. TECHNICA MEMOANDM To Cc repred By Endorsed By NZTA Network Mngement Consultnts nd Contrctors NZTA egionl Opertions Mngers nd Are Mngers Dve Btes, Opertions Mnger, NZTA Ntionl Office Jonn Towler, oding Engineer, rofessionl ervices, NZTA Ntionl Office Dve Btes, Opertions Mnger, NZTA Ntionl Office Dte 4 Jnury 0 ubject rocedure for Assessing Bitumens for Acceptnce by the enetrtion Test Highwys nd Network Opertions Technicl Memorndum No. TM6004 Contents.0 Introduction.0 Development of Acceptnce/ejection imits 3.0 Vribility Vlues of enetrtion Test esults 4.0 Acceptnce rocedure 4. enetrtion Tests 4. Acceptnce imits 4.3 Acceptnce Bsed on Two Test esults from Independent bortories 4.4 Acceptnce Bsed on Three Test esults from Independent bortories 5.0 Discussion of the ttisticl Bsis of the Test rocedures 5. Assigning Acceptnce/ejection enetrtion imits 5. esults from Independent bortories 5.3 epeted Within-bortory Testing 5.4 Detection of Outlying esults 6.0 egistered Testing bortories in New Zelnd 7.0 eferences NZTA TM 6004 Technicl Memo for Assessing Bitumens ge of
.0 Introduction The penetrtion test (ATM D5) crried out t 5C defines New Zelnd bitumen grdes (NZTA specifiction M: 00), nd the test cn be used to mke decisions s to whether to ccept or reject bitumen on the bsis of the upper nd lower limits for the grde. However, the inherent vribility of the penetrtion test method mens tht it is possible to reject bitumen for which the true vlue of penetrtion meets the specifiction requirements, nd lso to ccept s stisfctory bitumen for which the true vlue of penetrtion is outside the specifiction. As n exmple, consider 80/00 bitumen for which the true vlue of penetrtion is 90 penetrtion units 3. Figure shows the single test result probbility distribution for pen 90 bitumen, together with the upper nd lower limits of the New Zelnd stndrd, NZTA M: 00. 50 60 70 80 90 00 0 0 30 enetrtion dmm Figure : robbility distribution of single penetrtion result for bitumen with true penetrtion of 90. ower nd upper specifiction limits re indicted by broken lines. The res under the tils of the distribution outside the specifiction limits indictes tht there is 6.7% chnce of single penetrtion result flling outside the specifiction limits. The vribility of the penetrtion test nd the rnge of the specified penetrtion limits vry from grde to grde. Tble indictes the probbility, for the different bitumen grdes, of penetrtion result flling outside the specifiction rnge if the true penetrtion is in the middle of the rnge. For vribility dt see ATM specifiction D5: 006 nd Tble below, tken from this specifiction. The penetrtion of bitumen cn only be mesured by the stndrd penetrtion test, for which the results will vry from one mesurement to nother. Hence, for prcticl purposes we define the true vlue s the vlue towrds which the verge of single results obtined by n lbortories tends, s n tends towrds infinity (Interntionl tndrd EN IO 459:006). The term true penetrtion refers the true vlue of the bitumen penetrtion. 3 enetrtion units re tenths of millimetres, i.e. decimillimetres (dmm). NZTA TM 6004 Technicl Memo for Assessing Bitumens ge of
Bitumen Grde ercent robbility of Midgrde enetrtion esult Outside pecifiction imits 40/50 4.6 60/70 6.9 80/00. 30/50. 80/00 6.7 Tble : Effect of test vribility nd specifiction limits on cceptnce/rejection of binder.0 Development of Acceptnce/ejection imits We look to set cceptnce limits outside the specifiction limits by mounts tht depend on the vribility of the test method. In doing this we hve to reckon with two undesirble possibilities:. ejecting bitumen whose true penetrtion is ctully within the specifiction limits. Becuse the penetrtion test is inherently vrible there is lwys this possibility. etting the cceptnce limits well bove nd well below the specifiction mximum nd minimum reduces this possibility (ttisticlly speking this is referred to s Type I error).. Accepting bitumen tht is ctully outside the specifiction limits (Type error). etting the cceptnce limits well bove nd well below the specifiction mximum nd minimum increses the chnce of this type of error. The setting of rejection nd cceptnce limits is therefore compromise between these two risks. 3.0 Vribility Vlues of enetrtion Test esults The bitumen cceptnce procedures proposed below re bsed on the ltest single opertor nd multilbortory precisions for the 5C penetrtion test published in the Americn ociety for Testing nd Mterils pecifiction ATM D5-06e. The precisions, in terms of stndrd devitions of results, re listed in Tble. ingle Opertor recision, r () Multilbortory recision, () 60 0.8.5 > 60 0.8 + 0.03(-60).5 + 0.05(-60) Tble : recision levels for ATM penetrtion test ATM D5-06e. enetrtion vlues () nd precisions (stndrd devitions) re in stndrd units, tenths of millimetres (decimillimetres, dmm). If test procedure is repeted k times in the one lbortory, the multilbortory precision of the test,,k () becomes ;k () () r () k (.) NZTA TM 6004 Technicl Memo for Assessing Bitumens ge 3 of
4.0 Acceptnce rocedure The following procedure is proposed to del with cses where n in specifiction bitumen hs been retested fter delivery of crgo or production btch from the mnufcturer nd found to be outside the NZTA M: 00 specifiction limits (bitumens supplied with penetrtion, t the point of mnufcture, outside the NZTA M: 00 specifiction limits will not be ccepted s meeting the specifiction under ny circumstnces). The verge of the penetrtion t the point of mnufcture nd one or (if necessry) two retest vlues (from different lbortories) re verged nd the result compred to cceptnce limits s set out below, (Note: the penetrtion result from given lbortory my itself be the men of severl replictes). 4. enetrtion verifiction tests Tests shll be crried out by lbortories which re IANZ (Interntionl Accredittion New Zelnd) ccredited to perform the ATM D5 penetrtion test or from overses lbortories ccredited to n equivlent interntionl stndrd level. 4. Acceptnce limits enetrtion tests performed to verify tht bitumen complies with NZTA M: 00 shll be ssessed ccording to whether or not the result flls within the cceptnce/rejection limits listed in Tble 3. Bitumen Grde ower Acceptnce imit pper Acceptnce imit 40/50 37 53 60/70 57 74 80/00 75 05 30/50 58 80/00 70 0 Tble 3: Acceptnce limits for verge penetrtion results for different penetrtion grdes. These limits hve been estblished so tht cceptnce/rejection probbilities for the different grdes re, s fr s possible, the sme (llowing for the need to report penetrtions in integer units). The upper nd lower cceptnce limits hve been chosen so tht bitumen with true penetrtion equl to the upper specifiction limit hs only 6.8% chnce of being rejected on the bsis of the verge of two penetrtion test results from independent lbortories. imilrly bitumen of true penetrtion equl to the lower specifiction limit hs 4.8 % chnce of rejection. A bitumen tht hs true penetrtion equl to the midpoint of given specifiction rnge hs less thn 0.% chnce of being rejected on the bsis of the verge of two test results. robbilities of rejection of n in specifiction bitumen on the bsis of the verge of three test results from independent lbortories re lower (see, for exmple, Tble 5). Insmuch s the cceptnce limits lie outside the specifiction limits they represent the mximum probbility of the mteril not meeting specifiction tht the recipient of the NZTA TM 6004 Technicl Memo for Assessing Bitumens ge 4 of
mteril is prepred to ccept. A bitumen will not be ccepted on the bsis of penetrtion testing result outside the cceptnce limits, no mtter how close the penetrtion vlue is to flling within the cceptnce rnge. 4.3 Acceptnce bsed on Two Test esults from Independent bortories If the two penetrtion results re (penetrtion t the point of mnufcture) nd, (retest penetrtion) the procedure is s follows: 4.3. Clculte the verge of the two penetrtions: (4.) 4.3. Clculte the multilbortory precision, (), nd single opertor precision, r () for penetrtion. () =.5 60 =.5 0.05 60 60 r () = 0.8 60 0.8 0.03 60 60 (4.) = 4.3.3 Clculte the precision, ;k,k ( ) for the difference, where k nd k re the number of repetition mesurements used in obtining the vlues nd respectively. ;k,k () ;k () ;k () (4.3) where ;k () nd ;k () re defined s in eqution (.). 4.3.4 If.96 ;k,k, (4.4) the difference between the two penetrtion results is too lrge (t the 95% probbility level) for n ssessment of the bitumen to be mde. With the size of the difference between the penetrtion vlues being improbbly lrge, t lest one of the vlues is likely to be in error. It is, however, impossible to tell which of the two is the more ccurte unless third, independent, test is crried out (see ection 4.5 below). Note: If k = k =, expression (4.4) reduces to.77 (4.4) 4.3.5 If,.96 ;k,k (4.5) NZTA TM 6004 Technicl Memo for Assessing Bitumens ge 5 of
ccept the bitumen if A A (where A nd A re the upper nd lower cceptnce limit vlues from Tble 3). Otherwise, reject the bitumen s not meeting specifiction requirements. For k=k=, condition (4.5) becomes.77 (4.5) 4.4 Acceptnce bsed on Three Test esults from Independent bortories In the event of filure of the men from two independent ccredited lbortories to fll within the Tble 3 limits, the recipient nd supplier my gree to obtin further test result from further independent lbortory. mples tested by the third lbortory shll be tken from the initil mteril supplied for ssessment, with minimum of further heting. The penetrtion results,, nd 3, must be from three independent lbortories. 4.4. Clculte the verge of the three penetrtions: 3 (4.6) 3 4.4. Clculte the multilbortory precision, (), for the new vlue of, s in 4.3.. 4.4.3 Assess for the presence of n outlier result s follows: (i) et b c be the mximum vlue of 3, 3 nd 3. (ii) Clculte the precision ;k;kb, kc() for the quntity b c, where k, kb nd kc re the number of repetition mesurements used in obtining the vlues, b nd c respectively. (iii) If ;k;kb,kc kb kc () () () () ; ; ; k (4.7) 4 b c >.96 ;k;kb, kc(), (4.8) is n outlier result. Clculte new verge penetrtion, b c, nd retest s for 4.3.3 nd subsequent instructions. NZTA TM 6004 Technicl Memo for Assessing Bitumens ge 6 of
Note: If k = kb = kc =, expression (4.7) reduces to b c >.4005 () (4.8) 4.4.4 If b c.96 ;k;kb, kc(), (4.9) or, if k = kb = kc =, b c <.4005 () (4.9) ccept the bitumen if A A. (4.0) Otherwise reject the bitumen s not meeting specifiction. In ll instnces the men of ll penetrtion results for the bitumen shll be ssessed s flling within the cceptnce/rejection limits for the penetrtion grde. A penetrtion result shll only be excluded from contributing to the men if it fils to meet the outlier test (expression 4.8 or 4.8) 5.0 Discussion of the ttisticl Bsis of the Test rocedures 5. Assigning Acceptnce/ejection enetrtion imits The sttisticl ssessments of the cceptnce/rejection procedures described in ections 4.0 nd 5.0 re specil cse of generl rules for ssessing petroleum products (Interntionl tndrd EN IO 459:006). The methodology hs hd to be djusted slightly to llow for the fct tht the vribility of the penetrtion test depends on the size of the penetrtion vlue. If nd re the upper nd lower specifiction limits for prticulr penetrtion grde of bitumen, nd A nd A re the upper nd lower cceptnce/rejection limits, we write for the purposes of discussion: A = + K ( ) (5.) A = K ( ) (5.) ( ) nd ( ) re the multilbortory precision stndrd devitions for single penetrtion test ( ) t penetrtion vlues nd, clculted ccording to the formule in Tble. K nd K re therefore constnts indicting the number of multilbortory stndrd devitions between the respective specifiction penetrtions nd cceptnce/rejection penetrtion levels. In the present cse A nd A hve been chosen on the bsis of the most extreme test vlues tht client is likely to be prepred to ccept for 80/00 bitumen (A = 0 nd A = 70). NZTA TM 6004 Technicl Memo for Assessing Bitumens ge 7 of
A 0 00 0 We therefore hve K. 047 (5.3) ( ) (00) 9.55 0 imilrly K. 765 (5.4) 8.5 eferring to tbles of the norml probbility distribution this mens tht A nd A hve been chosen so tht bitumen with true penetrtion of 00 dmm hs n 85.% chnce of being ccepted on the bsis of single penetrtion test result, i.e. there is pproximtely 4.8 % chnce of penetrtion result bove 0. imilrly bitumen of true penetrtion 80 dmm hs n 87.5 % chnce of testing t 70 dmm or bove (.5% chnce of rejection). Vlues of A nd A for other grdes of bitumen (Tble 3) were obtined by pplying equtions 5. nd 5., clculting the pproprite vlues of ( ) nd ( ), nd using the sme vlues of K nd K (equtions 5.3 nd 5.4). Vlues of A were rounded up to the nerest integer, nd A down to the nerest integer, since penetrtion results re reported to the nerest integer. According to Interntionl tndrd EN IO 459:006, this provides slightly more rigorous requirement thn is typicl for petroleum products. The defult procedure, in the bsence of different greement between supplier nd recipient, is to set upper nd lower cceptnce limits so tht mteril with true vlue of the specifiction property hs 95% chnce of cceptnce. This mounts to writing K = K =.645 (5.5) For the NZTA M: 00 specifiction, this would produce the following cceptnce/rejection limits (Tble 4). ower pper Bitumen Acceptnce Acceptnce Grde imit imit 40/50 35 55 60/70 55 75 80/00 74 08 30/50 0 6 80/00 66 6 Tble 4: Acceptnce limits for different penetrtion grdes bsed on single penetrtion test result with 5% chnce of rejection of bitumen with true penetrtion t the upper or lower limit of the specifiction rnge. These re not the proposed limits. Accepting these wider limits would reduce the chnce of rejecting bitumen tht is within specifiction limits, but it would lso increse the chnce of ccepting bitumen with true penetrtion outside the limits (see.0 bove). The chnce of rejecting within-specifiction bitumen is reduced by testing t two or three lbortories. NZTA TM 6004 Technicl Memo for Assessing Bitumens ge 8 of
5. esults from Independent bortories The men vlue of the stndrd devition for severl lbortories hs lower stndrd devition thn tht of one lbortory; hence it will typiclly be closer to the true penetrtion. For two penetrtions nd the verge, devition, hs stndrd ;k,k (),k ( ),k ( ) (5.6) where result ws obtined s the men of k repetitions, nd of k repetitions. ince our operting hypothesis is tht =, we will use the multilbortory precision clculted t s the test stndrd devition: ;k,k () ;k () ;k () () k r () k ().707 () (5.7) 0 The distribution of the men of two independent mesurements therefore hs reduced stndrd devition, nd, becuse it is therefore nrrower, greter proportion of the distribution for within specifiction bitumen lies inside the cceptnce/rejection limits, i.e. the chnce of rejecting within-specifiction bitumen is reduced if the men of two independent test results is used. A men of three independent penetrtion tests reduces the chnces further. ee Tble 5 for detils with 80/00 bitumen. True enetrtion No. of Independent esults robbility Men enetrtion >0 robbility Men enetrtion <70 0.0%.0% 80 Negligible 4.8% 3 Negligible.%.3%.3% 90 0.08% 0.08% 3 Negligible Negligible 4.6% 0.08% 00 6.8% Negligible 3 3.4% Negligible Tble 5: robbility of Men enetrtion esults Outside Acceptnce imits for 80/00 Bitumen. Effect of Multiple enetrtion Testing (single results from ech lbortory (i.e. k = k = k3 = ). NZTA TM 6004 Technicl Memo for Assessing Bitumens ge 9 of
5.3 epeted Within-bortory Testing This prctice cn only tighten cceptnce requirements by smll mount. If test procedure is repeted k times, the multilbortory precision of the test,,k becomes ;k () () r () (5.8) k () nd r () re s defined in Tble. Clculting smple of vlues of ;k for k= nd 3 we obtin the results shown in Tble 4. enetrtion ; ; / ;3 ;3 / 45.50.435 0.974.43 0.965 65.75.667 0.970.638 0.959 90 3.95 3.769 0.954 3.707 0.939 40 6.50 6.093 0.937 5.95 0.96 90 9.00 8.364 0.99 8.4 0.905 Tble 6: Multilbortory precisions for multiple within-lbortory testing The proportionl chnges in ;k s k goes from to 3 re smll (this is consequence of r being significntly smller thn ), nd the effect on cceptnce/rejection limits is lso smll. Contrst this for number of single results from independent lbortories, where the stndrd devitions of the men re 0.707 nd 0.5774 respectively. For this reson, testing to check supplied penetrtion result should lwys comprise single results from independent lbortories (repet results contributing to the supplier s reported penetrtion vlue). 5.4 Detection of Outlying esults 5.4. Two Independent enetrtion esults For two penetrtions nd, the difference ( - ) hs stndrd devition of ;k,k ( ), with n expected vlue of zero. Following Interntionl tndrd EN IO 459:006 we require for cceptnce tht the bsolute vlue of ( - ) lies within the rnge for 95% probbility of cceptnce tht; i.e..96 ;k,k (5.9)/(4.5) If this reltionship is not obeyed the difference of the penetrtion vlues is lrge, nd t lest one of the vlues is likely to be in error. It is, however, impossible to tell which of the two results is the more ccurte unless third, independent, test is crried out. NZTA TM 6004 Technicl Memo for Assessing Bitumens ge 0 of
5.4. Three Independent enetrtion Tests We tke b c s the mximum vlue of 3 nd 3. 3, b c The stndrd devition of is ;k;kb,kc kb kc b c ; ( b ) ; (c ) ; k ( ) (5.0) 4 We hve evluted this quntity by substituting the verge penetrtion into eqution (5.0), on the grounds tht the cting hypothesis is tht the true vlue of penetrtion is. Operting t the 95% cceptnce level, the test for n outlier becomes b c >.96 ;k;kb, kc() (5.)/(4.8) or b c >.4005 () (5.)/(4.8) in the event tht k = k = k3 =. 6.0 egistered Testing bortories in New Zelnd se the following web ddress to serch for lbortories with IANZ (Interntionl Accredittion New Zelnd) registrtion for the penetrtion test, ATM D5. erch by keyword for D5:06 or D5-06 http://cbis.inz.govt.nz/inzwebportl/ 7.0 eferences Americn ociety for Testing nd Mterils specifiction ATM D5-06e (006) tndrd test method for penetrtion of bitumous mterils Interntionl tndrd EN IO 459:006 (006) etroleum projects Determintion nd ppliction of precision dt in reltion to methods of test NZ Trnsport Agency pecifiction NZTA M: 00 pecifiction for eding Bitumens NZTA TM 6004 Technicl Memo for Assessing Bitumens ge of