Iec tr 62461 2015

I E C TR 62 461 ® Edition 2.0 201 5-01 TE C H N I C AL RE P ORT colour i n sid e Rad i ati on protecti on i n s tru m e n tati on – D eterm i n ati on of u n certai n ty i n IEC TR 62461 :201 5-01 (en) m e as u rem en t T H I S P U B L I C AT I O N I S C O P YRI G H T P RO T E C T E D C o p yri g h t © I E C , G e n e v a , S wi tz e rl a n d All rights reserved Unless otherwise specified, no part of this publication may be reproduced or utilized in any form or by any means, electronic or mechanical, including photocopying and microfilm, without permission in writing from either IEC or IEC's member National Committee in the country of the requester If you have any questions about I EC copyright or have an enquiry about obtaining additional rights to this publication, please contact the address below or your local I EC member National Committee for further information IEC Central Office 3, rue de Varembé CH-1 21 Geneva 20 Switzerland Tel.: +41 22 91 02 1 Fax: +41 22 91 03 00 info@iec.ch www.iec.ch Ab ou t th e I E C The I nternational Electrotechnical Commission (I EC) is the leading global organization that prepares and publishes I nternational Standards for all electrical, electronic and related technologies Ab o u t I E C p u b l i ca ti o n s The technical content of IEC publications is kept under constant review by the IEC Please make sure that you have the latest edition, a corrigenda or an amendment might have been published I E C Catal og u e - webstore i ec ch /catal og u e The stand-alone application for consulting the entire bibliographical information on IEC International Standards, Technical Specifications, Technical Reports and other documents Available for PC, Mac OS, Android Tablets and iPad I E C pu bl i cati on s s earch - www i ec ch /search pu b The advanced search enables to find IEC publications by a variety of criteria (reference number, text, technical committee,…) It also gives information on projects, replaced and withdrawn publications E l ectroped i a - www el ectroped i a org The world's leading online dictionary of electronic and electrical terms containing more than 30 000 terms and definitions in English and French, with equivalent terms in additional languages Also known as the International Electrotechnical Vocabulary (IEV) online I E C G l os sary - s td i ec ch /g l oss ary More than 60 000 electrotechnical terminology entries in English and French extracted from the Terms and Definitions clause of IEC publications issued since 2002 Some entries have been collected from earlier publications of IEC TC 37, 77, 86 and CISPR I E C J u st Pu bl i s h ed - webstore i ec ch /j u stpu bl i sh ed Stay up to date on all new IEC publications Just Published details all new publications released Available online and also once a month by email I E C C u stom er S ervi ce C en tre - webstore i ec ch /csc If you wish to give us your feedback on this publication or need further assistance, please contact the Customer Service Centre: csc@iec.ch I E C TR 62 461 ® Edition 2.0 201 5-01 TE C H N I C AL RE P ORT colour i n sid e Rad i ati on protecti on i n s tru m en tati on – D eterm i n ati on of u n certai n ty i n m e as u re m e n t INTERNATIONAL ELECTROTECHNICAL COMMISSION ICS 3.280 ISBN 978-2-8322-221 6-4 Warn i n g ! M ake su re th a t you obtai n ed th i s pu bl i cati on from an au th ori zed d i s tri bu tor ® Registered trademark of the International Electrotechnical Commission –2– I EC TR 62461 : 201 © I EC 201 CONTENTS FOREWORD I NTRODUCTI ON Scope Norm ative references Terms and definitions List of sym bols The GU M and the GUM S1 concept General concept of uncertainty determ ination Overview in four steps Summ ary of the anal ytical method for steps and 5 Summ ary of the M onte Carlo m ethod for steps and 5 Which method to use: Anal ytical or M onte Carlo? Example of a model function Collection of data and existing knowledge for the exam ple General Calibration factor for the exam ple 3 Zero reading for the exam ple 20 Reading for the example 21 5 Relative response or correction factor for the exam ple 21 Comparison of probability density distributions for input quantities 23 Calculation of the result of a m easurem ent and its standard uncertainty (uncertainty budget) 25 General 25 Anal ytical m ethod 25 Monte Carlo m ethod 26 4 Uncertainty budgets 26 5 Statem ent of the measurement result and its expanded uncertainty 27 5 General 27 5 Anal ytical m ethod 28 5 Monte Carlo m ethod 28 5 Representation of the output distribution function in a sim ple form (Monte Carlo m ethod) 31 Results below the decision threshold of the measuring device 31 Overview of the annexes 32 Annex A (informative) Exam ple of an uncertainty anal ysis for a measurement with an electronic am bient dose equivalent rate m eter according to I EC 60846-1 : 2009 33 A General 33 A Model function 33 A Calculation of the complete result of the measurement (m easured value, probability density distribution, associated standard uncertainty, and the coverage interval) 34 A 3.1 General 34 A 3.2 Low level of consideration of m easuring conditions 35 A 3.3 High level of consideration of m easuring conditions 37 Annex B (informative) Exam ple of an uncertainty anal ysis for a measurement with a passive integrating dosimetry system according to I EC 62387: 201 40 I EC TR 62461 :201 © I EC 201 –3– B B B General 40 Model function 40 Calculation of the complete result of the measurement (m easured value, probability density distribution, associated standard uncertainty, and the coverage interval) 41 B 3.1 General 41 B 3.2 Low level of consideration of workplace conditions 41 B 3.3 High level of consideration of workplace conditions 43 Annex C (inform ative) Exam ple of an u ncertainty analysis for a measurement with an electronic direct reading neutron ambient dose equivalent m eter according to I EC 61 005: 2003 46 C General 46 C Model function 46 C Calculation of the complete result of the measurement (m easured value, probability density distribution, associated standard uncertainty, and the coverage interval) 47 C General 47 C Anal ytical m ethod 47 C 3 Monte Carlo m ethod 48 C Comparison of the result of the anal ytical and the Monte Carlo method 49 Annex D (informative) Exam ple of an uncertainty anal ysis for a calibration of radon activity monitor according to the I EC 61 577 series 51 D General 51 D Model function 51 D Calculation of the complete result of the measurement (m easured value, probability density distribution, associated standard uncertainty, and the coverage interval) 51 Annex E (informative) Exam ple of an uncertainty anal ysis for a measurement of surface emission rate with a contam ination meter according to I EC 60325:2002 54 E General 54 E Model function 54 E Calculation of the com plete result of the measurem ent (m easured value, probability density distribution, associated standard uncertainty, and the coverage interval) 54 E 3.1 General 54 E 3.2 Effects of distance 55 E 3.3 Contamination non-uniformity 55 E 3.4 Surface absorption 56 E 3.5 Other influence quantities 56 E 3.6 Uncertainty budget 56 Bibliograph y 59 Figure – Triangular probability density distribution of possible values n for the calibration factor N 20 Figure – Rectangular probability density distribution of possible values g0 for the zero reading G 21 Figure – Gaussian probability density distribution of possible val ues g for the reading G 21 Figure – Comparison of different probability density distributions of possible values: rectangular (broken line), triangular (dotted line) and Gaussian (solid lin e) distribution 24 Figure – Distribution function Q of the m easured value 29 –4– I EC TR 62461 : 201 © I EC 201 Figure – Probability density distribution (PDF) of the measured value 30 Figure C.1 – Results of the analytical (red dashed lines) and the Monte Carlo m ethod (grey histogram and blue dotted and solid lines) for H * (1 ) 50  Figure D.1 – Result of the anal ytical (red dashed lines) and the M onte Carlo method (grey histogram and blue dotted lines) for KT 53 Table – Symbols (and abbreviated terms) used in the m ain text (excluding annexes) Table – Standard uncertainty and method to com pute the probability density distributions shown in Figure 24 Table – Exam ple of an uncertainty budget for a measurem ent with an electronic dosemeter using the model function M = N K ( G – G ) and low level of consideration of the workplace conditions, see 5.3 27 Table – Exam ple of an uncertainty budget for a measurem ent with an electronic dosemeter using the model function M = N K ( G – G ) and high level of consideration of the workplace conditions, see 5.3 27 Table A – Example of an uncertainty budget for a dose rate measurem ent according to I EC 60846-1 : 2009 with an instrument having a logarithm ic scale and low level of consideration of the m easuring conditions, see text for details 36 Table A – Example of an uncertainty budget for a dose rate measurement according to I EC 60846-1 : 2009 with an instrum ent having a logarithmic scale and high level of consideration of the m easuring conditions, see text for details 38 Table B – Example of an uncertainty budget for a photon dose measurement with a passive dosimetry system according to I EC 62387-1 : 2007 and low level of consideration of the workplace conditions, see text for details 42 Table B – Example of an uncertainty budget for a photon dose m easurement with a passive dosimetry system according to I EC 62387-1 : 2007 and high level of consideration of the m easuring conditions, see text for details 44 Table C – Example of an uncertainty budget for a neutron dose m easurement according to I EC 61 005: 2003 using the anal ytical method 48 Table C – Example of an uncertainty budget for a neutron dose rate measurement according to I EC 61 005: 2003 using the M onte Carlo method 49 Table C – Results of the anal ytical and the M onte Carlo m ethod 50 Table D – List of quantities used in form ula (D ) 51 Table D – List of data available for the input quantities of formula (D ) 52 Table D – Example of an uncertainty budget for the calibration of a radon monitor according to I EC 61 577, see text for details 52 Table E – Example of an uncertainty budget for a surface em ission rate measurement according to I EC 60325: 2002, see text for details 57 Table E – Example of an uncertainty bu dget for a surface emission rate measurement according to I EC 60325: 2002 for the determ ination of the uncertainty at a measured value of zero 58 I EC TR 62461 :201 © I EC 201 –5– INTERNATI ONAL ELECTROTECHNI CAL COMMISSI ON R AD I AT I O N P RO T E C T I O N I N S T RU M E N T AT I O N – D E T E RM I N AT I O N O F U N C E RT AI N T Y I N M E AS U RE M E N T FOREWORD ) The I nternati on al Electrotechni cal Comm ission (I EC) is a worl d wid e organization for stan dardization com prisin g all n ation al el ectrotechnical comm ittees (I EC National Comm ittees) The object of I EC is to prom ote internati onal co-operation on all q uestions concerni ng stand ardi zati on in the el ectrical an d electronic fi elds To this en d and in additi on to other acti vities, I EC pu blish es I nternational Stan dards, Techn ical Specificati ons, Technical Reports, Publicl y Avail abl e Specificati ons (PAS) an d Gu ides (h ereafter referred to as “I EC Publication(s)”) Th ei r preparation is entrusted to tech nical comm ittees; any I EC N ational Comm ittee interested in the subj ect dealt with m ay partici pate in this preparatory work I nternational, governm ental an d n on governm ental organ izations l iaising with th e I EC also participate i n this preparation I EC collaborates closel y with the I ntern ational Organi zation for Stand ardization (I SO) in accordance with ditions determ ined by agreem ent between th e two organi zati ons 2) The form al decisions or ag reem ents of I EC on tech nical m atters express, as n early as possible, an i nternati onal consensus of opi nion on the rel evant subjects since each technical com m ittee has representati on from all interested I EC N ational Com m ittees 3) I EC Publications have the form of recom m endations for intern ational use an d are accepted by I EC National Com m ittees in that sense While all reasonable efforts are m ade to ensure that th e tech nical content of I EC Publications is accu rate, I EC cann ot be h eld responsi ble for th e way in which th ey are used or for an y m isinterpretation by an y en d u ser 4) I n order to prom ote intern ational u niform ity, I EC National Com m ittees und ertake to appl y I EC Publications transparentl y to the m axim um extent possible i n their national an d regi on al publicati ons Any d ivergence between an y I EC Publication and the correspondi ng national or regi on al publicati on sh all be clearl y in dicated in the latter 5) I EC itself d oes n ot provi de an y attestation of conform ity I n depend ent certificati on bodies provi de conform ity assessm ent services and, in som e areas, access to I EC m arks of conform ity I EC is not responsi ble for any services carri ed out by ind ependent certification bodi es 6) All users shou ld ensure that th ey h ave the l atest editi on of thi s publicati on 7) No liability shall attach to I EC or its directors, em ployees, servants or ag ents inclu din g in divi du al experts an d m em bers of its tech nical com m ittees and I EC Nati on al Com m ittees for any person al i nju ry, property d am age or other dam age of any n ature whatsoever, whether di rect or indirect, or for costs (includ i ng leg al fees) and expenses arisi ng out of the publ ication, use of, or relian ce upon, this I EC Publicati on or any other I EC Publications 8) Attention is drawn to th e N orm ative references cited in th is publ ication Use of the referenced publ ications is indispensable for the correct applicati on of this publication 9) Attention is drawn to the possibility that som e of the elem ents of this I EC Publication m ay be the su bject of patent rig hts I EC shall not be held responsibl e for identifyi ng any or all such patent ri ghts The m ain task of I EC technical com mittees is to prepare I nternational Standards H owever, a technical committee m ay propose the publication of a technical report when it has collected data of a different kind from that which is normally published as an I nternational Standard, for exam ple "state of the art" I EC 62461 , which is a technical report, has been prepared by subcomm ittee 45B: Radiation protection instrum entation, of I EC technical committee 45: Nuclear instrumentation This second edition of I EC TR 62461 cancels and replaces the first edition , published in 2006, and constitutes a technical revision The m ain changes with respect to the previous edition are as follows: – add to the anal ytical m ethod for the determination of uncertainty the Monte Carlo m ethod for the determination of uncertainty according to supplem ent of the Guide to the Expression of uncertainty in m easurement (GU M S1 ), and – add a very sim ple m ethod to judge whether a measured result is significantly different from zero or not based on I SO 1 929 –6– I EC TR 62461 : 201 © I EC 201 The text of this technical report is based on the following docum ents: Enqui ry draft Report on votin g 45B/783/DTR 45B/81 3/RVD Full information on the voting for the approval of this technical report can be found in th e report on voting indicated in the above table This publication has been drafted in accordance with the I SO/I EC Directives, Part The comm ittee has decided that the contents of this publication will remain unchanged until the stability date indicated on the I EC website under "http: //webstore iec.ch" in the data related to the specific publication At this date, the publication will be • • • • reconfirmed, withdrawn, replaced by a revised edition, or amended A bilingual version of this publication m ay be issued at a later date I M P O R T AN T th a t it – Th e co n ta i n s u n d e rs t a n d i n g c o l o u r p ri n t e r of ' co l ou r c o l o u rs i ts in si d e' wh i ch c o n te n ts l og o a re U s e rs on th e cover c o n s i d e re d sh ou l d p ag e to t h e re fo re of th i s be p ri n t p u b l i cati on u s e fu l th i s fo r i n d i c ate s th e d ocu m e n t c o rre c t u si n g a I EC TR 62461 :201 © I EC 201 –7– INTRODUCTION The I SO/I EC Guide 98-3: 2008, Uncertainty of measurement – Part 3: Guide to the expression of uncertainty in measurement (GUM:1995) as well as its Supplem ent :2008, Propagation of distributions using a Monte Carlo method (GU M S1 ), are general guides to assess the uncertainty in measurement This Technical Report lays emphasis on their application in the area of radiation protection and serves as a practical introduction to the GUM and its supplem ent (GUM S1 ) The process of determ ining the uncertainty delivers not onl y a num erical value of the uncertainty; in addition it produces the best estimate of the quantity to be measured which may differ from the indication of the instrum ent Thus, it can also im prove the result of the measurem ent by using information beyond the indicated value of the instrument, e g the energ y dependence of the instrum ent –8– I EC TR 62461 : 201 © I EC 201 R AD I AT I O N P RO T E C T I O N I N S T RU M E N T AT I O N – D E T E RM I N AT I O N O F U N C E RT AI N T Y I N M E AS U RE M E N T S cop e This Technical Report gives guidelines for the application of the uncertainty analysis accord ing to I SO/I EC Guide 98-3: 2008 (GUM describing an anal ytical method for the uncertainty determination) and its Supplement : 2008 (GU M S1 describing a Monte Carlo m ethod for the uncertainty determination) for m easurem ents covered by standards of I EC Subcommittee 45B It does not include the uncertainty associated with the concept of the m easuring quantity, e g., the difference between Hp (1 0) on the I SO water slab phantom and on the person This Technical Report explains the principles of the I SO/I EC Guide 98-3: 2008 (GU M),its Supplem ent :2008 (GUM S1 ) and the special considerations necessary for radiation protection at an example taken from individual dosimetry of external radiation I n the inform ative annexes, several examples are given for the application on instrum ents, for which SC 45B has developed standards This Technical Report is supposed to assist the understanding of the I SO/I EC Guide 983: 2008 (GU M), its Supplement : 2008 (GU M S1 ), and other papers on uncertainty analysis I t cannot replace these papers nor can it provide the background and justification of the argum ents leading to the concept of the I SO/I EC Guide 98-3: 2008 (GU M) and its Supplem ent : 2008 (GU M S1 ) Finally, this Technical Report gives a very sim ple method to j udge whether a measured result is significantl y different from zero or not based on I SO 1 929 For better readability the correct term s are not always used throughout this technical report For exam ple, instead of “random variables of a quantity” onl y the “quantity” itself is stated N o rm a t i ve re fe re n c e s The following documents, in whole or in part, are norm ativel y referenced in this document and are indispensable for its application For dated references, onl y the edition cited applies For undated references, the latest edition of the referenced docum ent (including an y amendments) applies I EC 60050 (all parts): http://www electropedia org) International Electrotechnical Vocabulary (available at I SO/I EC Guide 98-3: 2008, Uncertainty of measurement – Part 3: Guide to the expression of uncertainty in measurement (GUM:1995) I SO/I EC Guide 98-3, Supplement : 2008, Uncertainty of measurement – Part 3: Guide to the expression of uncertainty in measurement (GUM:1995) – Propagation of distributions using a Monte Carlo method – 48 – Tabl e C – E xa m p l e o f a n a c c o rd i n g I EC TR 62461 :201 © I EC 201 u n c e rt a i n t y b u d g e t fo r a n e u t ro n to I E C 61 0 5: 0 u s i n g th e a n a l yti c a l d o s e m e a s u re m e n t m eth o d U n c e rt a i n t y D i s t ri b u t i o n ; Best Ab s o l u t e m ean Qu a n ti t y e s ti m a te s t a n d a rd va l u e , u n c e rta i n t y h a l f- w i d t h , N0 , 00 G m Sv/h 0,1 Triangular; = 0, 041 0, 20 × m Sv/h = 2, mSv/h x; a , 54 3, m Sv/h Rectan gul ar; 4, m Sv/h , m Sv/h Rectangul ar; 1 , m Sv/h 4, m Sv/h Rectangul ar; 4, m Sv/h 2, m Sv/h Rectan gul ar; −1 5, m Sv /h 0, 89 m Sv/h Rectan gul ar; −1 5, m Sv /h 0, 89 m Sv/h Rectan gul ar; −1 5, m Sv /h , m Sv/h Rectan gul ar; 4, m Sv/h , m Sv/h Rectan gul ar; −1 5, m Sv /h , m Sv/h Rectan gul ar; −1 5, m Sv /h 0, 89 m Sv/h Rectan gul ar; −1 5, m Sv /h 0, 89 m Sv/h Rectan gul ar; −1 5, m Sv /h 0, 89 m Sv/h Rectan gul ar; −1 5, m Sv /h 0, 89 m Sv/h Rectan gul ar; −1 5, m Sv /h 0, 89 m Sv/h Rectan gul ar; −1 5, m Sv /h 0, 89 m Sv/h Gaussian with one readin g; = m Sv; a = m Sv , 04 0, 21 = 0, 21 KE x = , 04; a = 0, 21 , 33 0, 67 = 0, 387 Kϕ x = , 33; a = 0, 67 , 07 0, 27 = 0, 56 R ph ; rel x = , 07; a = 0, 27 , 00 0,1 = 0, 058 R po w; rel x = , 0; a = 0, 1 , 00 0,1 = 0, 058 R vi br; rel x = , 0; a = 0, 1 , 00 0,1 = 0, 087 Ktemp; rel x = , 0; a = 0, , 04 0, 21 = 0, 21 R te mpsh o ck; rel x = , 04; a = 0, 21 , 00 0,1 = 0, 087 R E MC, ; rel x = , 0; a = 0, , 00 0,1 = 0, 058 R E MC, 2; rel x = , 0; a = 0, 1 , 00 0,1 = 0, 058 R E MC, 3; rel x = , 0; a = 0, 1 , 00 0,1 = 0, 058 R E MC, 4; rel x = , 0; a = 0, 1 , 00 0,1 = 0, 058 R E MC, 5; rel x = , 0; a = 0, 1 , 00 0,1 = 0, 058 R E MC, 6; rel x = , 0; a = 0, 1 , 00 0,1 = 0, 058 x = , 0; a = 0, H * (1 0) 5, m Sv/h 7, m Sv/h (47 %) (Anal ytical m ethod ) to o u u t q u a n ti t y 0, 63 m Sv/h Kn  c o n t ri b u t i o n c o e ffi c i e n t 5, m Sv/h x = , 0; a = 0, x S e n s i ti vi t y The complete result of the measurem ent of the am bient dose equivalent rate for neutron radiation according to Table C.1 is: H * (1 )  = (1 ± 4) m Sv/h (C 3) The uncertainty stated is the expanded measurement uncertainty obtained by m ultipl ying the standard uncertainty by a coverage factor kcov = I t has been determ ined in accordance with the Guide to the Expression of Uncertainty in Measurement The value of the m easurand norm all y lies, with a probability of approxim atel y 95 %, within the attributed coverage interval C 3 M o n t e C a rl o m e t h o d Formula (C ) is used as model function I n Table C 2, the complete uncertainty budget for an indicated value of g = m Sv is given I EC TR 62461 :201 © I EC 201 – 49 – T a b l e C – E xa m p l e o f a n u n c e rt a i n t y b u d g e t fo r a n e u t ro n m e a s u re m e n t a c c o rd i n g t o I E C d o s e t e 0 : 0 u s i n g t h e M o n t e C a rl o m e t h o d D i s t ri b u t i o n ; Ab s o l u t e Qu a n ti t y m ean B e s t e s ti m a t e s t a n d a rd val u e , u n c e rt a i n t y h a l f- w i d t h , N0 , 00 G m Sv/h R n ; rel , 00 R E; rel x; a Triangu lar; = 0, 041 x = , 0; a = 0, 1 m Sv/h = 2, m Sv/h Gaussian with one readin g; x = m Sv; a = m Sv 0, 20 = 0, 1 x = , 0; a = 0, , 00 0,50 = 0, 289 R ϕ ; rel x = , 0; a = 0, , 00 0, 25 = 0, 44 R ph ; rel x = , 0; a = 0, 25 , 00 0,1 = 0, 058 R po w; rel x = , 0; a = 0, 1 , 00 0,1 = 0, 058 R vi br; rel x = , 0; a = 0, 1 , 00 0,1 = 0, 087 R temp; rel x = , 0; a = 0, , 00 0, 20 = 0, 1 R te mpsh ock; rel x = , 0; a = 0, , 00 0,1 = 0, 087 R EM C, ; rel x = , 0; a = 0, , 00 0,1 = 0, 058 R EM C, 2; rel x = , 0; a = 0, 1 , 00 0,1 = 0, 058 R EM C, 3; rel x = , 0; a = 0, 1 , 00 0,1 = 0, 058 R EM C, 4; rel x = , 0; a = 0, 1 , 00 0,1 = 0, 058 R EM C, 5; rel x = , 0; a = 0, 1 , 00 0,1 = 0, 058 R EM C, 6; rel x = , 0; a = 0, 1 , 00 0,1 = 0, 058 x = , 0; a = 0, H * (1 0) 2, m Sv/h  0,1 0, 20 × Rectan gul ar; Rectan gul ar; Rectan gul ar; Rectan gul ar; Rectan gul ar; Rectan gul ar; Rectan gul ar; Rectan gul ar; Rectan gul ar; Rectan gul ar; Rectan gul ar; Rectan gul ar; Rectan gul ar; Rectan gul ar; (M onte Carlo m ethod ) 6, m Sv/h (51 %) The complete result of the measurem ent of the am bient dose equivalent rate for neutron radiation according to Table C.2 is: H * (1 )  = (1 +1 ) mSv (C 4) −9 The uncertainty stated is the expanded measurement u ncertainty with a coverage probability of p = 95 % obtained from the distribution function of the output quantity I t has been determined in accordance with Supplement of the Guide to the Expression of Uncertainty in Measurement The value of the measurand norm all y lies, with a probability of approximatel y 95 %, within the attributed coverage interval (shortest interval) C C o m p a ri s o n o f t h e re s u l t o f t h e a n a l y t i c a l an d t h e M o n t e C a rl o m e t h o d I n Figure C the resulting probability density function (PDF) from the Monte Carlo m ethod and the resulting Gaussian PDF according to the anal ytical m ethod are shown I t can clearl y be seen that the realistic result from the Monte Carlo m ethod is not represented by the result of the anal ytical method, neither the mean value nor the coverage interval This can also be – 50 – I EC TR 62461 :201 © I EC 201 seen by comparing the data given in Table C and was formerly confirmed by measurements [1 ] The reason for the deviation of the best estimate from the indicated value of mSv/h com es for the M onte Carlo m ethod from the non-linear model function; the even stronger deviation for the anal ytical method has its reason in the artificial (but necessary) transformation of variables from response values to correction factors and the resulting ranges that are not symm etrical to unity, see C and (paragraph after the note) As a consequence, two different model functions are used which is the main reason for the strong deviations between the results of the anal ytical and the Monte Carlo m ethod In conclusion, the deviation of the best estim ate and the lim its of the coverage interval is much larger than the criterion of % introduced in Therefore, the Monte Carlo method should be used in this case Besides the shortest coverage interval also the probabilisticall y sym metric coverage interval is given in Figure C and Table C.2 As the probability distribution function (PDF) of the dose rate is quite non-sym metric (log-normal), quite different intervals occur although both cover 95 % of the PDF I n such cases the shortest coverage interval is clearly superior the probabilisticall y sym metric and should, therefore, always be stated (see 5 3) This exam ple clearl y dem onstrates the benefits of the Monte Carlo method , not onl y for the determination of uncertainty but also for the best estim ate of the m easured value itself For all cases with similar non-linear model functions with large standard uncertainties of the input quantities (above about %), the Monte Carlo m ethod should to be used 0, 044 ƒ [ H*(1 0)] in h/mSv 0, 088 0 10 20 H*(1 0) in m Sv/h 30 40 IEC NOTE The vertical li nes are the m ean val ues (thick lines), the bou nd ari es of th e coverag e interval from the anal ytical m ethod (thi n red d ashed l ines), the boundaries of the sh ortest coverage interval from the M onte Carl o m ethod (bl ue solid li nes), and the bou ndari es of the probabi listically sym m etric coverage i nterval form the Monte Carlo m ethod (bl ue d otted li nes) Figure C.1 – Results of the analytical (red dashed lines) and the Monte Carlo method (grey histogram and blue dotted and solid lines) for H * (1 )  Table C.3 – Results of the analytical and the Monte Carlo method Best estimate of the measured valu e 95 % coverage interval Analytical m ethod m Sv/h m Sv/h … 29 m Sv/h Monte Carl o m ethod (shortest coverage i nterval) m Sv/h m Sv/h … 24 m Sv/h Monte Carl o m ethod (probabil istically sym m etric coverag e interval ) m Sv/h m Sv/h … 28 m Sv/h I EC TR 62461 :201 © I EC 201 – 51 – An n e x D (informative) E x a m p l e o f a n u n c e rta i n t y a n a l ys i s fo r a c a l i b t i o n o f d o n a c ti vi t y m o n i t o r a c c o rd i n g t o th e I E C 7 s e ri e s D G e n e l I EC 61 577 consists of several parts with the general title Radiation protection instrumentation – Radon and radon decay product measuring instruments [23] to [25] The following example shows the result of a software based method (GU M workbench [1 2]) to determine the uncertainty The following text consists of the direct output of the software plus some additional text for enhancing the understanding The example com prises the calibration of a radon m onitor by a radon reference atm osphere (realisation of the quantity activity concentration) traceable to the input quantities activity and volume D M o d e l fu n c t i o n The model function used for the example is: KT = C ; C = A e − Λ Tc ; V + VRn CT − CT,bg Λ= ln T1 / × 24 × 60 ; CT = CT,Tc + CT,Tbg (D ) where Table D.1 gives the definitions and units of the quantities used Tabl e D Qu a n ti t y A V VRn T½ Λ Tc C CT CT, Tc CT, bg KT D – L i s t o f q u a n ti ti e s u s e d Unit in fo rm u l a ( D ) D e fi n i t i o n Bq Activity of the radon gas stand ard as certified ( t = 0) m3 Reference volum e as certified (displ aced vol um e considered ) m3 d /m in m in Bq/m Volum e of the radon gas stan d ard contai ner Half-life of Rad on -222 Nucl ear Data from NuDat 2002, Evalu ation BNL-N CS-521 42 [26] Decay constant of Radon -222 Point of tim e of the radon gas transfer into the reference volu m e Activity concentrati on of the reference atm osphere at th e point of tim e ( t = tc ) Bq/m Averag e of the observations ( t = tc ) Bq/m Param eter whil e averag ing the observations Bq/m Backgrou nd of th e radon m onitor – Measured val ue (calibrati on factor) C a l c u l a t i o n o f t h e c o m p l e t e re s u l t o f t h e m e a s u re m e n t ( m e a s u re d va l u e , p ro b a b i l i t y d e n s i t y d i s t ri b u t i o n , a s s o c i a t e d s t a n d a rd u n c e rt a i n t y , a n d th e c o ve g e i n t e rva l ) Table D gives all the available data for the input quantities These data are requested from the software – 52 – I EC TR 62461 :201 © I EC 201 T a b l e D – L i s t o f d a t a a v a i l a b l e fo r t h e i n p u t q u a n t i t i e s o f fo rm u l a ( D ) Qu a n ti t y D i s t ri b u t i o n E xp a n d e d C o v e g e u n c e rt a i n t y fa c t o r Bq Re m a rk Va l u e A V VRn T½ Type B norm al distri buti on 52 Bq Type B norm al distri buti on m3 0, 05 0, 000 m3 0, % 3, 823 d 0, 000 d – – – I nterim result Type B rectan gul ar distribution 499 m in – – Half wi dth of lim its: m in C CT – – – – I nterim resul t – – – – I nterim result Th e observations over a tim e of m ore than 24 h are averaged CT, Tc CT, bg KT Type A summ arized 883 Bq/m 25 Bq/m – Deg rees of freedom : 44 Type A summ arized Bq/m Bq/m – Deg rees of freedom : 44 – – – – Result Type B norm al distri buti on 0, 000 062 Type B norm al distri buti on Λ – Tc m3 I n Table D the complete uncertainty budget is given All the values are direct output of the software T a b l e D – E xa m p l e o f a n d o n u n c e rt a i n t y b u d g e t fo r t h e c a l i b t i o n m o n i t o r a c c o rd i n g t o I E C 7 , Ab s o l u t e Qu a n ti t y Λ Tc C CT CT, Tc CT, bg KT KT S e n s i ti vi t y U n c e rt a i n t y c o n t ri b u t i o n c o e ffi c i e n t to o u u t q u a n ti t y B e s t e s ti m a t e s t a n d a rd A V VRn T½ of a s e e t e xt fo r d e t a i l s u n c e rt a i n t y 52 Bq Bq 0, 006 Bq –1 0, 01 0, 050 m 0, 000 m –20 m –3 0, 005 62, 700 × –6 m ³ 0, 063 3, 823 d 25, 893 × 0, 001 499, m in 851 895 Bq/m –6 m 0, 000 d –6 /m in Bq/m × × –20 m –3 ,2 × –6 0, 01 d –1 4, × –6 interim result –6 /m in 5, m in 41 Bq/m 25 Bq/m –0, 000 0, 000 72 m in –1 interim result interim result 883 Bq/m 25 Bq/m –0, 00034 Bq –1 m 0, 008 Bq/m Bq/m Bq –1 m 0, 989 0, 01 (1 , %) (Anal ytical m ethod) 0, 989 0, 01 (1 , %) (Monte Carlo m ethod) The complete result of the measurem ent of the calibration factor of the radon monitor according to Table D is: KT = 0, 989 ± 0,033 (Analytical m ethod) KT = 0, 989 +0 , 034 − ,033 (Monte Carlo m ethod) (D 2) (D 3) The two results differ by less than %, therefore, the anal ytical method can be used and the corresponding statement is: I EC TR 62461 :201 © I EC 201 – 53 – The uncertainty stated is the expanded m easurement uncertainty obtained by multipl ying the standard uncertainty by a coverage factor kcov = I t has been determ ined in accordance with the Guide to the Expression of Uncertainty in Measurement The value of the m easurand norm all y lies, with a probability of approxim atel y 95 %, within the attributed coverage interval I n Figure D , the resulting probability density function (PDF) from the Monte Carlo m ethod and the resulting Gaussian PDF according to the anal ytical m ethod are shown I t can clearl y be seen that the result are equivalent and, therefore, both m ethods are adequate for similar cases For the Monte Carlo method, the shortest coverage interval and the probabilisticall y symm etric coverage interval are equivalent as the PDF is sym metrical, see 5 NOTE I n spite of th e non-l in ear m odel function, the results are equi val ent as th e in put quantities have rather sm all uncertainti es, and, th erefore, a l inear approxim ation of the m odel functi on is possibl e 12 ƒ [ KT] 24 0, 94 0, 96 0, 98 KT , 00 , 02 , 04 IEC NOTE The vertical lin es are the m ean valu es (at kt = 0, 989) and th e bound aries of the coverage intervals from both m ethods Figure D.1 – Result of the analytical (red dashed lines) and the Monte Carlo method (grey histogram and blue dotted lines) for KT – 54 – I EC TR 62461 :201 © I EC 201 An n e x E (informative) E xa m p l e o f a n u n c e rta i n t y a n a l ys i s fo r a m e a s u re m e n t o f s u rfa c e e m i s s i o n te w i th a c o n ta m i n a ti o n m e t e r a c c o rd i n g to I E C : 0 E G e n e l I EC 60325: 2002 has the title Radiation protection instrumentation – Alpha, beta and alpha/beta (beta energy > 60 keV) contamination meters and monitors [27] For the example a contam ination monitor is used to measure the surface em ission rate due to beta contam ination of C with the following rated range and ranges of use for influence quantities: M e a s u ri n g n g e : Are a o f d e t e c t o r: Ra t e d n g e s o f u s e : E M o d e l fu n c t i o n s –1 to 000 s –1 (in counts per second) 00 cm nominal ranges The model function used for the example is: A = C D− B F Kn Khv Ktemp Khum Kd,air Kd , geo Kuniform Ksurface where A C B D F Kn Kh v Ktem p Kh um Kd, r Kd, geo Ku niform Ksu rface E (E ) is the m easured surface em ission rate of C in term s of s –1 cm –2 ; is the indicated value of the activity in terms of s –1 ; is the indicated value of the background in term s of s –1 ; is the area of the detector in terms of cm ; is the calibration factor for the reference beta em itter (area related surface emission rate per indicated activity); is the correction factor for non-linearity; is the correction factor for detector suppl y; is the correction factor for ambient tem perature; is the correction factor for humidity; is the correction factor for distance effects due to air absorption; is the correction factor for distance effects due to geom etric changes; is the correction factor for effects of contam ination non-uniform ity; is the correction factor for effects of surface absorption C a l c u l a t i o n o f t h e c o m p l e t e re s u l t o f t h e m e a s u re m e n t ( m e a s u re d va l u e , p ro b a b i l i t y d e n s i t y d i s t ri b u t i o n , a s s o c i a t e d s t a n d a rd u n c e rt a i n t y , a n d th e c o ve g e i n t e rva l ) E G e n e l I EC 60325 provides for test requirem ents and methods and specifies the allowable variations in response for various influence quantities of the m onitoring equipm ent I t does not specify I EC TR 62461 :201 © I EC 201 – 55 – the way the m onitoring is to be carried out or the effects of the non-uniform ity in the contam ination being measured or the effect of absorption in the surface changing the spectrum of the particles being emitted (total absorption of particles is taken into account by monitoring surface em ission rate and not surface activity) The indicated activity value of the exam ple is c = 600 s –1 over a measuring time of s, the m easured background is b = 350 s –1 over a measuring tim e of s and the detector area is 00 cm with an upper lim it of 01 cm and an lower lim it of 99 cm ; the standard uncertainty of the count rate is 8, % The calibration factor is determ ined to be 40 with a standard uncertainty of For the purposes of this exam ple, the m onitoring is assumed to be between mm and mm distance, i.e at (1 ± 2) m m distance from the surface, whereas the calibration distance was mm This is considered by the correction factors Kd, air and Kd, geo , which, therefore, have to correct for mm additional distance E.3.2 Effects of distance I EC 60325 does not specify the actual distance from the source to detector during measurem ents, but mm is implied H owever, in the act of m onitoring, a fixed distance will not be adhered to, in fact it may be impossible to adhere to There will be two effects, air absorption and geom etric changes Air absorption will be sm all for the higher energ y beta em itters but will be significant in the m onitoring of C For this radionuclide, an additional distance of mm, m m or mm (equivalent to the above given exam ple) results in a reduction in efficiency of about %, % or 23 %, respectivel y For the correction factor Kd, r this results in 1 − 0,1 or , ≤ ≤ Kd ,air ≤ − 01 , 23 (E 2) Kd, air ≤ , 30, which gives Kd, r = , 24 ± 0, 06 Geometric changes alter the solid angle between the detector and source The effect of this would be zero for an infinite plane of uniform contamination The effect could go either way for non-uniform infinite contamination The greatest effect will be for points of contamination The inverse square law generall y will not appl y as the distance between the contam ination and detector is sm all by comparison to the dimensions of the source I t will approach a linear relationship For a contam ination nom inall y mm from a cm × cm detector plane, this geom etric effect alone would cause a % decrease in detection from the calibration value and changes of up to ± mm in this distance will change the value of this decrease of % and %, respectivel y For the correction factor for geom etric effects, Kd, geo , this results in 1 − 0, 08 or , 087 ≤ ≤ Kd , geo ≤ − 01 ,1 (E 3) Kd, g eo ≤ , 36, which gives Kd, geo = ,1 ± 0, 02 I t is assum ed that this is an upper estimate for the geometric effects of the change in distance from mm for the calibration to mm for the m easurem ent E.3.3 Contamination non-uniformity The standard onl y considers the non-uniformity of the detector not that of the contamination The non-uniform ity of the contam ination can onl y be determ ined by other tests but the effect – 56 – I EC TR 62461 :201 © I EC 201 on the measurem ent is likel y to be comparable to that due to the non-uniformity of the detector For the purposes of this exam ple, the effect of the non-uniformity of the contam ination will be sim ilar to the effect of the non-uniform ity of detection over the detector area and is assum ed to be Kuniform = , ± 0, 025 E.3.4 Surface absorption The effect of absorption in the surface again can onl y be determ ined by assessm ent with regard to the nature of the surface and experience The absorption below the surface could be regarded as not of interest since it is included in the definition of the surface em ission rate, however, on the surface there could be grease or dirt which could be removed later and so would be of particular interest For the purposes of this example, it is assum ed that the surface will be covered by a layer between mg cm –2 and m g cm –2 giving for C a reduction in efficiency from % to 76 % This is equivalent to 1 ≤ Ksurface ≤ − 0, − 0, 76 (E 4) or , ≤ Ksu rface ≤ 4, 7, which gives Ksurface = 2, 59 ± ,59 E.3.5 Other influence quantities For the purposes of the exam ple, it is assum ed for the rem aining influence quantities that their associated correction factors all have a value of ,0 with an uncertainty equivalent to the m axim um perm itted value This gives Kn = ,0 ± 0,1 ; Khv = , 00 ± 0, 01 ; Ktem p = , ± 0, 05 and Kh um = ,0 ± 0, 025 E.3.6 Uncertainty budget I n Table E , the complete uncertainty budget for this example is given I t can be seen, that the uncertainty is quite large, therefore, the significance of the result should be checked For this, in Table E the uncertainty for a measured value of zero is given I t yields a value of u ( a =0) = 250 s –1 cm –2 According to clause 6, the decision threshold is then given by a* = k0, 95 · u ( a =0) = 41 s –1 cm –2 with k0, 95 = ,65 for an error probability of α = % The result of the uncertainty anal ysis (360 s –1 cm –2 , see Table E ) is well below the decision threshold, therefore, it is assum ed that no effect of the probe is present Thus, the final statem ent for the result of the m easurement is as follows: The result of the measurem ent cannot be stated because the m easured value is below the decision threshold a* = k1 - α · u (0) = 41 s –1 cm –2 determined for an error probability of α = % The uncertainty at an indicated value of zero, u (0), has been determ ined in accordance with Supplem ent of the Guide to the Expression of Uncertainty in Measurement k1 - α is the quantile of the standardized norm al distribution Onl y if the m easured value exceeded the decision threshold, would the ph ysical effect to be m easured be recognized as detected I f in reality no ph ysical effect is present, then the m easured value is below a* = 41 s –1 cm –2 with a probability of 95 % Alternativel y, an error probability of only % can be chosen, leading to a* = k0, 99 · u ( a =0) = 580 s –1 cm –2 with k0, 99 = 2,32 for an error probability of α = % Then, the final statem ent for the result of the measurem ent is as follows: I EC TR 62461 :201 © I EC 201 – 57 – The result of the measurem ent cannot be stated because the measured value is below the decision threshold a * = k1 - α · u (0) = 580 s –1 cm –2 determined for an error probability of α = % The uncertainty at an indicated value of zero, u (0), has been determ ined in accordance with Supplem ent of the Guide to the Expression of Uncertainty in Measurement k1 - α is the quantile of the standardized norm al distribution Onl y if the m easured value exceeded the decision threshold, would the ph ysical effect to be measured be recognized as detected I f in reality no ph ysical effect is present, then the m easured value is below a * = 580 s –1 cm –2 with a probability of 99 % Tabl e E – E xam pl e o f an u n c e rt a i n t y b u d g e t fo r a s u rfa c e e m i s s i o n m e a s u re m e n t a c c o rd i n g t o I E C : 0 , t e s e e t e x t fo r d e t a i l s D i s t ri b u t i o n ; Ab s o l u t e Qu a n ti - m ean B e s t e s ti m a t e s t a n d a rd ty va l u e , u n c e rta i n t y h a l f- w i d t h , x; a S e n s i ti vi t y U n c e rt a i n t y c o n t ri b u t i o n c o e ffi c i e n t to o u u t q u a n ti t y C 600 s –1 36 s –1 Gaussian with one readin g; x = 600 s -1 ; σ = 8, % , cm –2 90 s –1 cm –2 B 350 s –1 1 s –1 Gaussian with one readin g; x = 350 s -1 ; σ = 8, % − , cm –2 60 s –1 cm –2 D 00 cm Rectan gul ar; x = 00 cm ; a = , cm –3, s – cm –4 2, s – cm –2 F 40 Gaussian; 8, s –1 cm –2 71 s –1 cm –2 Kn ,0 0,1 = 0, 058 x = , 0; a = 0, Rectan gul ar; 360 s –1 cm –2 21 s –1 cm –2 Kh v ,0 0, 01 = 0, 006 x = , 0; a = 0, 01 Rectan gul ar; 360 s –1 cm –2 2, s –1 cm –2 Kte mp ,0 0, 05 = 0, 029 x = , 0; a = 0, 05 Rectan gul ar; 360 s –1 cm –2 s –1 cm –2 Kh u m ,0 0, 025 = 0, 01 x = , 0; a = 0, 025 Rectan gul ar; 360 s –1 cm –2 5, s –1 cm –2 Kd, r , 24 0, 06 = 0, 035 x = , 24; a = 0, 06 Rectan gul ar; 290 s –1 cm –2 s –1 cm –2 Kd, g eo ,1 0, 02 = 0, 01 x = , 1 ; a = 0, 02 Rectan gul ar; 320 s –1 cm –2 3, s –1 cm –2 Ku n i form ,0 0, 025 = 0, 01 x = , 0; a = 0, 025 Rectan gul ar; 360 s –1 cm –2 5, s –1 cm –2 Ksu rface 2, 59 1, 59 = 0, 91 x = 2, 59; a = , 59 Rectan gul ar; 40 s –1 cm –2 30 s –1 cm –2 A A 360 s –1 cm –2 360 s –1 cm = 0, 58 cm 24/3 = cm –2 290 s –1 cm –2 (82 %) 31 s –1 cm –2 (86 %) x = 40; a = 24 (Anal ytical m ethod ) (M onte Carlo m ethod ) – 58 – T a b l e E – E xam p l e o f an I EC TR 62461 :201 © I EC 201 u n c e rt a i n t y b u d g e t fo r a s u rfa c e e m i s s i o n t e m e a s u re m e n t a c c o rd i n g t o I E C : 0 fo r t h e d e t e rm i n a t i o n o f t h e u n c e rt a i n t y a t a m e a s u re d v a l u e o f z e ro D i s t ri b u t i o n ; Ab s o l u t e Qu a n ti - m ean B e s t e s ti m a t e s t a n d a rd ty va l u e , u n c e rta i n t y h a l f- w i d t h , x; a S e n s i ti vi t y U n c e rt a i n t y c o n t ri b u t i o n c o e ffi c i e n t to o u u t q u a n ti t y C 350 s –1 1 s –1 Gaussian with one readin g; x = 350 s -1 ; σ = 8, % , cm –2 60 s –1 cm –2 B 350 s –1 1 s –1 Gaussian with one readin g; x = 350 s -1 ; σ = 8, % − , cm –2 60 s –1 cm –2 D 00 cm Rectan gul ar; x = 00 cm ; a = , cm s – cm –4 s –1 cm –2 F 40 Gaussian; s –1 cm –2 s –1 cm –2 Kn ,0 0,1 = 0, 058 x = , 0; a = 0, Rectan gul ar; s –1 cm –2 s –1 cm –2 Kh v ,0 0, 01 = 0, 006 x = , 0; a = 0, 01 Rectan gul ar; s –1 cm –2 s –1 cm –2 Kte mp ,0 0, 05 = 0, 029 x = , 0; a = 0, 05 Rectan gul ar; s –1 cm –2 s –1 cm –2 Kh u m ,0 0, 025 = 0, 01 x = , 0; a = 0, 025 Rectan gul ar; s –1 cm –2 s –1 cm –2 Kd, r , 24 0, 06 = 0, 035 x = , 24; a = 0, 06 Rectan gul ar; s –1 cm –2 s –1 cm –2 Kd, g eo ,1 0, 02 = 0, 01 x = , 1 ; a = 0, 02 Rectan gul ar; s –1 cm –2 s –1 cm –2 Ku n i form ,0 0, 025 = 0, 01 x = , 0; a = 0, 025 Rectan gul ar; s –1 cm –2 s –1 cm –2 Ksu rface 2, 59 1, 59 = 0, 91 x = 2, 59; a = , 59 Rectan gul ar; s –1 cm –2 s –1 cm –2 A A s –1 cm –2 230 s –1 cm –2 (Anal ytical m ethod) s –1 cm –2 250 s –1 cm –2 (M onte Carlo m ethod ) cm = 0, 58 cm 24/3 = x = 40; a = 24 I EC TR 62461 :201 © I EC 201 – 59 – Bibliography [1 ] I EC 60050-1 51 : 2001 , and magnetic devices International Electrotechnical Vocabulary – Part 151: Electrical [2] I EC 60050-300: 2001 , International Electrotechnical Vocabulary – Electrical and electronic measurements and measuring instruments – Part 311: General terms relating to measurements – Part 312: General terms relating to electrical measurements – Part 313: Types of electrical measuring instruments – Part 314: Specific terms according to the type of instrument [3] I SO/I EC Guide 98-1 :2009, Uncertainty of measurement – Part 1: Introduction to the expression of uncertainty in measurement [4] European co-operation for Accreditation (EA): Expression of Measurement in Calibration , EA-4/02 (previousl y EAL-R2), (http://www european-accreditation org/pdf/EA-4-02n y pdf) [5] PTB-Mitteilungen: Themenschwerpunkt Messunsicherheit, Sonderdruck aus Heft und Heft , Wirtschaftsverlag NW Verlag für neue Wissenschaft GmbH, (in Germ an) I SSN 0030-834X, 2001 [6] National Ph ysical Laboratory (N PL), Measurem ent Good Practice Guide N o 1 (I ssue 2): A Beginner’s Guide to Uncertainty of Measurement, Stephanie Bell, I SSN 368-6550, August 999, I ssue 22 with amendm ents, March 2001 [7] National I nstitute of Standards and Technology (NI ST), N I ST Technical Note 297, 994 Edition (Supersedes J anuary 993 edition): Guidelines for Evaluating and Expressing the Uncertainty of NIST Measurement Results , Barry N Taylor and Chris E Ku yatt [8] M G Cox and B Siebert , The use of a Monte Carlo method for evaluating uncertainty and expanded uncertainty, Metrologia 43 , S1 78-S1 88, 2006 [9] J W E van Dijk, U ncertainties in personal dosim etry for external radiation: a Monte Carlo approach, Rad Prot Dosim 21 , 31 -39, 2006 [1 0] J W E van Dijk, Measurement m odels for passive dosem eters in view of uncertainty evaluation using the Monte Carlo m ethod, Rad Prot Dosim , 62 , 438-445, 201 [1 ] R Behrens, Uncertainties in external dosimetry: Anal ytical vs Monte Carlo method, Rad Prot Dosim , 38 , 346-352, 201 [1 2] GUM Workbench, Version 2.4, Software for the determination of uncertainty in measurement Metrodata GmbH, Germ an y (see www.m etrodata de/index_en htm l) [1 3] UncertRadio, Software for the determination of uncertainty in measurement3 [1 4] [1 5] the Uncertainty of December 999, C Chatfield, Model uncertainty, data mining and statistical inference, Journal 58(3) , 41 9-466, 995 Royal Statistical Society, Series A (Statistics in Society), M Cl yde and E I George, M odel uncertainty, Statistical Science, of the , 81 -94, 2004 _ Note th at this id entificati on is for inform ation al purposes only and does not im ply that it is the best or onl y product avail abl e, an d does not im ply endorsem ent by I EC – 60 – I EC TR 62461 :201 © I EC 201 [1 6] A Possolo and B Tom an, Assessment of m easurem ent uncertainty via observation equations, Metrologia, 44 , 464-475, 2007 [1 7] I EC 61 526: 201 0, Radiation protection instrumentation – Measurement of personal dose equivalents Hp (1 0) and Hp (0, 07) for X, gamma, neutron and beta radiations – Direct reading personal dose equivalent meters and monitors [1 8] I SO 1 929: 201 0, Determination of the characteristic limits (decision threshold, detection limit and limits of the confidence interval) for measurements of ionizing radiation – Fundamentals and application [1 9] I EC 60846-1 : 2009, Radiation protection instrumentation – Ambient and/or directional dose equivalent (rate) meters and/or monitors for beta, X and gamma radiation – Part : Portable workplace and environmental meters and monitors [20] I EC 62387: 201 2, [21 ] I EC 61 005: 2003, Radiation protection instrumentation – Neutron ambient dose equivalent (rate) meters [22] Passive integrating dosimetry systems environmental monitoring of photon and beta radiation for personal and I SO 21 909: 2005, Passive personal neutron dosemeters – Performance and test requirements [23] I EC 61 577-1 : 2006, Radiation protection instrumentation – Radon and radon decay product measuring instruments – Part : General requirements [24] I EC 61 577-2: 201 4, Radiation protection instrumentation – Radon and radon decay product measuring instruments – Part 2: Specific requirements for 222 Rn and 220 Rn measuring instruments [25] I EC 61 577-3: 201 , Radiation protection instrumentation – Radon and radon decay product measuring instruments – Part 3: Specific requirements for radon decay product measuring instruments [26] Brookhaven national laboratory, N ational N uclear http://www nndc bnl gov/, accessed at the 03 December 2004 [27] I EC 60325: 2002, Radiation protection instrumentation – Alpha, beta and alpha/beta (beta energy > 60 keV) contamination meters and monitors Data Center, INTERNATIONAL ELECTROTECHNICAL COMMISSI ON 3, rue de Varembé PO Box 31 CH-1 21 Geneva 20 Switzerland Tel: + 41 22 91 02 1 Fax: + 41 22 91 03 00 info@iec.ch www.iec.ch