Supersedes: 1.3 This procedure assumes that the minimal conditions for applying ISO 3301:1975 have been met, but additional criteria can be used.

Transcription

1 Procedures Category: STATISTICAL METHODS Procedure: P-S-01 Page: 1 of 9 Paired Differece Experiet Procedure 1.0 Purpose 1.1 The purpose of this procedure is to provide istructios that ay be used for perforig a experiet to assess the effect of a chage o a characteristic of a saple uit, usig the saple uit as its ow cotrol. 1. This procedure 1 ca be used as a referece by orgaizatios to develop their ow procedures for perforig a replicated paired differece experiet. 1.3 This procedure assues that the iial coditios for applyig ISO 3301:1975 have bee et, but additioal criteria ca be used..0 Scope.1 This procedure applies where: (a) a replicated paired differece experiet ay be coducted o retrofitted diaphrag gas eters i service with a autoatic eter readig (AMR) device ad/or register; (b) the eters tested are siilar i all respects except for the systeatic differece which is beig evaluated; (c) the aalysis of the test results is based o ISO 3301:1975; ad (d) a sigle operator is ivolved i effectig the chage; or Note 1 : The use of this procedure etails iheret risks ad liitatios with regard to the coclusios that ay be draw fro it. Meter owers are therefore advised that, although cofority with the requireets of this procedure ay qualify eter owers to seek accreditatio for the istallatio of AMR devices o diaphrag eters i situ, relyig solely o the use of this procedure will ot provide eter owers with a assurace of copliace with the eterig accuracy obligatios prescribed uder the Electricity ad Gas Ispectio Act. Cotractors are ultiately resposible for esurig the perforace quality of the i-service eter lots which they ow.

2 Category: STATISTICAL METHODS Procedure: P-S-01 Page: of 9 (e) ore tha oe operator is ivolved i effectig the chage ad a techical professioal thoroughly exaies the procedure ad deteries that there is o possibility for iter-operator variability. 3.0 Referece 3.1 S-S-01 Specificatios for Rado Saplig ad Radoizatio 4.0 Teriology For the purposes of this procedure, the followig ters ad defiitios ad those i the orative referece apply. Experiet (desiged experiet) Experietal pla selected so as to eet a specific objective. Replicatio Repetitio of a experiet ore tha oce for a give group of variables used i regressio to predict others variables. Operator Perso perforig the operatio of iterest i the experiet. Grad ea Mea of a set of eas. 5.0 Sybols For the purposes of this procedure, the sybols i the orative referece ad the followig sybols apply. d x y the siged differece betwee paired observatios the uber of easureet replicatios the uber of uits i the saple the easured value of a characteristic uder the iitial set of coditios the easured value of a characteristic followig the itroductio of the chage beig evaluated

3 Category: STATISTICAL METHODS Procedure: P-S-01 Page: 3 of 9 x ii the value of x correspodig to the jth replicate of the ith saple uit x ı the ea value of x i for the saple of uits S the estiate fro the saple of the variace v the uber of degrees of freedo the su of i=1 x i the su of all the x values whe i takes itegral values fro 1 to g the absolute value of a arbitrary variable g 6.0 Procedure 6.1 Plaig (a) Defie the populatio or uiverse to which the results of the experiet will apply. (b) Defie the ature of the chage that will be itroduced to the populatio uder study. (c) Specify the characteristics of the populatio uits which will be easured. (d) For each saple uit, establish the size of the saple to be chose fro the populatio ad the uber of replicated easureets to be perfored. (e) Maitai a record of the data obtaied i steps (a) to (d). 6. Saple Selectio ad Preparatio (a) Radoly select a represetative saple fro the defied populatio or uiverse i accordace with the referece cited i sectio 3.1. (b) Coditio the uits of the saple to stabilize the characteristics to be easured.

4 Category: STATISTICAL METHODS Procedure: P-S-01 Page: 4 of Saple Evaluatio (a) Measure the characteristics specified for each of the saple uits, replicatig the easureets the sae uber of ties for each characteristic. (b) Record all easureet results o the for supplied i Appedix A. (c) Itroduce the chage to be evaluated to each of the saple uits. (d) Repeat steps (a) ad (b). 6.4 Statistical Calculatios The followig calculatios are to be applied whe usig Appedix A. (a) For each characteristic of subject i uder cotrolled coditios, calculate the ea ( xi) of each set of replicated easureets i accordace with the followig equatio: = x ı j=1 x ii (b) Fro the eas obtaied i step (a), calculate the grad ea i accordace with the followig equatio: x = i=1 x ı (c) For each characteristic of subject i uder experietal coditios, calculate the ea ( ) of each set of replicated easureets i accordace with the followig equatio: y i = y ı j=1 y ii (d) Fro the eas obtaied i step (c), calculate the grad ea i accordace with the followig equatio: y = i=1 y ı

5 Category: STATISTICAL METHODS Procedure: P-S-01 Page: 5 of 9 (e) Calculate the siged differeces (d i ) betwee the eas of the replicated easureets take before ad after the itroduced chage for each characteristic i accordace with the followig equatio: d i = x ı y ı (f) Calculate the ea ( d i) of the siged differeces (d i ) for each characteristic i accordace with the followig equatio: = d ı i=1 d i (g) Calculate the variace ( S d ) ad the associated degrees of freedo (v) of the siged differeces (d i ) for each characteristic i accordace with the followig equatios: S d = d i d i=1 1 v = 1 (h) Calculate the ratio of Studet s t-distributio for the saple size i accordace with the followig equatio: t 0.95(v) (i) Calculate the tolerace adjustet for the cofidece iterval ad the variace of the saple for each characteristic i accordace with the followig equatio: A 1 = t 0.95(v) s d (j) Maitai a record of the results of all statistical calculatios perfored i steps (a) through (i).

6 Category: STATISTICAL METHODS Procedure: P-S-01 Page: 6 of Aalysis of Results Statistically Sigificat Mea Paired Differece Experiet (a) Deterie if a statistically sigificat ea paired differece is withi upper ad lower bias liits usig the two oe-sided cases below: Case 1 The hypothesis that the populatio ea of the differeces for each characteristic is at least equal to the upper tolerace liit (d 1 ) (ull hypothesis) is rejected if: Case d < d 1 A 1 The hypothesis that the populatio ea of the differeces for each characteristic is at ost equal to the lower tolerace liit (d ) (ull hypothesis) is rejected if: d < d A 1 (b) There is isufficiet evidece that a ea paired differece outside a ±0.% liit exists if the ull hypothesis is rejected for Case 1 ad Case for each characteristic.

7 Category: STATISTICAL METHODS Procedure: P-S-01 Page: 7 of 9 Appedix A Test Results Fors Saple Uit A.1 Test Results For Cotrolled Coditios Cotrolled Coditios (before chage itroduced) xi1 xi xi3 xi4 xi5 i Grad ea of the eas for the saple uits

8 Category: STATISTICAL METHODS Procedure: P-S-01 Page: 8 of 9 A. Test Results For Experietal Coditios Saple Uit Experietal Coditios (after chage itroduced) yi1 yi yi3 yi4 yi5 i Grad ea of the eas for the saple uits

9 Category: STATISTICAL METHODS Procedure: P-S-01 Page: 9 of 9 Appedix B Aalytical Results For Descriptio Sybol Characteristic 1 Characteristic Critical Value Saple Size Replicates Degrees of freedo Cotrolled Coditios Experietal Coditios v = 1 x y Cofidece Iterval (%) 95 d S d Differece Statistics t 0.95(v) A 1 d 1 0. Aalysis of depedet variables based o ISO 3301:1975 d -0. Case 1 (at ost) Iside/Outside Iside/Outside Case (at least) Iside/Outside Iside/Outside Coclusio (95%) Iside/Outside Iside/Outside Iside/Outside Tolerace