncertainty components or calibration o beam monitor Uncertainty budget or measurement o kerma rate Reported result alibration o Portable Dose Rate Meter Method Uncertainty components or calibration o portable dose rate meter Instrument reading Other eects Uncertainty budget or calibration o portable dose rate meter Reported result alibration o Neutron Area Survey Monitor Use o Field Produced Using a Radionuclide Neutron Source Method Uncertainty components or calibration o neutron area survey monitor Uncertainty budget or calibration o neutron area survey monitor Reported result Use o Accelerator-produced Neutron Field Standardisation o ield Rate eects... 1

8 4 alibration o Surace ontamination Monitors and Radioactive alibration Sources alibration o Large Area Sources used or alibrating Surace ontamination Monitors Method Uncertainty components Uncertainty budget Reported result alibration o Surace ontamination Monitor Method Uncertainty components Uncertainty budget Reported result Reerences...30 Appendix 1 overage Factors and Use o the t-distribution A1.1 t-distribution...31 A1. Degrees o Freedom A1.3 Examples... 3 A1.3.1 Uncertainty budget or calibration o dose rate meter... 3 A1.3. Uncertainty budget or calibration o neutron area survey monitor...3 hanges to March 003 version...33

9 Glossary The ollowing terms are used in this document: Bias alibration alibration oeicient alibration Factor onidence Level overage Factor (k) Divisor Degrees o Freedom Error Expanded Uncertainty onstant error that produces a consistent deviation rom true value. Procedure to establish a quantitative relation between the response o an instrument and the quantity to be measured. oeicient by which a reading is multiplied to obtain the quantity being measured. Reciprocal o response. Factor by which a reading is multiplied to obtain the quantity being measured. The term actor is used instead o coeicient when the reading and quantity have the same dimension. Number expressing degree or level o conidence in the result. Usually expressed as a percentage or as a number o standard deviations. Number that is multiplied by the combined standard uncertainty to give an expanded uncertainty or a given conidence level. Number by which an uncertainty is divided in order to obtain the associated standard uncertainty The number o terms in a sum minus the number o constraints on the terms o the sum. A deviation rom the true value. The standard uncertainty (or combined standard uncertainty) multiplied by a coverage actor or a given conidence level Probability Distribution A unction giving the probability that a random variable takes any given value. Repeatability Reproducibility Response Sensitivity coeicient (c i ) Intrinsic instrument variability a measure o the agreement between repeated measurements o the same quantity under unchanged conditions o measurement. A measure o the agreement between repeated measurements o the same quantity under changed conditions o measurement. Ratio o the observed reading o an instrument to the true value o quantity producing the reading. Reciprocal o calibration coeicient oeicient by which the uncertainty o an input parameter is multiplied to give the corresponding uncertainty component o the quantity being measured.

10 Standard Deviation Standard Deviation o the Mean (SDOM) Standard Uncertainty Traceability Uncertainty Variance Positive square root o the variance. Standard deviation o mean o a series o results o measurements o the same quantity made under unchanged conditions. Formerly known as Standard Error o the Mean. Uncertainty o a measurement expressed as a margin equivalent to plus or minus one standard deviation Ability to relate measurements to national or international standards through an unbroken chain o calibrations that are carried out in a technically sound manner. Parameter associated with the result o a measurement that characterises the dispersion o the values that could reasonably be attributed to the quantity being measured. A term used to describe the dispersion o a set o observations with respect to its arithmetic mean. Variance is equal to the mean square deviation rom the arithmetic mean.

11 1 Treatment o Uncertainties The expression o the value o the result o a measurement, y, is incomplete without a statement o its evaluated uncertainty, U. This characterises the range in which the true value is estimated to lie with a given level o conidence. The measured value (or output quantity) is determined as a unction (x i ), o input parameters x i that must be either known, measured or otherwise estimated. The uncertainty associated with a measurement is due to a combination o the uncertainties, δy i, arising rom those o the input quantities, δx i. There is no undamentally correct method o combining these uncertainties. This section describes an internationally-accepted procedure or the treatment and expression o uncertainty. It is based on the published ISO Guide to the Expression o Uncertainty in Measurement [1]. 1.1 Basic oncepts Each x i has an associated uncertainty δx i that is a parameter characterizing the spread o values within which x i is believed to lie. I x i may lie anywhere within a speciied range o values with equal probability, it is said to have a rectangular probability distribution and the uncertainty is expressed in terms o the value or the semi-range. Alternatively, the probability distribution can be normal (i.e. Gaussian), and the standard deviation (or a given multiple o the standard deviation) may be used. An uncertainty should always be expressed in terms o a numerical value with an associated level o conidence. The type o probability distribution should also be given. Each uncertainty may be expressed as a standard uncertainty, u(x i ), that may be derived by dividing δx i by a number that depends on the probability distribution o δx i. The standard uncertainty is equivalent to one standard deviation and is a key quantity in the combination o uncertainties (see 1.4 below). Some common types o probability distribution associated with uncertainties along with the parameters usually chosen, the conidence levels and the divisors are shown in Table 1.1. Table 1.1 ommon types o uncertainty Distribution Parameter onidence level Divisor Normal 1 standard deviation 67.7% 1.0 Normal standard deviations 95.5%.0 Normal 3 standard deviations 99.7% 3.0 Rectangular semi-range 100% 3 Triangular semi-range 100% 6 1

12 Each u(x i ) gives rise to a corresponding standard uncertainty, u i (y), in the output quantity. This may be expressed as u i (y) c i u(x i ), where c i is a sensitivity coeicient that is equal to the partial derivative c i y/ x i. To express the standard uncertainty in the output quantity in ractional terms the relative sensitivity coeicient is ( y/ x i)/y. For simple expressions such as y x 1 / x, the standard uncertainties then become u(x 1 )/x 1 and u(x )/x in ractional terms. More oten, the standard uncertainties are derived in percentage terms as 100.u(x 1 )/x 1 and 100.u(x )/x. Examples o the derivation o sensitivity coeicients are given in Section Type A Uncertainties The traditional classiication o uncertainty components as random and non-random (sometimes termed systematic ) has been superseded by a system based on the method used to estimate their values. By deinition, Type A uncertainties are those that can be evaluated using statistical techniques and Type B uncertainties are those that are evaluated by other means. A Type A component o uncertainty is a measure o the repeatability o a result under constant conditions and can usually be assumed to have a normal probability distribution. It can be determined by series o measurements (y i ) in which an estimate, s(σ), o the standard deviation, σ, is obtained by a series o n measurements, applying s ( σ ) ( y i ( n y 1 ) m ) 1 where y m is the mean value o y. The standard deviation o the mean is s(σ) / n. This is the value to be used or the summation in quadrature or obtaining the combined standard uncertainty (see 1.4 below). 1.3 Type B Uncertainties All uncertainties that are not Type A, that is those that cannot be determined by a series o repeated measurements, are Type B uncertainties. These are eectively uncertainties that remain constant during one or more series o measurements. They arise rom a variety o sources and the probability distributions may take a variety o shapes. Practical guidance on evaluating Type B components is given in [1].

13 The values or some Type B components may be already determined and quoted by an external agency, e.g. the uncertainty or a reerence standard is usually given on the certiicate issued by the standardising body. The uncertainties o some input quantities or ancillary data used may be ound in published documents. The most important source o inormation on Type B uncertainties is invariably the use o past experience o measurements by the operator to derive inormed estimates. I the value o an uncertainty is not known, conservatively wide limits should be adopted and, where possible, an attempt should be made to quantiy it, or example, by measurement. I the probability distribution o an uncertainty is not known, then urther inormation should be sought, e.g. rom the manuacturer. Oten a rectangular distribution may be assumed. A more conservative route would be to assume a standard uncertainty with a normal distribution, so that the divisor would be unity. 1.4 ombination o Uncertainties ombined standard uncertainty The combined standard uncertainty o the output quantity, u(y), is derived by the summation in quadrature o all Type A and Type B standard uncertainties due to the input parameters: u(y) [ Σ u i (y) ] ½ The combined standard uncertainty is generally a standard deviation with a normal probability distribution unless one component dominates the combined eect o all others (see below). The above expression applies only when the input quantities are independent o each other (i.e. a change in one input quantity does not aect another). The ISO Guide [1] should be consulted or a more accurate approach i there are correlations Expanded uncertainty The key uncertainty to be quoted or the output quantity is the expanded uncertainty, U, which represents the total uncertainty or a speciic level o conidence. It is derived by multiplying the combined standard uncertainty, u(y), by a coverage actor, k, that is selected to give the desired level o conidence or a normal distribution. Typical choices or k are the integers 1,, or 3; which correspond to conidence levels o 67.7%, 95.5% and 99.7% respectively. For most radiological applications, a 95% conidence level, or which k 1.96, is recommended. For convenience, this is rounded upwards to a value o exactly.0. It is recommended that an uncertainty budget be produced listing relevant components and their numerical values, conidence levels, probability distributions, sensitivity coeicients and the corresponding standard uncertainties in the output quantity. Uncertainty budgets are usually in the orm o spreadsheets that are used to calculate the expanded uncertainties. Examples are given in Sections, 3 and 4. (Note that the output quantity uncertainties in each 3

14 table are expressed either all in absolute units or all as percentages.) overage actors or non-ideal situations The choice o k or the coverage actor assumes that the Type A uncertainties are based on a large number o readings so that the distribution is eectively normal. Otherwise the value o k should be derived rom a t-distribution. As a rule o thumb, i the number o readings is less than 10 and the Type A contribution is more than 50% o the overall uncertainty, the eective number o degrees o reedom, υ e, should be derived and used in conjunction with t-distribution tables to obtain the appropriate k-value. Further guidance is given in Appendix Dominant component The probability distribution o the expanded uncertainty may be assumed to be normal unless a dominant component such as a large uncertainty with a rectangular distribution is present. In such a situation, the expanded uncertainty may exceed the arithmetic sum o the values o all components because the divisor or the dominant component ( 3) is smaller than the k- actor used to calculate the expanded uncertainty (k or 95% conidence level). To avoid this problem, the dominant component, u dom, should not be combined with the other uncertainty components, but should be quoted separately [3]. The expanded uncertainty may be expressed as - U u dom + U where U is derived rom the combination o the other components. 1.5 Expression o Uncertainty The statement o the value o a measured quantity must include the value o the expanded uncertainty. The reported value must be accompanied by a statement giving the method o derivation o the uncertainty and the conidence level employed. This statement could be o the orm - The reported uncertainty is based on a standard uncertainty multiplied by a coverage actor k, that provides a level o conidence o approximately 95%. I a dominant component is present, this statement could be replaced by one o the orm - The reported uncertainty is dominated by the uncertainty due to or which a rectangular probability distribution has been assumed Signiicant digits The number o signiicant digits o the value o the uncertainty should be appropriate or the accuracy with which the uncertainty is assessed. The accuracy o a radiological measurement is seldom better than 1% unless an unrealistic eort is made. It is not usually practical to determine an uncertainty with an accuracy better than 10% o the uncertainty itsel. Thus, 4

15 there should be no more than two digits in the uncertainty value; oten only one is justiied. It is recommended that - uncertainties are reported as either one-digit integers between 3 and 9 or two-digit integers between 10 and 9, rounding o uncertainty values should be upwards, values o measured quantities should be rounded to the same least signiicant digit as the uncertainty. The ollowing result: ± 0.9 is reported as 95.1 ± ± 1.5 is reported as 95.1 ± ±.9 is reported as 95.1 ± ± 3.1 is reported as 95 ± Summary o Steps Involved in Deriving an Uncertainty Determine Type A uncertainties at one standard deviation. Determine Type B uncertainties and their probability distributions. alculate the standard uncertainties u(x i ) by dividing the uncertainties by the divisors appropriate to the probability distributions. Derive sensitivity coeicients c i and calculate u i (y). All u i (y) should be in the same units (either absolute or percentage) ombine Type A and Type B components in quadrature [Σ u i (y) ] ½ to give the combined standard uncertainty u(y). heck or presence o dominant component Derive or select coverage actor, k, or the desired level o conidence. The recommended value is k, or 95% conidence level. Multiply u(y) by coverage actor k to give expanded uncertainty U. Round the result to the appropriate number o signiicant igures. Report U, coverage actor and level o conidence. The inal value should always be examined to judge whether it makes sense. 5

16 Photon Monitoring This section covers the calibration o gamma-ray and X-ray ields and the calibration o portable radiation protection instruments. It does not explicitly cover radiotherapy applications, although there are similarities in the sources o uncertainty in the two areas. A photon ield is calibrated by measuring the dose delivered by the photon beam at a reerence position, using a secondary standard instrument, against the response o an appropriate monitor. For ields produced using X-ray sets or accelerators, the monitor could be a transmission-type o ionisation chamber in the radiation beam. For ields produced using radionuclide sources, the monitoring could be o time since the kerma rate is constant (allowing or decay o the source). For radiation protection instrument calibration, there is the urther step o measuring the response o the instrument being calibrated to a standardised ield. The examples below deal with the calibration o a photon ield and its use or calibrating portable dose rate meters..1 alibration o a Photon Beam A photon ield (normally a beam) is calibrated using a secondary standard such as an ionisation chamber to measure air kerma, K, (or air kerma rate) at selected reerence points along the axis o the radiation beam against the response o a beam monitor [4]..1.1 Measurement o air kerma rate using a secondary standard The direct air kerma on the beam axis is related to the instrument reading by the expression: K (M s - M B B) s F nl F r F dd F nu F room F scim F rate F T F P F H F Ti where: M s - reading o (integrating) secondary standard instrument, M B B - background reading o secondary standard instrument, s - calibration coeicient o secondary standard or relevant radiation quality, F nl - instrument scale non-linearity correction, F r - instrument range correction actor, F dd - instrument directional dependence correction actor, F nu - ield non-uniormity correction actor, F room - correction or room- and air- scatter, F scim - correction or scatter rom instrument mount F rate - rate correction actor, F T - temperature correction actor, F P - pressure correction actor, F H - humidity correction actor, F Ti - correction or timer. The correction actors are normally deined so that they are unity under standard or ideal (e.g. zero scatter) operating conditions. 6

17 .1. Uncertainty components or measurement o air kerma.1..1 Reading o secondary standard instrument, Ms The secondary standard normally has a digital display. The uncertainty o the mean reading is the standard deviation o the mean o a series o values provided that the resolution o the display is suiciently sensitive. This is a Type A uncertainty with a normal distribution. The uncertainties or the various types o outputs and displays are discussed in Section Reading o secondary standard instrument due to background, M B The reading is corrected or background and eects such as leakage currents by subtraction o a reading made with the radiation source switched o or removed. The uncertainty or the background reading is the standard deviation o the mean o a series o readings. This is a Type A uncertainty with a normal distribution. It may be necessary to include the eect o temporal luctuation o the background alibration actor o the secondary standard instrument, s The uncertainty or the calibration actor is reported on the calibration certiicate supplied by the standardising laboratory. It is quoted or a 95% conidence level and has a normal distribution. The value is corrected or the change in sensitivity that is revealed as a drit in its response to a check-source since the last calibration. A typical value or drit is around 0.3 %, with an uncertainty o less than 0.1% that is olded into the uncertainty or s Instrument scale non-linearity correction, F nl This is dependent on the instrument and its value along with the associated uncertainty should be obtained rom the manuacturer s data or the calibration certiicate Instrument range correction actor, F r This is dependent on the instrument and its value along with the associated uncertainty should be obtained rom the manuacturer s data or the calibration certiicate Directional dependence o the ionisation chamber, F dd This is dependent on the instrument and the relevant inormation should be obtained rom the manuacturer s data Non-uniormity o ield, F nu Because the ionisation chamber averages kerma over a cross section o the beam, a correction is applied to give the kerma at a point on the beam axis. The intensity proile o the radiation ield across this area depends on the collimation o the source, the distance between source and ionisation chamber, and the radius o the latter. The proile is measured on a convenient occasion using a small probe. The correction may amount to % (i.e. F nu 1.00) or a large- 7

18 volume ionisation chamber used at short source distances. It is obtained by olding the proile into the area o the ionisation chamber. The uncertainty is assumed to have a rectangular distribution usually with a semi-range o up to 5% o the correction, e.g. F nu ± Scatter rom the surroundings, F room The eect o lower energy room- and air-scattered radiation or the secondary standard depends on the energy dependence o the response. This component should be measured and subtracted, yielding the direct component. In avourable geometries, this correction is usually small and the associated uncertainty is correspondingly low. However, whereas the direct beam component varies with distance rom source approximately according to an inverse square law, the scatter component is relatively constant and thereore its eect increases markedly with distance. The eect o scatter on the response o instruments subsequently calibrated in the ield can be similar to that or the secondary standard and the overall uncertainty o the calibration would be lessened accordingly. See Section Scatter rom the instrument mounts, F scim This correction is generally in the region o 1 to %, depending on the structure o the table top, with a correspondingly low uncertainty. The eect can be assessed by bringing an extra mount up to the instrument. The same remarks as or the room- and air-scatter correction apply except that it varies in a similar manner to the direct component and the correction is thereore approximately constant with distance Rate correction actor, F rate This is dependent on the instrument and the kerma rate. The actor and its uncertainty should be obtained using the manuacturer s data. For typical ionisation chambers the uncertainty due to recombination eects is generally less than 0.1 %, but there can be other eects contributing to this actor such as the perormance o any analogue to digital converter Ambient temperature, F T When measuring kerma rate with an unsealed ionisation chamber a correction must be applied or the eect o temperature and pressure on air density. The correction actor or temperature, F T, is (T + 73) / 93 where T is the temperature o ionisation chamber in degrees elsius. Temperature variation may aect also the calibration o the instrument s electronics Ambient pressure, F P The correction actor or pressure, F P, is /P where P is pressure in mbar. (Note: 1 mbar 100 Pa; 1 atmosphere kpa) 8

19 Humidity correction actor, F H The values or the humidity correction actor or relative humidity ranging rom 0% to 70% indicate that or a small, typical uncertainty in relative humidity the related uncertainty in the ionisation chamber response is o the order o 0.05% Time, F Ti The timer used to set the period or the dose integration must be calibrated against the UK national time standard. Normally the uncertainty in this correction would be negligible. Another uncertainty may arise due to the resolution o the reading o the timing device..1.3 alibration o beam monitor In the case o a ield produced by a radionuclide source the air kerma measurement may be made with respect to time as the output is constant ater allowance is made or source decay. In order to allow or the variation o the output o X-ray sources, the air kerma measurement is made with respect to a monitor ixed in an appropriate position elsewhere in the ield. This is usually a transmission-type ionisation chamber. The monitor response is calibrated in terms o reading per kerma (rate) at reerence positions along the beam axis..1.4 Uncertainty components or calibration o beam monitor These are in addition to those or the measurement o air kerma Monitor reading The uncertainties associated with instrument readings are discussed in Section Position o secondary standard The uncertainty or a single position is a combination o the uncertainty due to the position o the eective centre o the secondary standard with respect to a reerence mark on the stand holding the instrument mount and that in the distance between the reerence mark and the source o radiation. Both have rectangular distributions. In order to calculate the associated uncertainty in the calibration, it is suiciently accurate to assume an inverse square law with distance, s, between source and instrument or the radiation ield, although the eect o collimator, air attenuation, background and scatter is to produce a deviation rom an inverse square relationship. The sensitivity coeicient or the uncertainty in calibration is thus ( / s). Note: For the calibration o a tertiary instrument using the same stand in the same reerence position, the second uncertainty component would be cancelled out. (Reer to Section..4.7.) 9

20 Interpolation or positions between those where kerma is measured Interpolation is necessary because kerma rate does not ollow an inverse square law exactly due to the eects mentioned above. The accuracy depends on that o the kerma measurements and the positions o the secondary standard and is calculated by the itting program Ambient conditions orrection actors may have to be applied or the eects o ambient temperature, pressure and humidity i the ionisation chamber beam monitor is unsealed. The uncertainties associated with the correction actors or ambient conditions are discussed in Sections.1..11, 1, 13. Note: I the beam monitor is calibrated using an unsealed secondary standard ionisation chamber, the pressure corrections and also the humidity corrections or both instruments would cancel out. However, the two chambers may be at dierent temperatures as one could be ree-in-air and the other could be located in a machine..1.5 Uncertainty budget or measurement o kerma rate An example o an uncertainty budget or the calibration o a beam produced by a radionuclide source ( 137 s) in terms o air kerma rate at a reerence position is given in Table.1. The calibration is carried out by measuring air kerma over a set time interval. A series o ten readings has been made or both beam and background measurements. The uncertainties or these readings are assumed to have normal distributions. The eective number o degrees o reedom has been calculated using the Welch-Satterthwaite ormula (given in Appendix 1 o this guide) in order to demonstrate that the eect on the coverage actor o having a relatively small number o readings is negligible in this case. The ormulae or the partial dierentials used to derive the sensitivity coeicients, c i, are given in the table. In line with common practice in this area, the standard uncertainties, u i (y), are expressed as percentages o the result quantity and the values or the relative sensitivity coeicients are calculated accordingly. Their units are the reciprocal o those o the input quantities to which they correspond. The values used or the quantities and their uncertainties are or illustration only and should not be assumed or other situations. This example is chosen in order to match the example given in the next section..1.6 Reported result For the example shown above, the calibration report could state: 10 The 137 s air kerma rate at the,000 mm reerence position is (83.4 ±.1) μgy h -1 The reported uncertainty is based on a standard uncertainty multiplied by a coverage actor o k, which provides a level o conidence o approximately 95%.

21 Table.1 Uncertainty budget or measurement o kerma rate at a reerence position in a 137 s beam Quantity Mean reading o secondary standard, MS Mean background reading, MB Secondary standard calibration, S Non-linearity actor, Fnl Range correction actor, Fr Directional dependence, Fdd Non-uniormity o beam, Fnu Room scatter, Froom Scatter rom mount, Fscim Rate eects, Frate Temperature, T Pressure, P Humidity Distance, s position o eective centre distance o stand rom source Time, t Air kerma rate, K Expanded uncertainty or K, (k.09) Value μgy mbar 50 %.000 m 100 s 83.4 μgy/h.1 μgy/h Uncertainty ( δxi ) μgy < mbar 5 % mm mm 0. s Probability distribution normal normal normal rectangular rectangular rectangular rectangular rectangular rectangular rectangular rectangular rectangular rectangular rectangular rectangular rectangular normal normal Divisor ( / xi) / y (Ms - MB) -1 (Ms - MB) -1 S 1 / Fnl 1 / Fr 1 / Fdd 1 / Fnu 1 / Froom 1 / Fscim 1 / Frate 1 / (T+73) 1 / P 1 / 100 / s / s 1 / t ci / y 100 / / / / / 600 u(k) U ui ( % ) < vi or ve ui(y) ( δxi / divisor ) x ( ci / y ) The values used or the quantities and their uncertainties are or illustration only and should not be assumed or other situations. 11

22 . alibration o Portable Dose Rate Meter This section deals with the calibration o a portable dose rate meter by measuring its response to the radiation ield that has been calibrated using a secondary standard, as dealt with in the above section. Owing to the wide variety o quality, sensitivity and display devices o radiation monitors, it is impossible to give the uncertainty o calibration o a 'typical' instrument. Instead, the various eects that are taken into account are listed and the range o uncertainties that may contribute to the overall uncertainty are indicated...1 Method The instrument calibration actor, K, in terms o kerma, is derived using the relationship between the kerma, K, (or kerma rate) at the calibration point and the instrument reading K K {(M M B B) ( nu room scim rate T P H ) } -1 with: M - dose rate meter reading, M B B - background reading o dose rate meter. The -actors are analogous to the F-actors in section.1... Uncertainty components or calibration o portable dose rate meter...1 Kerma rate, K The assessment o the uncertainty o kerma at the instrument position in the photon beam per unit o beam monitor response is described in section alibration in terms o dose equivalent, H The dose equivalent (or dose equivalent rate) is given by - D h K The coeicient h converts kerma to the required dose equivalent quantity. The instrument calibration actor in terms o a dose equivalent quantity is equal to K h. The value o h varies with photon energy and is derived rom radiobiological data. Values are published in a standard [5] that also recommends that the value or any mono-energetic ield should be regarded as having no associated uncertainty. In practice however, the spectra rom sources like 137 s and 41 Am are not truly mono-energetic, but include scattered radiation, particularly rom the source encapsulation. The standard thereore urther recommends that an uncertainty, quoted as %, is included or calibrations using such sources. The calibration certiicate should state i this component is omitted rom the uncertainty budget....3 Position The uncertainty in position is a combination o the uncertainty due to the position o the 1

23 eective centre with respect to the instrument support stand and that in the position o the stand with respect to the source o radiation. Both have rectangular distributions. Account should be taken o correlations with uncertainties in the position o the secondary standard instrument. (For example, i the instrument under test is mounted in the same position as the secondary standard the second source o uncertainty would cancel out.) These correlations are relatively small and usually have negligible eect on the overall uncertainty...3 Instrument reading, M The reading may be a digital display or an analogue display (LD or moving needle on a graduated scale) that may be linear or logarithmic. The uncertainty is sometimes reerred to as the resolution o the instrument Analogue display: statistical luctuations At high, constant dose rates, the meter reading o a dose-rate meter will be reasonably steady and thereore could be averaged accurately by eye. The range o the reading and hence the uncertainty may also be estimated by visual inspection with an accuracy that is comparable with, say, the uncertainties due to scale resolution and parallax. The problem with determining the mean and standard deviation o the mean o eye-averaged readings is that each reading is a subjective judgment. The irst estimate o the eye average reading can inluence subsequent estimates, especially i the reading is close to a scale division, and result in an underestimate o the true uncertainty o the estimated readings. At low dose rates the meter indication can luctuate signiicantly, and suicient readings must be taken to enable an average or median value to be derived with the desired accuracy. In order to do this objectively, irst the response time (time to reach 90% o inal reading) at the dose rate is derived either rom manuacturer's instructions or by eye estimate. Then a series o readings is taken over consecutive periods equal to the response time or longer. The mean value and standard deviation o the mean are calculated in the usual manner. Another method that is widely employed is to note the maximum and minimum readings over a period o time and derive the standard uncertainty rom this range. For a constant dose rate, the process is essentially random (stochastic) and thereore a normal distribution should be assumed rather than a rectangular one. The main problem is the assessment o the conidence level to which the maximum and minimum correspond. A long time period would have a greater level o conidence than a shorter one, but a greater range o values would be observed. As a rule o thumb, the total observation time o about twenty times the response time should be used or a conidence level o 95% to be assumed and, in turn, a value o employed or the divisor used to derive the standard deviation o the distribution. The standard deviation o the mean is obtained by dividing this by n, where n is the number o response times in the observation period. 13

24 It may be necessary to treat the instrument reading uncertainty as a dominant component (see Section 1.4.4). Alternatively, this component along with the uncertainty derived by combining all other components may be reported separately. The instrument reading uncertainty could be reported in terms o the minimum and maximum readings observed over a stated period o time. This period should be suiciently long to ensure a conidence level o about 95%...3. Analogue display: parallax I the pointer o a moving-needle display is not very close to the scale, the log-scaled meter o an instrument may read up to 5% high at the top end o the scale and 5% low at the bottom end when viewed by a television camera positioned central to the scale. The error can sometimes be estimated visually and a correction applied or the eect or which the residual uncertainty may be less than ± 1%. The error in linearly-scaled indications can be much higher than this. Note: This uncertainty can be reduced by mounting the optical axis o the TV camera lens on the axis o the meter pivot Analogue display: instrument scale resolution The scale resolution can be estimated by visual inspection. For a linear analogue display, the uncertainty o the reading may be about % near 90% FSD and about 4% at hal-scale. For analogue quasi-logarithmic scales, the percentage uncertainty o observation may be no better than ± 10% and even as high as ± 0% i several decades are compressed into a short scale length. The uncertainty tends to be dominated by the sparseness or otherwise o the scale markings which tend to be closer or readings o around 7, 8, 9, than around 10, 15, Digital display The electronics o most units display the reading to the selected precision and ignore the other digits, i.e. the reading is usually rounded downwards. Thus, or example, a reading o 30 units would mean that the value lies between 30 and 31 with equal probability. The uncertainty is equal to hal o the resolution and has a rectangular distribution [1]. Thereore the result would be 30.5 ± 0.5. Note: In some instruments the last digit displayed is not the least signiicant digit. I the reading wavers between readings o 30 and 31, a airly accurate estimate o the value may be obtained by taking the mean values o a series o readings made at ixed time intervals (and i necessary, adding 0.5 as above). The interval should be equal to or greater than the response time. The reading must be recorded or all intervals in the series - even when it does not change between consecutive intervals. The uncertainty is a combination o the standard 14

25 deviation o the mean (SDOM) o the set o readings and the resolution uncertainty as deined above. This is discussed in [6]. This also applies i the number displayed luctuates between several numbers. Alternatively, instead o deriving the SDOM, the technique o deriving the uncertainty rom the observed maximum and minimum readings (as outlined in..3.1 above) can be employed. As the luctuation increases the eect o the resolution uncertainty decreases...4 Other eects..4.1 Reading due to background, M BB The reading is corrected or background and eects such as leakage currents by subtraction o a reading made with the radiation source o. The uncertainty or the background reading is derived according to the guidance given in section..3.1 above. It may be necessary to take account o the eect o temporal luctuation o the background...4. Field non-uniormity, nu This correction may amount to ± % or an instrument with a large-volume ionisation chamber calibrated at short source distances. It will be much less or small Geiger-Muller tubes and solid-state detectors Scatter rom the surroundings, room These eects are discussed in Sections Scatter rom the instrument mount, scim The correction will usually be less than ± % Rate (dead time) eects, rate Rate eects may arise rom the meter having a dead time (or those based on Geiger-Müller tubes) or rom saturation phenomena (or ionisation chambers). ompensation may be provided electronically (although the correction is not always perect) or be incorporated in the scale gradations o an analogue meter. Thereore rate corrections are not made routinely. I dead time corrections are necessary, the ractional loss or an uncompensated train o pulses may be derived as the product o dead time and eective count rate. (However, dead time is usually rate dependent and it can be diicult to know what value to apply unless the manuacturer gives speciic data or the complete unit.) The sensitivity coeicient or deriving the uncertainty in the calibration actor rom that in the dead time value is thus the count rate. It is generally not possible to observe the count rate directly, in which case it has to be 15

26 derived rom the meter reading and a known conversion actor relating reading to count rate Ambient temperature, pressure and humidity, T, P, H I the beam monitor is an unsealed ionisation chamber, no corrections or pressure are necessary when the instrument under calibration is also an unsealed ionisation chamber, but a correction or any temperature dierence should be applied. Temperature and pressure corrections should be applied to the beam monitor response or the calibration o instruments based on Geiger- Müller tubes or solid-state detectors. I the beam monitor is not an unsealed ionisation chamber then the response o an unsealed ionisation chamber under calibration should be corrected or ambient conditions. Instruments based on Geiger- Müller tubes need no correction...5 Uncertainty budget or the calibration o portable dose rate meter An example o an uncertainty budget or the calibration o monitor in a beam produced by a 137 s source at a non-reerence position is given in Table.. The monitor is based on a small Geiger-Müller tube and has a linear analogue display with several selectable ranges. It is insensitive to ambient conditions. A series o ten readings has been made or beam measurements and the mean value and the standard deviation o the mean calculated. The background and its associated uncertainty were calculated rom the upper and lower readings obtained over about twenty response times...6 Reported result For the example shown below, the calibration certiicate could state: The measured value o the calibration actor or 137 s at an ambient dose equivalent rate o 30 μsv h -1 is: H 1.03 ± 8% An air kerma to ambient dose equivalent conversion coeicient o 1.0 Sv/Gy [4] has been used. The reported uncertainty is based on a standard uncertainty multiplied by a coverage actor o k, which provides a level o conidence o approximately 95%. 16

27 Table. Uncertainty budget or calibration o a portable dose rate meter using using a 137 s beam Quantity Value Uncertainty ( δxi ) Probability distribution Divisor ( / xi) / y ci / y ui ( % ) vi or ve Ambient dose equ. rate at 3460 mm, H 30.0 μsv/h 0.9 μgy/h normal 1 / H 100 / Mean reading o monitor, M 31.0 μsv/h 0.9 μgy/h normal 1 (M MB ) / Parallax uncertainty % rectangular 3 M / (M MB) 31 / Mean background reading, MB 1.0 μsv/h 0.1 μsv/h normal (M MB) / Parallax uncertainty % rectangular 3 MB / (M MB) 1 / 30 < 0.01 onversion coeicient, h % normal Non-uniormity o beam, nu Room scatter, room rectangular 3 1 / nu rectangular 3 1 / room 100 / / Scatter rom mount, scim rectangular 3 1 / scim 100 / Distance, r position o eective centre distance o stand rom source 3.46 m mm 3 mm rectangular rectangular 3 3 / r / r 00/ / alibration actor, H normal u(h) Expanded uncertainty (k.09) normal U ui(y) ( δxi / divisor ) x ( ci / y ) The uncertainty or air kerma rate includes a component or interpolation between measurements at 3 m and 4 m. The values used or the quantities and their uncertainties are or illustration only and should not be assumed or other situations. The eective number o degrees o reedom has been calculated using the Welch-Satterthwaite ormula (see Appendix A1.3). ) 17

28 B Measurement Good Practice Guide No alibration o Neutron Area Survey Monitor A neutron area survey monitor is calibrated by positioning its eective centre at the point o test in a standardised neutron ield and measuring its response. Usually the ield is produced using a radionuclide neutron source with known emission rate and anisotropy actor. The calibration is normally expressed in terms o ambient dose equivalent rate. This is derived by the application o a conversion actor to the neutron luence rate at the monitor position. Neutron monitors are generally based on detectors that produce a pulse or each detected event. The pulse trains are used to produce an analogue or digital display o ambient dose equivalent rate (or ambient dose equivalent), H. Some monitors also have a pulse output channel. 3.1 Use o Field Produced Using a Radionuclide Neutron Source Method In the ollowing example, the monitor is calibrated using an 41 Am- 9 Be(α,n) neutron source. The neutron luence rate is calculated rom the emission rate o the source, assuming an inverse square relationship with the distance rom the source. The reading, M, is given by the expression M R h E 4π r AmBe AmBe A + M aa sc B where: R AmBe - response or 41 Am-Be ield in terms o ambient dose equivalent, h AmBe - luence to ambient dose equivalent conversion coeicient or 41 Am-Be spectrum E - emission rate o source, r - distance o eective centre o meter rom source, A - anisotropy actor or source, aa - air attenuation actor, (depends on the distance between source and dosemeter ront surace), sc - room scatter actor or dosemeter type and 41 Am-Be neutrons, - background reading. M B Note: A geometrical correction [7] is required or distances less than twice the monitor diameter. The calibration actor or an 41 Am-Be spectrum, AmBe, is given by h E 4π r AmBe AmBe A aa sc M / ( M B ) 18