Guidelines on the calibration of non-automatic weighing instruments

Transcription

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2 This pblition is identil to the originl EURAMET "Gidelines on the librtion of nontomti weighing instrments" (EURAMET/g-18/v.). The opyright of the originl doment is held by EURAMET e.v. 7. The Clibrtion Gide my not be opied for resle nd my not be reproded other thn in fll. In no event shll EURAMET, the thors or nyone else involved in the retion of the doment be lible for ny dmges whtsoever, rising ot of the se of the informtion ontined herein. The pblition of this doment s SIM Gide hs been spported by fnds of OAS s proet "Implementtion of Metrology Infrstrtre of the Ameris to Spport Free Trde nd Qlity of Life. The prtil or totl reprodtion of this doment is forbidden withot the expressed thoriztion of SIM. 9 1

3 PURPOSE This pblition hs been disssed within the SIM Metrology Working Grop of Mss nd Relted Qntities (SIM MWG7) with the gol of improving the hrmonistion of methods for the librtion of Non-Atomti Weighing Instrments (NAWI) within SIM ontries. This doment provides gidne to ntionl redittion bodies to set p minimm reqirements for the librtion of Non-Atomti Weighing Instrments nd gives dvie to librtion lbortories to estblish prtil proedres. This doment ontins detiled exmples of the estimtion of the nertinty of mesrements. OFFICIAL LANGUAGE This doment ws originlly written in English, nd therefore the English version old be onsidered s the primry referene, however the Spnish version old be sed s referene s lose s possible to the English version. FURTHER INFORMATION For frther informtion bot this pblition, ontt the member of the SIM MWG7 of the Ntionl Metrology Institte of yor ontry. See ) 9

4 CONTENTS 1 INTRODUCTION 5 SCOPE 5 3 TERMINOLOGY AND SYMBOLS 6 4 GENERAL ASPECTS OF THE CALIBRATION Elements of the Clibrtion 7 4. Test lod nd indition Test lods Inditions 15 5 MEASUREMENT METHODS Repetbility test Test for errors of indition Eentriity test Axiliry mesrements 18 6 MEASUREMENT RESULTS Repetbility Errors of indition 6.3 Effet of eentri loding 1 7 UNCERTAINTY OF MEASUREMENT Stndrd nertinty for disrete vles 7. Stndrd nertinty for hrteristi Expnded nertinty t librtion Stndrd nertinty of weighing reslt Expnded nertinty of weighing reslt 37 8 CALIBRATION CERTIFICATE Generl Informtion Informtion bot the librtion proedre Reslts of mesrement Additionl informtion 4 9 VALUE OF MASS OR CONVENTIONAL VALUE OF MASS Vle of mss 4 9. Conventionl vle of mss 4 1 REFERENCES

5 APPENDICES (Informtive) A ADVICE FOR ESTIMATION OF AIR DENSITY 44 A1 Formle for the density of ir 44 A Vritions of prmeters onstitting the ir density 46 A3 Unertinty of ir density 47 B COVERAGE FACTOR K FOR EXPANDED UNCERTAINTY OF 49 MEASUREMENT B1 Obetive 49 B Bsi onditions for the pplition of k = 49 B3 Determining k in other ses 49 C FORMULAE TO DESCRIBE ERRORS IN RELATION TO THE 51 INDICATIONS C1 Obetive 51 C Fntionl reltions 51 C3 Terms withot reltion to the redings 56 D SYMBOLS AND TERMS 57 D1 Symbols of generl pplition 57 D Lotions of importnt terms nd expressions 59 E INFORMATION ON AIR BUOYANCY 6 E1 Density of stndrd weights 6 E Exmples for ir boyny in generl 6 E3 Air boyny for weights onforming to R F EFFECTS OF CONVECTION 66 F1 Reltion between tempertre nd time 66 F Chnge of the pprent mss 68 G EXAMPLES 7 G1 Instrment g pity, sle intervl,1 mg 7 G Instrment 6 kg pity, mlti-intervl 74 G3 Instrment 3 t pity, sle intervl 1 kg

6 1 INTRODUCTION Nontomti weighing instrments re widely sed to determine the qntity of lod in terms of mss. While for some pplitions speified by ntionl legisltion, they re sbet to legl metrologil ontrol i.e. type pprovl, verifition et. - there is n inresing need to hve their metrologil qlity onfirmed by librtion, e.g. where reqired by ISO 91 or ISO/IEC 175 stndrds. SCOPE This doment ontins gidne for the stti librtion of self-inditing, nontomti weighing instrments (herefter lled instrment ), in prtilr for 1. mesrements to be performed,. lltion of the mesring reslts, 3. determintion of the nertinty of mesrement, 4. ontents of librtion ertifites. The obet of the librtion is the indition provided by the instrment in response to n pplied lod. The reslts re expressed in nits of mss. The vle of the lod indited by the instrment will be ffeted by lol grvity, the lod s tempertre nd density, nd the tempertre nd density of the srronding ir. The nertinty of mesrement depends signifintly on properties of the librted instrment itself, not only on the eqipment of the librting lbortory; it n to some extent be reded by inresing the nmber of mesrements performed for librtion. This gideline does not speify lower or pper bondries for the nertinty of mesrement. It is p to the librting lbortory nd the lient to gree on the ntiipted vle of the nertinty of mesrement whih is pproprite in view of the se of the instrment nd in view of the ost of the librtion. While it is not intended to present one or few niform proedres the se of whih wold be obligtory, this doment gives generl gidne for the estblishing of librtion proedres the reslts of whih my be onsidered s eqivlent within the SIM Member Orgnistions. Any sh proedre mst inlde, for limited nmber of test lods, the determintion of the error of indition nd of the nertinty of mesrement ssigned to these errors. The test proedre shold s losely s possible resemble the weighing opertions tht re rotinely being performed by the ser e.g. weighing disrete lods, weighing ontinosly pwrds nd/or downwrds, se of tre blning fntion. 9 5

7 The proedre my frther inlde rles how to derive from the reslts dvie to the ser of the instrment with regrd to the errors, nd ssigned nertinty of mesrement, of inditions whih my or nder norml onditions of se of the instrment, nd/or rles on how to onvert n indition obtined for weighed obet into the vle of mss or onventionl vle of mss of tht obet. The informtion presented in this gideline is intended to serve, nd shold be observed by, 1. bodies rediting lbortories for the librtion of weighing instrments,. lbortories redited for the librtion of nontomti weighing instrments, 3. testhoses, lbortories, or mnftrers sing librted nontomti weighing instrments for mesrements relevnt for the qlity of prodtion sbet to QM reqirements (e.g. ISO 9 series, ISO 11, ISO/IEC 175) A smmry of the min terms nd eqtions sed in this doment is given in Appendix D. 3 TERMINOLOGY AND SYMBOLS The terminology sed in this doment is minly bsed on existing doments: GUM [1] for terms relted to the determintion of reslts nd the nertinty of mesrement, OIML R111 [3] for terms relted to the stndrd weights, OIML R76 [] for terms relted to the fntioning, to the onstrtion, nd to the metrologil hrteristion of nontomti weighing instrments. VIM [7] for terms relted to the librtion. Sh terms re not explined in this doment, bt where they first pper, referenes will be indited. Symbols whose mening is not self-evident, will be explined where they re first sed. Those tht re sed in more thn one setion re olleted in Appendix D1. 9 6

8 4 GENERAL ASPECTS OF THE CALIBRATION 4.1 Elements of the librtion Clibrtion onsists in 1. pplying test lods to the instrment nder speified onditions,. determining the error or vrition of the indition, nd 3. estimting the nertinty of mesrement to be ttribted to the reslts Rnge of librtion Unless reqested otherwise by the lient, librtion extends over the fll weighing rnge [] from Zero to the mximm pity Mx. The lient my speify ertin prt of weighing rnge, limited by minimm lod Mi n nd the lrgest lod to be weighed M x, or individl nominl lods, for whih he reqests librtion. On mltiple rnge instrment [], the lient shold identify whih rnge(s) shll be librted. The preeding prgrph pplies to eh rnge seprtely Ple of librtion Clibrtion is normlly performed on the site where the instrment is being sed. If n instrment is moved to nother lotion fter the librtion, possible effets from 1. differene in lol grvity elertion,. vrition in environmentl onditions, 3. mehnil nd therml onditions dring trnsporttion re likely to lter the performne of the instrment nd my invlidte the librtion. Moving the instrment fter librtion shold therefore be voided, nless immnity to these effets of prtilr instrment, or type of instrment hs been lerly demonstrted. Where this hs not been demonstrted, the librtion ertifite shold not be epted s evidene of trebility Preonditions, preprtions Clibrtion shold not be performed nless 1. the instrment n be redily identified,. ll fntions of the instrment re free from effets of ontmintion or dmge, nd fntions essentil for the librtion operte s intended, 3. presenttion of weight vles is nmbigos nd inditions, where given, re esily redble, 4. the norml onditions of se (ir rrents, vibrtions, stbility of the weighing site et.) re sitble for the instrment to be librted, 9 7

9 5. the instrment is energized prior to librtion for n pproprite period, e.g. s long s the wrm-p time speified for the instrment, or s set by the ser, 6. the instrment is levelled, if pplible, 7. the instrment hs been exerised by loding pproximtely p to the lrgest test lod t lest one, repeted loding is dvised. Instrments tht re intended to be reglrly dsted before se shold be dsted before the librtion, nless otherwise greed with the lient. Adstment shold be performed with the mens tht re normlly pplied by the lient, nd following the mnftrer s instrtions where vilble. As fr s relevnt for the reslts of the librtion, the stts of softwre settings whih n be ltered by the lient shold be noted. Instrments fitted with n tomti zero-setting devie or zero-trking devie [] shold be librted with the devie opertive or not, s set by the lient. For on site librtion the ser of the instrment shold be sked to ensre tht the norml onditions of se previl dring the librtion. In this wy distrbing effets sh s ir rrents, vibrtions, or inlintion of the mesring pltform will, so fr s is possible, be inherent to the mesred vles nd will therefore be inlded in the determined nertinty of mesrement. 4. Test lod nd indition 4..1 Bsi reltion between lod nd indition In generl terms, the indition of n instrment is proportionl to the fore exerted by n obet of mss m on the lod reeptor: I ~ mg( 1 ρ ρ) (4..-1) with g lol grvity elertion ρ density of the srronding ir ρ density of the obet The terms in the brkets ont for the redtion of the fore de to the ir boyny of the obet. 9 8

10 4.. Effet of ir boyny It is stte of the rt to se stndrd weights tht hve been librted to the onventionl vle of mss m 1, for the dstment nd/or the librtion of weighing instrments. The dstment is performed sh tht effets of g nd of the tl boyny of the stndrd weight m s re inlded in the dstment ftor. Therefore, t the moment of the dstment the indition I s is I s = m s (4..-1) This dstment is, of orse, performed nder the onditions hrterized by the tl vles of g s, ρ s ρ, nd ρ s ρ, identified by the sffix s,nd is vlid only nder these onditions. For nother body with ρ ρ s, weighed on the sme instrment bt nder different onditions: g g s y ρ ρ s the indition is in generl (negleting terms of nd or higher order): ( g / ){ 1 ( ρ ρ )( 1ρ 1ρ ) ( ρ ρ )/ ρ } I = m (4..-3) g s If the instrment is not displed, there will be no vrition of g, so g g s = 1. This is ssmed herefter. The forml simplifies frther in sittions where some of the density vles re eql: ) weighing body in the referene ir density: ρ = ρ, then I m s s { 1 ( ρ ρ )/ ρ } = (4..-4) b) weighing body of the sme density s the dstment weight: ρ = ρ s, then gin (s in se ) s s s I m { 1 ( ρ ρ )/ ρ } = (4..-5) s s ) weighing in the sme ir density s t the time of dstment: ρ =, then ρ s I m { 1 ( ρ ρ )( 1 ρ 1 ρ )} = (4..-6) s 1 The onventionl vle of mss m of body hs been defined in [3] s the nmeril vle of mss m of weight of referene density ρ = 8 kg/m³ whih blnes tht body t C in ir of densityρ : m = m{ ( 1 ρ ρ) /( 1 ρ ρ) } (4..-) with ρ = 1, kg/m³ = referene vle of the ir density 9 9

11 Figre 4.-1 shows exmples for the mgnitde of the reltive hnges I / I s = ( I I s) / I s for n instrment dsted with stndrd weights of ρ s = ρ, when librted with stndrd weights of different bt typil density. Line is vlid for body of ρ = 7 81 kg/m³, weighed in ρ = ρ Line is vlid for body of ρ = 8 4 kg/m³, weighed in ρ = ρ Line is vlid for body of ρ ρ s = ρ = fter dstment in s s s ρ = ρ It is obvios tht nder these onditions, vrition in ir density hs fr greter effet thn vrition in the body s density. Frther informtion is given on ir density in Appendix A, nd on ir boyny relted to stndrd weights in Appendix E Effets of onvetion Where weights hve been trnsported to the librtion site they my not hve the sme tempertre s the instrment nd its environment. Two phenomen shold be noted in this se: An initil tempertre differene T my be reded to smller vle T by limtistion over time t ; this ors fster for smller weights thn for lrger ones. When weight is pt on the lod reeptor, the tl differene T will prode n ir flow bot the weight leding to prsiti fores whih reslt in n pprent hnge monv on its mss. The sign of monv is normlly opposite to the sign of T, its vle is greter for lrge weights thn for smll ones. 9 1

12 The reltions between ny of the qntities mentioned: T, t, T, m nd m onv re nonliner, nd they depend on the onditions of het exhnge between the weights nd their environment see [5]. Figre 4.- gives n impression of the mgnitde of the pprent hnge in mss in reltion to tempertre differene, for some seleted weight vles. This effet shold be tken into ont by either letting the weights omodte to the extent tht the remining hnge monv is negligible in view of the nertinty of the librtion reqired by the lient, or by onsidering the possible hnge of indition in the nertinty bdget. The effet my be signifint for weights of high ry, e.g. for weights of lss E or F 1 in R 111 [3]. More detiled informtion is given in Appendix F Referene vle of mss The generl reltions (4..-3) to (4..-6) pply lso if the body weighed is stndrd weight sed for librtion. To determine the errors of indition of n instrment, stndrd weights of known onventionl vle of mss m Cl re pplied. Their density ρ Cl is normlly different from the referene vle ρ nd the ir density ρ Cl t the time of librtion is normlly different from ρ. The error E of indition is E = I (4..4-1) m ref 9 11

13 where m ref is onventionl tre vle of mss, frther lled referene vle of mss. De to effets of ir boyny, onvetion, drift nd others whih my led to minor orretion terms δ mx, m ref is not extly eql to m Cl : m = m + δ m + δm + δm + δm... (4..4-) ref Cl B The orretion for ir boyny δ mb is ffeted by vles of ρ s nd ρ s, tht were vlid for the dstment bt re not normlly known. It is ssmed tht weights of the referene densityρ s = ρ hve been sed. (4..-3) then gives the generl expression for the orretion δm = [( ρ ρ )( 1ρ 1ρ ) + ( ρ ρ ) ρ ] (4..4-3) B m Cl For the ir density ρ s two sittions re onsidered: Cl Cl onv D Cl s A B B1 The instrment hs been dsted immeditely before the librtion, so ρ =. This simplifies (4..4-3) to: s ρ Cl B m Cl ( ρ ρ )( 1ρ ρ ) δm = 1 (4..4-4) Cl Cl The instrment hs been dsted independent of the librtion, in nknown ir density ρ s for whih resonble ssmption shold be mde. For on-site librtions, ρ s my be expeted to be similr to ρ Cl, with the possible differene δρ = ρ ρ. (4..4-3) is then modified to B m Cl s Cl s [( ρ ρ )( 1ρ ρ ) δρ ρ ] δ m = 1 + (4..4-5) Cl Cl s B A simple, strightforwrd ssmption old be ρ s = ρ, then δ m = ρ ρ / ρ (4..4-6) B m Cl ( Cl ) Cl See lso Appendies A nd E for frther informtion. The other orretion terms re delt with in setion 7. The sffix Cl will from now on be omitted nless where neessry to void onfsion. 4.3 Test lods Test lods shold preferbly onsist of stndrd weights tht re treble to the SI nit of mss. Other test lods my be sed, however, for tests of omprtive ntre e.g. test with eentri loding, repetbility test or for the mere loding of n instrment e.g. preloding, tre lod tht is to be blned, sbstittion lod. 9 1

14 4.3.1 Stndrd weights The trebility of weights to be sed s stndrds shll be omplished by librtion onsisting of 1. determintion of the tl onventionl vle of mss m nd/or the orretion δ m to its nominl vle m : δ m = m m, together with the expnded nertinty of the librtion U 95, or. onfirmtion tht m is within speified mximm permissible errors mpe : m ( mpe U 95 ) < m < m + ( mpe U 95 ) The stndrds shold frther stisfy the following reqirements to the extent s pproprite in view of their ry: 3. density ρ s sffiiently lose to ρ C = 8 kg/m³ 4. srfe finish sitble to prevent hnge in mss throgh ontmintion by dirt or dhesion lyers 5. mgneti properties sh tht intertion with the instrment to be librted is minimized. Weights tht omply with the relevnt speifitions of the Interntionl Reommendtion OIML R 111 [3] shold stisfy ll these reqirements. The mximm permissible errors, or the nertinties of librtion of the stndrd weights shll be omptible with the sle intervl d [] of the instrment nd/or the needs of the lient with regrd to the nertinty of the librtion of his instrment Other test lods For ertin pplitions mentioned in 4.3, nd sentene, it is not essentil tht the onventionl vle of mss of test lod is known. In these ses, lods other thn stndrd weights my be sed, with de onsidertion of the following: 1. shpe, mteril, omposition shold llow esy hndling,. shpe, mteril, omposition shold llow the position of the entre of grvity to be redily estimted, 3. their mss mst remin onstnt over the fll period they re in se for the librtion, 4. their density shold be esy to estimte, 5. lods of low density (e.g. ontiners filled with snd or grvel), my reqire speil ttention in view of ir boyny. Tempertre nd brometri pressre my need to be monitored over the fll period the lods re in se for the librtion. ILAC-P 1-, nr. (b): Trebility shll be derived, where possible,... from librtion lbortory tht n demonstrte ompetene, mesrement pbility nd trebility with pproprite mesrement nertinty, e.g. n redited librtion lbortory... nd Note 3: It is reognised by ILAC tht in some eonomies librtions performed by verifying thorities ppointed nder their eonomies Legl metrology frmeworks re lso epted. 9 13

15 4.3.3 Use of sbstittion lods A test lod the onventionl vle of mss of whih is essentil, shold be mde p entirely of stndrd weights. Bt where this is not possible, ny other lod whih stisfies 4.3. my be sed for sbstittion. The instrment nder librtion is sed s omprtor to dst the sbstittion lod L so tht it brings bot pproximtely the sme indition I s the orresponding lod stndrd weights. sb L St mde p of A first test lod L T1 mde p of stndrd weights m 1 is indited s: I L = I ( ) ( ) ( ) St m 1 After removing L St sbstittion lod L sb1 is pt on nd dsted to give pproximtely the sme indition: I( Lsb 1) I( m1) (4.3.3-) so tht L = m + I L I m = m + ( ) ( sb1) ( 1) 1 1 sb1 1 I The next test lod L T is mde p by dding m 1 LT = Lsb 1+ m 1 = m 1+ I1 ( ) m 1 is gin repled by sbstittion lod of sb1 I. L T L with dstment to ( ) The proedre my be repeted, to generte test lods LT3,...LTn : L K ( ) Tn = nm 1+ I1+ I + + I n 1 The vle of LTn is tken s the onventionl vle of mss m of the test lod. With eh sbstittion step however, the nertinty of the totl test lod inreses sbstntilly more thn if it were mde p of stndrd weights only, de to the effets of repetbility nd resoltion of the instrment. f. lso Exmple: for n instrment with Mx = 5 kg, d = 1 kg, the stndrd nertinty of 5 t stndrd weights my be g, while the stndrd nertinty of test lod mde p of 1 t stndrd weights nd 4 t sbstittion lod, will be bot kg 9 14

16 4.4 Inditions Generl Any indition I relted to test lod is bsilly the differene of the inditions I L nder lod nd I t no-lod: I = I ( ) L I It is to be preferred to reord the no-lod inditions together with the lod inditions for ny test mesrement. However, reording the no-lod inditions my be redndnt where test proedre lls for the setting to zero of ny nolod indition whih is not = zero of itself, before test lod is pplied. For ny test lod, inlding no lod, the indition I of the instrment is red nd reorded only when it n be onsidered s being stble. Where high resoltion of the instrment, or environmentl onditions t the librtion site prevent stble inditions, n verge vle shold be reorded together with informtion bot the observed vribility (e.g. spred of vles, nidiretionl drift). Dring librtion tests, the originl inditions shold be reorded, not errors or vritions of the indition Resoltion Inditions re normlly obtined s integer mltiples of the sle intervl d. At the disretion of the librtion lbortory nd with the onsent of the lient, mens to obtin inditions in higher resoltion thn in d my be pplied, e.g. where ompline to speifition is heked nd smllest nertinty is desired. Sh mens my be: 1. swithing the inditing devie to smller sle intervl dt < d ( servie mode ). In this se, the indition I x is then obtined s integer mltiple of dt.. pplying smll extr test weights in steps of d T = d 5 or d 1 to determine more preisely the lod t whih n indition hnges nmbigosly from I to I + d. ( hngeover point method ). In this se, the indition I is reorded together with the mont L of the n dditionl smll test weights neessry to inrese I by one d. The indition I L is ' I = I + d L= I + d (4.4.-1) L nd T Where the hngeover point method is pplied, it is dvised to pply it for the inditions t zero s well where these re reorded. 9 15

17 5 MEASUREMENT METHODS Tests re normlly performed to determine the repetbility of inditions, the errors of inditions, the effet of eentri pplition of lod on the indition. A Clibrtion Lbortory deiding on the nmber of mesrements for its rotine librtion proedre, shold onsider tht in generl, lrger nmber of mesrements tends to rede the nertinty of mesrement bt to inrese the ost. Detils of the tests performed for n individl librtion my be fixed by greement of the lient nd the Clibrtion Lbortory, in view of the norml se of the instrment. The prties my lso gree on frther tests or heks whih my ssist in evlting the performne of the instrment nder speil onditions of se. Any sh greement shold be onsistent with the minimm nmbers of tests s speified in the following setions. 5.1 Repetbility test The test onsists in the repeted deposition of the sme lod on the lod reeptor, nder identil onditions of hndling the lod nd the instrment, nd nder onstnt test onditions, both s fr s possible. The test lod(s) need not be librted nor verified, nless the reslts serve for the determintion of errors of indition s per 5.. The test lod shold, s fr s possible, onsist of one single body. The test is performed with t lest one test lod L T whih shold be seleted in resonble reltion to Mx nd the resoltion of the instrment, to llow n pprisl of the intrment's performne. For instrments with onstnt sle intervl d lod of,5mx LT Mx is qite ommon; this is often reded for instrments where L T >, 5Mx wold mont to severl 1 kg. For mltiintervl instrments [] lod lose to Mx1 my be preferred. A speil vle of L T my be greed between the prties where this is stified in view of speifi pplition of the instrment. The test my be performed t more thn one test point, with test lods 1 k L with k L = nmber of test points. L T, Prior to the test, the indition is set to zero. The lod is to be pplied t lest 5 times, nd t lest 3 times where L T 1 kg. Inditions I Li re reorded for eh deposition of the lod. After eh removl of the lod, the indition shold t lest be heked for showing zero, nd my be reset to zero if it does not; reording of the no-lod inditions I i is dvisble s per In ddition, the stts of the zero devie if fitted is reorded. 9 16

18 5. Test for errors of indition 1. This test is performed with k L 5 different test lods L T, 1 distribted firly evenly over the norml weighing rnge 4 or t individl test points greed pon s per The prpose of this test is n pprisl of the performne of the instrment over the whole weighing rnge. Where signifintly smller rnge of librtion hs been greed to, the nmber of test lods my be reded ordingly, provided there re t lest 3 test points inlding Mi n nd M x, nd the differene between two onsetive test lods is not greter thn,15mx. It is neessry tht test lods onsist of pproprite stndrd weights, or of sbstittion lods s per Prior to the test, the indition is set to zero. The test lods L T re normlly pplied one in one of these mnners: 1. inresing by steps with nloding between the seprte steps orresponding to the mority of ses of the instrments for weighing single lods,. ontinosly inresing by steps similr to 1; my inlde reep effets in the reslts, redes the mont of lods to be moved on nd off the lod reeptor s ompred to 1, 3. ontinosly inresing nd deresing by steps proedre presribed for verifition tests in [], sme omments s for, 4. ontinosly deresing by steps strting from Mx - simltes the se of n instrment s hopper weigher for sbtrtive weighing, sme omments s for. On mlti-intervl instrments see [], the methods bove my be modified for lod steps smller thn Mx, by pplying inresing nd/or deresing tre lods, operting the tre blning fntion, nd pplying test lod of lose to bt not more thn Mx 1 to obtin inditions with d1. Frther tests my be performed to evlte the performne of the instrment nder speil onditions of se, e.g. the indition fter tre blning opertion, the vrition of the indition nder onstnt lod over ertin time, et. The test, or individl lodings, my be repeted to ombine the test with the repetbility test nder 5.1. Inditions I L re reorded for eh lod. After eh removl of lod, the indition shold t lest be heked for showing zero, nd my be reset to zero if 4 Exmples for trget vles:: k L = 5: zero or Min;,5 Mx;,5 Mx;,75 Mx; Mx. Atl test lods my devite from the trget vle p to,1 Mx, provided the differene between onsetive test lods is t lest, Mx. k L = 11: zero or Min, 1 steps of,1 Mx p to Mx. Atl test lods my devite from the trget vle p to,5 Mx, provided the differene between onsetive test lods is t lest,8 Mx. k L, 9 17

19 it does not; reording of the no-lod inditions 5.3 Eentriity test The test onsists in pling test lod I s per L e in different positions on the lod reeptor in sh mnner tht the entre of grvity of the lod tkes the positions s indited in Figre or eqivlent positions, s losely s possible. Fig Centre. Front left 3. Bk left 4. Bk right 5. Front right Positions of lod for test of eentriity The test lod L e shold be t lest Mx 3, or t lest Mi n + ( Mx Min ) 3 for reded weighing rnge. Advie of the mnftrer, if vilble, nd limittions tht re obvios from the design of the instrment shold be onsidered e.g. see OIML R76 [] for weighbridges. The test lod need not be librted nor verified, nless the reslts serve for the determintion of errors of indition s per 5.. Prior to the test, the indition is set to Zero. The test lod is first pt on position 1, is then moved to the other 4 positions in rbitrry order, nd my t lst be gin pt on position 1. Inditions I Li re reorded for eh position of the lod. After eh removl of the lod, the zero indition shold be heked nd my, if pproprite, be reset to zero; reording of the no-lod inditions I s per Axiliry mesrements The following dditionl mesrements or reordings re reommended, in prtilr where librtion is intended to be performed with the lowest possible nertinty. In view of boyny effets f. 4..: The ir tempertre in resonble viinity to the instrment shold be mesred, t lest one dring the librtion. Where n instrment is sed in ontrolled environment, the spn of the tempertre vrition shold be noted, e.g. from tempertre grph, from the settings of the ontrol devie et. Brometri pressre or, by deflt, the ltitde bove se-level of the site my be sefl. In view of onvetion effets f 4..3: Speil re shold be tken to prevent exessive onvetion effets, by observing limiting vle for the tempertre differene between stndrd weights nd instrment, nd/or reording n limtistion time tht hs been omplished. A thermometer kept inside the box with stndrd weights my be helpfl, to hek 9 18

20 the tempertre differene. In view of effets of mgneti intertion: On high resoltion instrments hek is reommended to see if there is n observble effet of mgneti intertion. A stndrd weight is weighed together with sper mde of non-metlli mteril (e.g. wood, plsti), the sper being pled on top or nderneth the weight to obtin two different inditions. If the differene of these two inditions is different from zero, this shold be mentioned s wrning in the librtion ertifite. 6 MEASUREMENT RESULTS The formle in hpters 6 nd 7 re intended to serve s elements of stndrd sheme for n eqivlent evltion of the reslts of the librtion tests. Where they re being pplied nhnged s fr s pplible, no frther desription of the evltion is neessry. It is not intended tht ll of the formle, symbols nd/or indies re sed for presenttion of the reslts in Clibrtion Certifite. The definition of n indition I s given in 4.4 is sed in this setion. 6.1 Repetbility From the n inditions I i for given test lod L T, the stndrd devition s is llted with s n 1 ( I ) = ( I i I ) n 1 i= 1 (6.1-1) I = 1 n n i= 1 I i (6.1-) Where only one test lod hs been pplied, the index my be omitted. 9 19

21 6. Errors of indition 6..1 Disrete vles For eh test lod L Ti, the error of indition is llted s follows: E = I m (6.-1) ref Where n indition I is the men of more thn one reding, I is nderstood s being the men vle s per (6.1-). m ref is the referene weight or tre vle of the lod. f , The referene weight is either the nominl vle or its tl vle m ref m m of the lod, m ref = m (6.-) ( m + δm ) Where test lod ws mde p of more thn 1 weight, nd δ m is repled by ( δ m ) in the formle bove. = m = (6.-3) m is repled by ( m ) Where n error nd/or indition is listed or sed frther in reltion to the test lod, it shold lwys be presented in reltion to the nominl vle m of the lod, even if the tl vle of mss of the test lod hs been sed. In sh se, the error remins nhnged, while the indition is modified by I ( m ) I ( m) δm with I being the (interim) indition determined when (6.-1) then tkes the form = (6.-4) m ws pplied. E ( I m) m = I m = δ (6.-1b) 6.. Chrteristi of the weighing rnge In ddition, or s n lterntive to the disrete vles I, E, hrteristi, or librtion rve my be determined for the weighing rnge, whih llows to estimte the error of indition for ny indition I within the weighing rnge. 9

22 A fntion ( I) E ppr = f (6.-5) my be generted by n pproprite pproximtion whih shold in generl, be bsed on the lest sqres pproh: with v = residl f = pproximtion fntion The pproximtion shold frther = ( f( I ) E ) = v minimm (6.-6) tke ont of the nertinties ( ) of the errors, se model fntion tht reflets the physil properties of the instrment, e.g. the form of the reltion between lod nd its indition I = g( L), inlde hek whether the prmeters fond for the model fntion re mthemtilly onsistent with the tl dt. It is ssmed tht for ny m the error E remins the sme if the tl indition I is repled by its nominl vle I. The lltions to evlte (6.- 6) n therefore be performed with the dt sets m, E, or I, E. Appendix C offers dvie for the seletion of sitble pproximtion forml nd for the neessry lltions. 6.3 Effet of eentri loding From the inditions I i obtined in the different positions of the lod s per 5.3, the differenes I e re llted I 1 E I = I (6.3-1) ei i Where the test lod onsisted of stndrd weight(s), the errors of indition my be llted insted: E ei = I m (6.3-) i 7 UNCERTAINTY OF MEASUREMENT In this setion nd the ones tht follow, there re terms of nertinty ssigned to smll orretions, whih re proportionl to speified mss vle or to speified indition. For the qotient of sh n nertinty divided by the relted vle of mss or indition, the bbrevited nottion wˆ will be sed. 9 1

23 Exmple: let ( m ) m( orr) with the dimensionless term ( orr), then δ orr = (7-1) ( m ) ( orr) wˆ orr = (7-) Aordingly, the relted vrine will be denoted by w ( m orr ) expnded nertinty by Wˆ ( m orr ). 7.1 Stndrd nertinty for disrete vles The bsi forml for the librtion is m ref ˆ nd the relted E= I (7.1-1) with the vrines ( E) ( I) + ( ) = (7.1-) m ref Where sbstittion lods re employed see m ref is repled by L Tn in both expressions. The terms re expnded frther herefter Stndrd nertinty of the indition To ont for sores of vribility of the indition, ( ) is mended by orretion terms δ I s follows: xx I = I + δi + δi + δi I δi ( ) L digl rep e dig All these orretions hve the expettion vle zero. Their stndrd nertinties re: δ I dig onts for the ronding error of no-lod indition. Limits re ± d or ± s pplible; retnglr distribtion is ssmed, therefore or d T respetively. ( I ) ( 3) δ dig = (7.1.1-) d ( I dig ) d ( 3) δ = (7.1.1-b) T 9

24 Note 1: f for signifine of d T. Note : on n instrment whih hs been type pproved to OIML R76 [], the ronding error of zero indition fter zero-setting or tre blning opertion is limited to ± 4, therefore d ( I ) ( 4 3) δ dig = (7.1.1-) d δ I digl onts for the ronding error of indition t lod. Limits re ± d I or ± s pplible; retnglr distribtion to be ssmed, therefore or d T ( ) 3 δ I digl = d I ( ( ) 3 δ I digl = d T ( b) Note: on mlti-intervl instrment, d I vries with I! δ I rep onts for the error de to imperfet repetbility; norml distribtion is ssmed, estimted with ( I ) s s per 6.1. Where n indition nertinty is ( I ) s( I ) δ = ( ) rep I is the men of n redings, the orresponding stndrds ( I ) s( I ) n δ ( ) rep = Where only one repetbility test hs been performed, this stndrd devition my be onsidered s being representtive for ll inditions of the instrment in the weighing rnge onsidered. Where severl s ( s = s( I ) in bbrevited nottion) hve been determined with different test lods, the greter vle of s for the two test points enlosing the indition whose error hs been determined, shold be sed. Where it n be estblished tht the vles of s determined t different test lods L T, re in fntionl reltion to the lod, this fntion my be pplied to ombine the s vles into pooled stndrd devition s pool. Exmples for sh fntions re s s + s = onst ( ) r ( L Mx) = s ( ) T The omponents lltion. s nd s r hve to be determined either by grph or by 9 3

25 Note: For stndrd devition reported in librtion ertifite, it shold be ler whether it is relted to single indition or to the men of n inditions δ I e onts for the error de to off-entre position of the entre of grvity of test lod. This effet my or where test lod is mde p of more thn one body. Where this effet nnot be negleted, n estimte of its mgnitde my be bsed on these ssmptions: the differenes determined by (6.3-1) re proportionl to the distne of the lod from the entre of the lod reeptor nd to the vle of the lod; the eentriity of the effetive entre of grvity of the test lod is no more thn1 of the vle t the eentriity test. While there my be instrments on whih the effet of eentri loding is even greter t other ngles thn those where the test lods hve been pplied, bsed on the lrgest of the differenes determined s per 6.3, the effet is estimted to be δ I { I ( L )}I ( ) e e, i mx e Retnglr distribtion is ssmed, so the stndrd nertinty is δ I = I I L 3 ( ) ( ) ( ) e e, i mx e or, in reltive nottion, wˆ δ I = I L 3 ( ) ( ) ( ) e e, i mx e The stndrd nertinty of the indition is normlly obtined by ( I) = d 1+ d 1+ s ( I) + wˆ ( δi ) I ( ) Note 1: the nertinty ( I) I is = onstnt only where s = onstnt nd no eentriity error hs to be onsidered. Note : the first two terms on the right hnd side my hve to be modified in speil ses s mentioned in nd Stndrd nertinty of the referene mss From 4..4 nd the referene vle of mss is: m = m + δ m + δm + δm + δm + δ (7.1.-1) ref B D The rightmost term stnds for frther orretions tht my in speil onditions be neessry to pply, it is not frther onsidered herefter. The orretions nd their stndrd nertinties re: δ m is the orretion to onv e m K m to obtin the tl onventionl vle of mss given in the librtion ertifite for the stndrd weights, together with the nertinty of librtion U nd the overge ftor k. The Stndrd nertinty is ( m ) U k m ; δ = (7.1.-) Where the Stndrd weight hs been librted to speified tolernes Tol, e.g. to the mpe given in R 111, nd where it is sed its nominl vle m, then δ m =, 9 4

26 nd retnglr distribtion is ssmed, therefore δ m = Tol (7.1.-3) ( ) 3 Where test lod onsists of more thn one stndrd weight, the stndrd nertinties re smmed p rithmetilly not by sm of sqres, to ont for ssmed orreltions For test lods prtilly mde p of sbstittion lods see Note 1: f for se of m or m. Note : Where onformity of the stndrd weight(s) to R 111 is estblished, ( ) my be modified by repling Tol by mpe. For weights of m,1 kg the qotient mpe/ m is onstnt for ll weights belonging to the sme ry lss, mpe = m with lss lss from Tble (7.1.-3) my then be sed in the form δ m = m (7.1.-3) ( ) 3 lss or s reltive stndrd nertinty w ˆ( δ m ) = 3 (7.1.-3b) Tble Qotient lss lss = mpe m for stndrd weights Clss lss 1 6 E 1,5 E 1,6 F 1 5 F 16 M 1 5 M 16 M 3 5 m 1 g ording to R 111 [3] For weights of nominl vle of x 1 n of the following lsses: E, F nd M, the vle of lss 1 6 shold be sbstitted by 1,5, 15 nd 15 respetively B m δ is the orretion for ir boyny s introded in The vle depends on the density ρ of the librtion weight, on the ssmed rnge of ir density ρ, nd on the dstment of the instrment f ses A nd B in

27 Cse A: B m ( ρ ρ )( 1ρ ρ ) δm = 1 (7.1.-4) with the reltive stndrd nertinty from 4 wˆ ( m ) = ( ρ )( 1ρ 1ρ ) + ( ρ ρ ) ( ρ) ρ (7.1.-5) B Cse B1: B m Cl [( ρ ρ )( 1ρ ρ ) δρ ρ ] δ m = 1 + (7.1.-6) s with the reltive stndrd nertinty from 4 wˆ ( m ) = ( ρ )( 1ρ 1ρ ) + ( ρ ρ ) ( ρ) ρ + ( δρ ) ρ (7.1.-7) Cse B: B ( ρ ρ ) ρ δ B = m m (7.1.-8) with the reltive stndrd nertinty from 4 wˆ ( m ) = ( ρ ) ρ + ( ρ ρ ) ( ρ) ρ (7.1.-9) As fr s vles for ρ, ( ρ), ρ nd ( ) sed to determine wˆ ( m B ). B ρ, re known, these vles shold be The density ρ nd its stndrd nertinty my in the bsene of sh informtion, be estimted ording to the stte of the rt. Appendix E1 offers interntionlly reognized vles for ommon mterils sed for stndrd weights. The ir density ρ nd its stndrd nertinty n be llted from tempertre nd brometri pressre if vilble (the reltive hmidity being of minor inflene), or my be estimted from the ltitde bove se-level. For the differene nertinty ( ) s δρ s (Cse B1), zero my be ssmed with n pproprite δρ for whih limit ρ s shold be estimted tking into ont the vribility of brometri pressre nd tempertre t the site, over longer period of time. A simple pproh my be to se the sme estimtes forρ nd ρ s the sme nertinty for both vles. Appendix A offers severl formle, nd informtion bot expeted vrines. Appendix E offers vles of wˆ ( m B ) for some seleted ombintions of vles for ρ nd ρ. For se A librtions, the vles re mostly negligible. s 9 6

28 For se B librtions, it my mostly be dvisble to not pply orretion δ mb bt to llte the nertinty bsed onρ nd on ρ ρ ± ρ Where onformity of the stndrd weights to R 111[3], is estblished, nd no informtion on ρ nd ρ, is t hnd, reorse my be tken to setion 1 of R No orretion is pplied, nd the reltive nertinties re for se A, wˆ ( mb) mpe ( 4m 3) ( ) For ses B1 nd B, w m,1ρ ρ + mpe 4m (7.1.-9) ( ) ( ( )) 3 ˆ B = From the reqirement in footnote 5, these limits n be derived for ρ : For lss E : ρ ρ kg/m³, nd for lss F 1 : ρ ρ 6 kg/m³. Note: De to the ft tht the density of mterils sed for stndrd weights is normlly loser to ρ thn the R111 limits wold llow, the lst formle my be onsidered s pper limits for wˆ ( m B ) with the resoltion of the instrment ( n M = d Mx). Where simple omprison of these vles 1 shows they re smll enogh, more elborte lltion of this nertinty omponent bsed on tl dt, my be sperflos δ md is orretion for possible drift of vle D is best ssmed, bsed on the differene in librtion ertifites of the stndrd weights. m sine the lst librtion. A limiting m evident from onsetive In the bsene of sh informtion, D my be estimted in view of the qlity of the weights, nd freqeny nd re of their se, to mltiple of their expnded U : nertinty ( ) m where k D my be hosen from 1 to 3. ( ) D= k U (7.1.-1) D m It is not dvised to pply orretion bt to ssme even distribtion within ± D (retnglr distribtion). The stndrd nertinty is then δ m = D D ( ) ( ) 3 Where set of weights hs been librted with stndrdized expnded reltive Wˆ, it my be onvenient to introde reltive limit vle for drift nertinty ( ) m D rel = D m nd reltive nertinty for drift w ˆ( m ) = D 3 = k Wˆ ( m ) 3 (7.1.-1) D rel D 5 The density of the mteril sed for weights shll be sh tht devition of 1 % from the speified ir density (1. kg/m³ ) does not prode n error exeeding one qrter of the mximm permissible error. 9 7

29 For weights onforming to R111 [3], the estimte my be see Tble D mpe, or Drel lss δ monv is orretion for onvetion effets s per A limiting vle monv my be tken from Appendix F, depending on known differene in tempertre T nd on the mss of the stndrd weight. It is not dvised to pply orretion bt to ssme even distribtion within ± m onv. The stndrd nertinty is then ( ) = 3 δ m onv m onv ( ) The stndrd nertinty of the referene mss is obtined from f m = δm + δm + δm + δm ( ) ( ) ( ) ( ) ( ) ( ) with the ontribtions from to ref As n exmple the terms re speified for se A librtion with stndrd weights of m,1 kg onforming to R111, sed with their nominl vles: wˆ ( m ) ( m m ) 3 ref lss lss lss B = ( ) Where test lod is prtilly mde p of sbstittion lods s per 4.3.3, the stndrd nertinty for the sm LTn = nm 1+ I1+ I + K + I n 1 is given by the following expression: L n m + I + I + K + I ( ) D onv onv [ ] ( ) ( ) ( ) ( ) ( ) Tn = 1 1 n 1 with ( m 1 ) = ( ) from , nd ( I ) from for I = I( ) m ref Note: the nertinties ( I ) hve to be inlded lso for inditions where the sbstittion lod hs been so dsted tht the orresponding I beomes zero! Depending on the kind of the sbstittion lod, it my be neessry to dd frther nertinty ontribtions: for eentri loding s per to some or ll of the tl inditions I ( L T ); for ir boyny of the sbstittion lods, where these re mde p of low density mterils (e.g. snd, grvel) nd the ir density vries signifintly over the time the sbstittion lods re in se. Where ( I ) = onst, the expression simplifies to [ ] ( L ) n ( m ) + ( n 1) ( I) Tn = ( ) Stndrd nertinty of the error The stndrd nertinty of the error is, with the terms from nd 7.1., s L T 9 8

30 pproprite, llted from E = d 1+ d + ( ) I 1+ s ( I) + ( δi e) ( δm ) + ( δm ) + ( δm ) + ( δm ) or, where reltive nertinties pply, from E = d 1+ d 1+ s I + B D onv ( ) I ( ) + wˆ ( I e) w ( m ) + w ( m ) + w ( m ) m + { ˆ ˆ ˆ } ( δm ) B D ref I onv ( ) ( b) All inpt qntities re onsidered to be norrelted, therefore ovrines re not onsidered. The index hs been omitted. Where the lst terms in ( , b) re smll ompred to the first 3 terms, the nertinty of ll errors determined over the weighing rnge is likely to be qite similr. If this is not the se, the nertinty hs to be llted individlly for eh indition. In view of the generl experiene tht errors re normlly very smll ompred to the indition, or my even be zero, in ( , b) the vles for m nd I my be repled by I. The terms in ( , b) my then be groped into simple forml whih better reflets the ft tht some of the terms re bsolte in ntre while others re proportionl to the indition: E = α + β I (7.1.3-) ( ) Where ( ) or ( ) pplies to the stndrd devition determined for the librted instrment, the orresponding terms re of orse inlded in (7.1.3-). 7. Stndrd nertinty for hrteristi Where n pproximtion is performed to obtin forml f( I) E = for the whole weighing rnge s per 6.., the stndrd nertinty of the error per hs to be modified to be onsistent with the method of pproximtion. Depending on the model fntion, this my be ref single vrine ppr whih is dded to ( ), or set of vrines nd ovrines whih inlde the vrines in ( ). The lltions shold lso inlde hek whether the model fntion is mthemtilly onsistent with the dt sets E, I, ( E ). The minχ, pproh whih is similr to the lest sqres pproh, is proposed for pproximtions. Detils re given in Appendix C 9 9

31 7.3 Expnded nertinty t librtion The expnded nertinty of the error is U E = k E (7.3-1) ( ) ( ) The overge ftor k, shold be hosen sh tht the expnded nertinty orresponds to overge probbility of pproximtely 95 %. The vle k =, orresponding to 95,5% probbility, pplies where ) norml (Gssin) distribtion n be ttribted to the error of indition, nd b) the stndrd nertinty ( E) is of sffiient relibility (i.e. it hs sffiient nmber of degrees of freedom). Appendix B offers dditionl informtion to these onditions, nd Appendix B3 dvises how to determine the ftor k where one or both of them re not met. It is eptble to determine only one vle of k, for the worst se sittion identified by experiene, whih my be pplied to the stndrd nertinties of ll errors of the sme weighing rnge. 7.4 Stndrd nertinty of weighing reslt The ser of n instrment shold be wre of the ft tht in norml sge of n instrment tht hs been librted, the sittion is different from tht t librtion in some if not ll of these spets: 1. the inditions obtined for weighed bodies re not the ones t librtion,. the weighing proess my be different from the proedre t librtion:. ertinly only one reding for eh lod, not severl redings to obtin men vle, b. reding to the sle intervl d, of the instrment, not with higher resoltion,. loding p nd down, not only pwrds or vie vers, d. lod kept on lod reeptor for longer time, not nloding fter eh loding step or vie vers, e. eentri pplition of the lod, f. se of tre blning devie, et. 3. the environment (tempertre, brometri pressre et.) my be different, 9 3

32 4. on instrments whih re not redsted reglrly e.g. by se of bilt-in devie, the dstment my hve hnged, de to geing or to wer nd ter. Unlike the items 1 to 3, this effet is slly depending on the time tht hs elpsed sine the librtion, it shold therefore be onsidered in reltion to ertin period of time, e.g. for one yer or the norml intervl between librtions. In order to lerly distingish from the inditions I obtined dring librtion, the weighing reslts obtined when weighing lod L on the librted instrment, these terms nd symbols re introded: R = reding, ny indition obtined fter the librtion; W = weighing reslt, reding orreted for the error E. R is nderstood s single reding in norml resoltion (mltiple of d ), with orretions to be pplied s pplible. For reding tken nder the sme onditions s those previling t librtion, for lod well entered on the lod reeptor, only orretions to ont for points nd b bove pply. The reslt my be denominted s the weighing reslt nder the onditions of the librtion W *: W* R+ δ R + δr R + δr (7.4-1) with the ssoited nertinty ( ) E = digl rep dig ( W *) { ( E) + ( δr ) + ( δr ) + ( δr )} = dig digl rep (7.4-) W * nd ( W *) n be determined diretly sing the informtion, nd the reslts of the librtion s given in the librtion ertifite: Dt sets I l, E l, U ( E l ), nd/or A hrteristi E ( R) = f( I) nd ( E( R) ) g( I) This is done in nd in U =. To tke ont of the remining possible inflenes on the weighing reslt, frther orretions re formlly dded to the reding in generl mnner reslting in the weighing reslt in generl: with the ssoited nertinty W = W * +δ R instr + δr pro (7.4-1b) ( W) ( W *) + ( δr ) + ( δ ) = (7.4-b) instr R pro The dded terms nd the orresponding stndrd nertinties re disssed in nd The stndrd nertinties ( W *) nd ( W) re finlly presented in Setions nd 7.4.4, nd the informtion on ( W) nd U ( W) in setions nd 7.5, re ment s dvie to the ser of the instrment on how to estimte the 9 31

33 nertinty of weighing reslts obtined nder his norml onditions of se. They re not ment to be exhstive nor mndtory. Where librtion lbortory offers sh estimtes to its lients whih re bsed pon informtion tht hs not been mesred by the lbortory, the estimtes my not be presented s prt of the librtion ertifite Stndrd nertinty of reding in se To ont for sores of vribility of the reding, ( ) pplies, with I repled by R : R= RL + δ RdigL + δrrep ( R + δrdig ) L{ + δre} ( ) Term in {} to be dded if pplible The orretions nd their stndrd nertinties re: δ R dig onts for the ronding error t zero reding pplies with the exeption tht the vrint Note in pplies. d T < d, is exlded, so ( R ) 1 δ dig = (7.4.1-) d δ RdigL onts for the ronding error t lod reding pplies with the exeption tht the vrint d T < d is exlded, so L ( ) 1 δ R digl = d L ( ) δ Rrep onts for the error de to imperfet repetbility pplies, the relevnt stndrd devition s or s ( I) for single reding, is to be tken from the librtion ertifite, so ( δ R rep ) = s or ( δ Rrep ) = s( R) ( ) Note: In the librtion ertifite, the stndrd devition my be reported s being relted to single indition, or to the men of n inditions. In the ltter se, the vle of s hs to be mltiplied by n to give the stndrd devition for single reding δ Re onts for the error de to off-entre position of the entre of grvity of lod. It hs been pt in brkets s it is normlly relevnt only for W not for W *, nd will therefore be onsidered in The stndrd nertinty of the reding is then obtined by ( R) = d ( ) { ( ) 1+ d R 1+ s R L + wˆ Re R } ( ) Term in{} to be dded if pplible Note: the nertinty ( R) is = onstnt where s = onstnt; where in exeptionl ses the eentriity error hs to be onsidered, the term shold be tken from

34 7.4. Unertinty of the error of reding Where reding R orresponds to n indition I l reported in the librtion ertifite, ( ) E l my be tken from there. For other redings, ( E( R) ) my be llted by (7.1.3-) if α nd β re known, or it reslts from interpoltion, or from n pproximtion forml s per 7.. The nertinty ( E( R) ) is normlly not smller thn ( ) E l for n indition I tht is lose to the tl reding R, nless it hs been determined by n pproximtion forml. Note: the librtion ertifite normlly presents U 95 ( E l ) from whih ( E l ) be derived onsidering the overge ftor k stted in the ertifite Unertinty from environmentl inflenes The orretion term δ Rinstr onts for p to 3 effets whih re disssed herefter. They do normlly not pply to instrments whih re dsted right before they re tlly being sed f 4..4, se A. For other instrments they shold be onsidered s pplible. No orretions re tlly being pplied, the orresponding nertinties re estimted, bsed on the ser s knowledge of the properties of the instrment A term δ Rtemp onts for hnge in the hrteristi (or dstment) of the instrment sed by hnge in mbient tempertre. A limiting vle n be estimted to δ = TK T with the following terms. R temp Normlly there is mnftrer s speifition like TK I( Mx) T ses qoted s is to =, in mny TK TC in 1-6 /K. By deflt, for instrments with type pprovl nder OIML 76 [], it my be ssmed TC mpe( Mx) ( Mx ) T Appr where TAppr is the tempertre rnge of pprovl mrked on the instrment; for other instrments, either onservtive ssmption hs to be mde, leding to mltiple (3 to 1 times) of the omprble vle for instrments with type pprovl, or no informtion n be given t ll for se of the instrment t other tempertres thn tht t librtion. The rnge of vrition of tempertre T (fll width) shold be estimted in view of the site where the instrment is being sed, s disssed in Appendix A... Retnglr distribtion is ssmed, therefore the reltive nertinty is wˆ R temp = TC T ( ) ( ) A term boy R δ onts for hnge in the dstment of the instrment de to the vrition of the ir density; no orretion to be pplied, nertinty ontribtion to be onsidered s in 7.1.., where vribility of the ir density lrger thn tht t librtion is expeted. 9 33