ISO tadard o determiatio of the Detectio Limit ad Deciio threhod for ioiig radiatio meauremet ISO/CD : Determiatio of the Detectio Limit ad Deci
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1 ICRM Gamma Spectrometry Workig Group Workhop Pari, Laoratoire atioa d Eai 3-4 Feruary 9 Detectio imit Deciio threhod Appicatio of ISO 1199 P. De Feice EEA atioa Ititute for Ioiig Radiatio Metroogy defeice@caaccia.eea.it.1/13
2 ISO tadard o determiatio of the Detectio Limit ad Deciio threhod for ioiig radiatio meauremet ISO/CD : Determiatio of the Detectio Limit ad Deciio Threhod for Ioizig Radiatio Meauremet - Part 1: Fudameta ad Appicatio to Coutig Meauremet without the Ifuece of Sampe Treatmet. ISO/CD 1199-: Determiatio of the Detectio Limit ad Deciio Threhod for Ioizig Radiatio Meauremet - Part : Fudameta ad Appicatio to Coutig Meauremet with the Ifuece of Sampe Treatmet. ISO/CD : Determiatio of the Detectio Limit ad Deciio Threhod for Ioizig Radiatio Meauremet - Part 3: Fudameta ad Appicatio to Coutig Meauremet y High Reoutio Gamma Spectrometry, without the Ifuece of Sampe Treatmet. ISO/CD : Determiatio of the Detectio Limit ad Deciio Threhod for Ioizig Radiatio Meauremet - Part 4: Fudameta ad Appicatio to Meauremet y Ue of Liear Aaogue Ratemeter, without the Ifuece of Sampe Treatmet. ISO/CD : Determiatio of the Detectio Limit ad Deciio Threhod for Ioizig Radiatio Meauremet - Part 5: Fudameta ad Appicatio to Meauremet of Fiter Durig Accumuatio of Radioactive Materia. ISO/CD : Determiatio of the Detectio Limit ad Deciio Threhod for Ioizig Radiatio Meauremet - Part 6: Fudameta ad Appicatio to Meauremet y Ue of a Traiet Meaurig Mode. ISO/CD : Determiatio of the Detectio Limit ad Deciio Threhod for Ioizig Radiatio Meauremet - Part 7: Fudameta ad Geera Appicatio. ISO/CD : Determiatio of the Detectio Limit ad Deciio Threhod for Ioizig Radiatio Meauremet - Part 8: Fudameta ad Appicatio to Ufodig of Spectrometric Meauremet without the Ifuece of Sampe Treatmet../13
3 Detectio Limit ad Deciio threhod: Defiitio DECISIO QUATITY: radom variae for the deciio whether the phyica effect to e meaured i preet or ot DECISIO THRESHOLD: fixed vaue of the deciio quatity y which, whe exceeded y the reut of a actua meauremet of a meaurad quatifyig a phyica effect, oe decide that the phyica effect i preet DETECTIO LIMIT: maet vaue of the meaurad which i detectae y the meaurig method COFIDECE ITERVAL: vaue which defie cofidece iterva to e pecified for the meaurad i quetio which, if the reut exceed the deciio threhod, icude the true vaue of the meaurad with a give proaiity.3/13
4 Three impe quetio i partice coutig : BACKGROUD cout : SAMPLE cout QUESTIO 1: Which i the vaue of the et cout that, whe exceeded y the reut of a actua meauremet, oe decide that there i a rea cotriutio from the ampe? QUESTIO : Which i the maet vaue of the ampe cotriutio that i detectae y the meaurig ytem? QUESTIO 3: If uch a cotriutio ha ee detected, which i the iterva that icude the true vaue with a give proaiity?.4/13
5 Poie awer to quetio. 1 Compare with, coiderig the tatitica fuctuatio of : o Var( = (Poio o L=3 ( 1/ (3 Criteria, ICRU, 1979 PROBLEMS: 1: aritrary choice of the factor 3; : S>L: ca e a ackgroud fuctuatio? 3: S<: there i o cotriutio from the ampe? A A MORE RIGOROUS ASWER IS EEDED:.5/13
6 Awer to quetio. 1 (Deciio threhod BACKGROUD SAMPLE ET COUTS HP: = ( = =( 1/ EXPECTATIO VALUE STADARD DEVIATIO O cotriutio from ampe DECISIO THRESHOLD: =K a (Currie, 1968 THE DECISIO THRESHOLD i the critica vaue for the tatitica tet for the deciio etwee the hypothei that the ampe effect i ot preet ad the aterative hypothei that it i preet. Whe the critica vaue i exceeded y the reut of a actua meauremet thi i take to idicate that the hypothei houd e rejected. The tatitica tet ha e deiged uch that the proaiity of wrogy rejectig the hypothei (error of the firt kid i equa to a give vaue a. =( K,1 1,8,5 1,64,5 1,96,1 3,9 = k.5.3.6/13
7 Awer to quetio. (Detectio imit BACKGROUD SAMPLE ET COUTS HP: ( > =( 1/ EXPECTATIO VALUE STADARD DEVIATIO YES cotriutio from ampe =( DECISIO THRESHOLD: = +K =(K a +K (Currie, 1968 THE DETECTIO LIMIT i the maet true vaue of the meaurad which i aociated with the tatitica tet ad hypothei (made for the deciio threhod y the foowig characteritic: If i reaity the true vaue i equa to or exceed the detectio imit, the proaiity of wrogy ot rejectig the hypothei (error of the ecod kid ha e at mot equa to a give vaue. K,1 1,8,5 1,64,5 1,96,1 3, /13
8 Geeraizatio (a: Tet of Hypothei HYPOTHESIS H : o ampe cotriutio to the cout. H accepted H rejected Ho true OK P=1- Type I error P= Ho fae Type II error OK P= P=1- a: Proaiity of rejectig the hypothei H whe, i reaty, it i true : Proaiity of acceptig the hypothei H whe, i reaty, it i fae Aaogue coideratio ca e made i cae of coutig with preet cout coditio.8/13
9 BACKGROUD SAMPLE COUTS Geeraizatio (: Defiitio COUTIG TIME COUT RATE EXPECTATIO VALUE t R ET - - R t R R R STADARD DEVIATIO DECISIO THRESHOLD: Critica vaue R of the tatitica tet for the deciio etwee the aterative hypothei: A r =r B r >r with give proaiity a of type I error: R =k a. R R DETECTIO LIMIT: maet expectatio vaue r, aociated to the tatitica tet etwee the hypothei A ad B aove, which determie a type II error with give proaiity. r =(k a + k.9/13
10 Geeraizatio (c: Ue of R ad r R houd e compared with meauremet reut to ae weather a ampe cotriutio ha ee detected (a-poteriori criteria: R > R ampe cotriutio detected; R < R ampe cotriutio ot detected. r houd e ued to check weather a meaurig procedure i uitae for the purpoe of the meauremet. It houd e compared with a pecific guideie vaue S( a pecific requiremet o the eitivity of the meaurig procedure for cietific, ega or other reao (a-priori criteria: r >r the ampe cotriutio wi e detected with proaiity greater tha 1-; r <r the ampe cotriutio wi e detected with proaiity e tha 1-. r <S( meauremet procedure i ot adequate for the iteded purpoe. Whe reportig deciio threhod ad detectio imit it i importat to give the vaue of a ad ued. A kowedge i divided ito two categorie: a priori ad a poteriori kowedge, I. Kat, Critique of Pure Reao ( /13
11 Etimatio of ackgroud repeataiity a Aume Poio (or other tatitic ad ue the ucertaity propagatio aw (pectrometric meauremet Meaure the ackgroud variaiity if ource of fuctuatio ee tha coutig tatitic are eviaged (ampe treatmet, coutig ytem itaiity, evirometa coditio.11/13
12 Exampe: Deciio Threhod ad Detectio Limit Exampe: Deciio Threhod ad Detectio Limit i gamma i gamma-ray pectrometry ray pectrometry h=fwhm Cout Cout. time Cout rate Expectatio vaue Stadard deviatio Backgroud t R Gro peak area t R et peak area t R R R ( 1 4 ( 1 1 chae.1/13 : RO.I (1 ( (1 (1 var( var( t R k k t R k R t
13 Exampe of appicatio of a deciio threhod without threhod with threhod.13/13
14 Thak you.14/13
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