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GS-UTP-04-06.2 The Determination of Measurement Uncertainty of

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					   The Determination of Measurement Uncertainty of
   Diaphragm Transfer Meters calibrated using a Manual Master Bell Prover and
   the Correlation Process (LMB-EG-13)

               Note: This spreadsheet is provided by Measurement Canada Gas Engineering and is for developmental purpose only.
                       Please forward comments regarding problems, error or suggestions to the undersigned.


   File Description: This spreadsheet provides specific data inputs for the population of the templates for Manual Bell-provers such as Master Bell Provers and
                       is based on Measurement Uncertainty Toolbox ™ version 2.8 (January 2008) developed by Quametec Corporation.

                       The spreadsheet is designed in accordance with the requirements of
                       LMB-EG-13: Specifications and Procedures for the Calibration, Certification and Use of Gas Measuring Apparatus, Section 1 - Bell Provers (May 29, 1989)
                       GS-ENG-04-06: Guidelines for the Determination of Measurement Uncertainty For Automated Master Bell Provers
                       GS-ENG-07-06: Determination of Short-term Repeatability and Long-term Reproducibility of Bell Provers Using Diaphragm Transfer Meters
                       GS-ENG-07-07: Evaluation of Process Stability for Individual Observations using Moving Averages


              Notes: This template applies to non-temperature correcting meters only and
                       manual bell provers with no direct pressure measurement. The template does provide for pressure inputs however

                       these inputs are provided to allow for introduction of uncertainty components for simplifying assumptions.

                       This spread sheet supersedes GS-ENG-04-06(Manual Bell) rev3.2.en.xls



       Instructions: The yellow boxes are for data fill.
                       The light yellow boxes contain default values but can be changed.
                       Supporting values of uncertainty of each contributor must be provided in the templates.
                       The automatic calculation function in excel is disabled: press CTRL+SHIFT+ALT+F9


                 File: GS-UTP-04-06.2(Manual_Master_Bell)rev4.3.xls          (web version)
                       GS-ENG-04-06.2(Manual_Master_Bell)rev4.3.xls
               Date: 2009.11.26


Measurement Model:         Vm    P   t 0  tr 
                            1                       1  em 100%
                           Vr   Pb  Pr   t 0  tm 



          Figure 1: Schematic Representation of Manual Bell proving systems and Related Modeling Equations
                       for Type 2 Measuring Apparatus




            Contact: Patrick (Pat) J. Hardock, P.Eng.
                       Senior Engineer - Gas Measurement
                       Engineering and Laboratory Services
                       Measurement Canada
                       E-mail: Hardock.pat@ic.gc.ca




         Disclaimer: Measurement Canada and Measurement Canada Engineering assumes no responsibility, legal or implied, for the use of this spreadsheet.
                       It is the responsibility of the user to obtain any and all licenses needed for the supporting software used in the development of this spreadsheet.
                       This spread sheet is for developmental purposes only.
   Détermination de l'incertitude de mesure
   des compteurs de transfert à parois déformables étalonnés à l'aide du gazomètre de contrôle
   primaire manuel et du processus de corrélation (LMB-EG-13)
                   Remarque : Le présent tableur est distribué par le groupe d'ingénierie en gaz naturel de Mesures Canada à des fins d'amélioration seulement.
                                   Veuillez faire part de vos commentaires ou de vos suggestions d'amélioration à la personne soussignée.


             Desc. du fichier : Le présent tableur permet d'entrer des données pour les gazomètres de contrôle manuels comme les gazomètres
                                   de contrôle primaires et il est fondé sur l'équation de calcul de l'incertitude de la mesure (Measurement Uncertainty Toolbox),
                                   version 2.8 (janvier 2008), élaborée par Quametec Corporation.
                                   Le tableur est conforme aux exigences des normes suivantes :
                                   LMB-EG-13 : Norme et procédures pour l'étalonnage, la certification et l'utilisation des appareils de mesure du gaz,
                                    section 1 - gazomètres de contrôle (29 mai 1989).
                                   GS-ENG-04-06 : Recommandations visant la détermination de l'incertitude de mesure pour les gazomètres de contrôle primaires automatisés.
                                   GS-ENG-07-06 : Détermination de la répétabilité à court terme et de la reproductivité à long terme des gazomètres de contrôle
                                   utilisant le compteur de transfert à parois déformables.
                                   GS-ENG-07-07 : Évaluation de la stabilité du processus pour les observations individuelles fondées sur la moyenne chevauchante.


                  Remarques : Le présent tableur s'applique aux compteurs sans correction de température seulement et
                                   aux gazomètres de contrôle sans mesure de pression directe. Le tableur permet d'entrer les données relatives à la pression, même si
                                   elles sont fournies pour permettre l'introduction des composantes de l''incertitude pour simplifier les hypothèses.
                                   Le présent tableur remplace le fichier GS-ENG-04-06 (Manual Bell) rev 3.2.en.xls


                   Instructions: Les cases jaunes servent à l'entrée de données.
                                   Les boîtes jaune-clair contiennent des valeurs par défaut mais peuvent être changées.
                                   Les valeurs de chaque source d'incertitude doivent être entrées dans les modèles.
                                   La fonction de calcul automatique d'Excel n'est pas activée : appuyez simultanément sur les touches CTRL+SHIFT+ALT+F9

                        Fichier : GS-UTP-04-06.2(Manual_Master_Bell)rev4.3.xls                      (web version)
                                   GS-ENG-04-06.2(Manual_Master_Bell)rev4.3.xls
                           Date : 2009.11.26

       Modèle de mesurage :                 Vm    P   t 0  tr 
                                             1                       1  em 100%
                                            Vr   Pb  Pr   t 0  tm 



                      Figure 1: Représentation schématique des systèmes de gazomètres de contrôle manuels et des équations de modélisation connexes
                                pour les appareils de mesure de type 2.




                                                                                                                                                   Data Collection and Control
                                                                                                                                                    = Collecte et contrôle des données




       Personne-ressource :: Patrick (Pat) J. Hardock, P.Eng.
                                   Ingénieur principal - Mesure du gaz
                                   Ingénierie et Services de laboratoire
                                   Mesures Canada
                                   Courriel : Hardock.pat@ic.gc.ca




Avis de non-responsabilité : Mesures Canada et la Direction de l'ingénierie et des services de laboratoire n'assument aucune responsabilité, juridique ou implicite, pour l'utilisation de ce tableur.
                                   Il incombe à l'utilisateur d'obtenir toutes les licences nécessaires pour le logiciel de soutien utilisé pour son élaboration.
                                   Le présent tableur est distribué à des fins d'amélioration seulement.
Table 1: Administrative Records                                              Table 3: Input constants for Manual Bell Prover
Test Date:                                       11/26/2009                  Input Constant Name                                                 Value               Units
Report Number:                                   1                           Bell Calibration Temperature (Tc)                                    20        °C
Evaluation Performed By:                         Client                      Base Temperature (To)                                              273.15      °C
Meter Under Test Information                     Transfer Meter #2           Bell Pressure (Pr)                                                  2.001      in H2O @ 60 °F
Serial number:                                   12345678                    Pressure differential (ΔP)                                         0.003       in H2O @ 60 °F
Manufacturer:                                    abc company                 Barometric Pressure (Pb)                                            360        in H2O @ 60 °F
Rated Flow rate:                                 600 cfh
Owner/Client:                                    somebody                    Table 4: Uncertainty Inputs For Budgets (k=2)
Prover Information                               Master Manual Bell Prover   Uncertainty Budget Reference                                        Value               Units
Prover Serial number:                            n/a                         Uncorrected Bell Prover Volume (Vr)
Prover Certificate number:                       n/a                         Bell prover Strapping (from certificate)                             0.04                 %
Recertification date:                            n/a                         Scale Reading error (scale grad size)                              0.0002                ft³
Prover Certified Capacity:                       n/a                         Oil film error Unc. (reference GS-ENG-04-06)                        0.021                 %
Notes:                                                                       Bell alignment error Unc. (reference GS-ENG-04-06)                  0.009                 %
                                                                             Bell area temp. effect (reference GS-ENG-04-06)                    0.0003              % per °C
                                                                             Bell Prover Temperature (Tr)
Long-term estimate not included                                              Reference Temperature Device CAL Uncertainty                         0.13                 °C
Approved: Reviewed by:                                                       Temperature Device Resolution Unc.                                   0.01                 °C
                                                                             Temperature stability during run (limits)                            0.10                 °C

                                                                             Uncorrected Transfer Meter Volume (Vm)
                                                                             Transfer Meter Resolution                                           0.0001               ft³
Table 2: Test Readings                                                       Long-term-Stability (spec)                                            0               check note
Input Variable Name                                    Value         Units   Transfer Meter Repeatability (Rep_Q_MUT_A)                        0.01111969             ft³
Transfer Meter Under Test                                                    Transfer Meter Temperature (Tm) Uncertainties
Transfer Meter Volume (Vm)                       10            ft³           Temperature Device CAL Uncertainty                                  0.25                  °C
Transfer Meter Temperature (Tm)                  20            °C            Temperature Device Resolution Unc.                                   0.01                 °C
Master Bell Prover                                                           Temperature stability during run (limits)                            0.20                 °C
Number of tests in run (n)                       6             count         Proving Process
Bell Volume Reading (Vr)                         10.03         ft³           Process Repeatability (ur it) at 66.6 % confidence                    0                   %
Bell Temperature (Tr)                            21            °C            MUT correction Limit or installation effect (urio)                   0.1                  %
Temperature differences                                                      Pressure effects
Room to MUT- temperature differance (∆Troom-m)   0.1           °C            Barometric Pressure (Pb) (Estimation Unc.)                           0.01           in H2O @ 60 °F
TC error - temperature differance (∆Ttc-m)       0             °C            Pressure Differential (ΔP) (Estimation Unc.)                        0.005           in H2O @ 60 °F
Total Temperture difference (∆Tr-m)              0.1           °C            Reference Pressure (Pr) (Estimation Unc.)                            0.01           in H2O @ 60 °F


                                                                              Table 5: Output values for Transfer Meter using Manual Master Bell Prover
    Transfer Meter #2 Error = 0.04 ±0.3 % @ the 95% confidence
                                                                             Output Variable Name                                                Value               Units
                                  interval k=2
                                                                             Estimated Meter Error (em)                                          0.04                  %

                                                                             Transfer Meter Expanded Uncertainty
Tempate Version:                                                                                                          Uc(em) @ 95% = ±       0.30                  %
GS-UTP-04-06.2(Manual_Master_Bell)rev4.3.xls                                                              Effective Degrees of Freedom = 128     with k= 2.020
GS-ENG-04-06.2(Manual_Master_Bell)rev4.3.xls
2009.11.26
Printed: 9/10/2011                                     Type A Data    File: ee5ee42b-acdf-4bd8-b946-47287df4e7d5.xls
8:29 PM                                                                                     Sheet: Transfer_Meter_Rep


                                Type A Data Uncertainty Estimator
                     Template Version GS-UTP-04-06.2(Manual_Master_Bell)rev4.3.xls
                                            MUT Repeatablity
                                           n
                                      1
                                       (x
    Applied
                           sx                          x )2
    Formula                              i 1
                                                   i

                                                                                               Nominal Value
                       Type A Experimental Data
                                                                            ft³                     Units
     Sequence of Measures                 Operator(s)                 Measured Values        Dev. From Nominal
        Measurement 1                        PJ                                   10.065       10.06536524
        Measurement 2                                                             10.025       10.02548728
        Measurement 3                                                             10.092       10.09157717
        Measurement 4                                                             10.081       10.08136827
        Measurement 5                                                             10.116       10.11604649
        Measurement 6                                                             10.078       10.07837554
        Measurement 7                                                             10.097       10.09745067
        Measurement 8                                                             10.120       10.12004133
        Measurement 9                                                             10.065       10.06531155
       Measurement 10                                                             10.093         10.092866
       Measurement 11                                                             10.108       10.10827733
       Measurement 12                                                             10.101         10.101227
       Measurement 13                                                             10.121        10.1208023
       Measurement 14                                                             10.065       10.06498257
       Measurement 15                                                             10.089       10.08880919
       Measurement 16                                                             10.094       10.09361224
       Measurement 17                                                             10.075       10.07512421
       Measurement 18                                                             10.113       10.11336221
       Measurement 19                                                             10.045       10.04522459
       Measurement 20                                                             10.089        10.0889493
       Measurement 21                                                             10.102       10.10249404
       Measurement 22                                                             10.154       10.15440297
       Measurement 23                                                             10.061       10.06148711
       Measurement 24                                                             10.150       10.14968924
       Measurement 25                                                             10.099       10.09941133
       Measurement 26                                                             10.100       10.09996903
       Measurement 27                                                             10.087       10.08708489
       Measurement 28                                                             10.102        10.1015877
       Measurement 29                                                             10.109       10.10906218
       Measurement 30                                                             10.112       10.11237084
       Rev. Date: 24 APR 2007                Standard Deviation (uncertainty) =              0.027237573
                                                         Degrees of Freedom:                        29
                                          Reported Value = Mean of n Samples:                        6
                                               Standard Error of the Mean equals:            0.011119693
        Spread of Values:                 0.12891569                       Mean Value:       10.09372733
                                                                                                         sx
   Utilized Formula for the "Standard Error of the Mean", also known as the
   "Sampling Distribution".
                                                                                           sx 
                                                                                                          n

                                                       Page 4 of 17
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                                                                                                                        BUDGET




                                                                               Template Version GS-UTP-04-06.2(Manual_Master_Bell)rev4.3.xls

                            Title of Analysis:        Level 2 Master Bell Prover
                                                                                                                                                                                     Student's t-
                              Analysis Units:                      % error                   Measured Value:                  0.042 %                k-factor =       2.020          Distribution       3.0E-01             % error
                                            Date:             30-Oct-07                         Performed by:                  P.J. Hardock                 MTE:                                     Manual Bell Prover


                                                                      Parameter                                                                                      Effective                          Computed          Effective
                                                                                                                           Level of    Coverage       Std Dev in                     Sensitivity                                         Relative %
             Description of Uncertainty Contributor    Type A/B       Uncertainty   Parameter Units     Distribution                                                Degrees of                         Uncertainty in   Uncertainty in
                                                                                                                          Confidence   Factor (k)   Parameter Units                  Coefficient                                          of Total
                                                                        Limits                                                                                       Freedom                           Analysis Units   Analysis Units

      A        Barometric Pressure (Pb)                   B          1.0000E-02 in H2O @ 60 °F        Std Dev             1 Std Dev       1         1.0000E-02         50.0          2.29E-06          2.2902E-08       2.2902E-08         0.00
      B        Pressure Differential (ΔP)                 B          5.0000E-03 in H2O @ 60 °F        Std Dev             1 Std Dev       1         5.0000E-03         50.0          0.276356          1.3818E-03       1.3818E-03         0.47
      C         Reference Pressure (Pr)                   B          1.0000E-02 in H2O @ 60 °F        Std Dev             1 Std Dev       1         1.0000E-02         50.0          2.29E-06          2.2902E-08       2.2902E-08         0.00
      D       Reference Temperature (Tr)                  B          6.8905E-02       °C              Std Dev             1 Std Dev       1         6.8905E-02         50.0          0.340105          2.3435E-02       3.1339E-02         10.62
      E         Base Temperature (To)                     B          1.0000E-09       °C              Rectangular         100.00%       1.732       5.7735E-10         50.0          0.340114          1.9637E-10       2.7770E-10         0.00
      F         MUT Temperature (Tm)                      B          1.4071E-01       °C              Std Dev             1 Std Dev       1         1.4071E-01         50.0          0.341265          4.8020E-02       6.4216E-02         21.76
      G         Base Temperature (To)                     B          1.0000E-09       °C              Rectangular         100.00%       1.732       5.7735E-10         50.0          0.341268          1.9703E-10       2.7864E-10         0.00
      H       Referance Volume (Vr) Uc                    B          2.9209E-03       ft³             Std Dev             1 Std Dev       1         2.9209E-03         50.0          9.974261          2.9134E-02       2.9134E-02         9.87
      I          MUT Volume (Vm) Uc                       B          1.1120E-02       ft³             Std Dev             1 Std Dev       1         1.1120E-02         50.0          10.00418          1.1124E-01       1.1124E-01         37.70
      J       Process Repeatability (Ur it)               A          0.0000E+00     %error            Std Dev             1 Std Dev       1         0.0000E+00         50.0              1             0.0000E+00       0.0000E+00         0.00
      K        MUT correction limit (Urio)                A          1.0000E-01     %error            Rectangular         100.00%       1.732       5.7735E-02         50.0              1             5.7735E-02       5.7735E-02         19.57
      L
      M
      N
      O
      P
      Q
      R
      S
      T
      U
      V
      W
      X
      Y
                                                                      Variable 1     Variable 2              Correlation Coefficient from 1.0 to -1.0                  "Percent of Total" takes        Corr Values                          GUM
                                                                                                                                                                     correlations into account via                      Uncertainty
                                                                          D              F              ρ of 1,2 =       1.0      2.34E-02      4.80E-02                 use of the "Effective          2.2507E-03                         Method
                                                                                                                                                                                                                         Toolbox          Calculator
                                                                          E              G              ρ of 1,2 =       1.0      1.96E-10      1.97E-10                 Uncertainty" values.           7.7380E-20
           Bolded Percent of Total Values are > or = to:                25%         of Expanded Uncertainty                   Total Eff. Degrees of Freedom (u)= 128.282058 Std Unc =                   1.4719E-01      1.4719E-01       Std Unc
                                                                    Student's t-           To achieve the stated "Level of Confidence" using t-statistics and                        Expanded                                                     4
                       u2                           95.45%                                                                                                        2.020                            2.9728E-01        % error         
                                                                                                                                                                                                                                                 uT
       u1eff  u12    2 1 2  2 1,2u1u2 
                      u u                 
                                                                    Distribution                    Effective Degrees of Freedom, the calculated k-factor =                              Unc =                                                 n
                                                                                                                                                                                                                                                  u4
                      1    2                      Level of      Normal            To achieve the stated "Level of Confidence" for an assumed "Normal"
                                                                                                                                                                      2.000
                                                                                                                                                                                     Expanded
                                                                                                                                                                                                       2.9438E-01        % error               i
                                                                                                                                                                                                                                              i 1 i
         Where u1 & u2 are correlated                 Confidence    Distribution                                        distribution, the calculated k-factor =                          Unc =




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                                                                                                          BUDGET




        Uncertainty Contributors                                                           ANALYSIS DETAILS                                                                      Rev. Date: 9 Jan 07




                    ux 
              Barometric Pressure (Pb)     Constant in units of in H20




              Pressure Differential (ΔP)   Estimate of pressure difference between bell and MUT




              Reference Pressure (Pr)      Pressure of bell operation Varation from certificate of calibration




            Reference Temperature (Tr)     Temperature in bell prover (includes variablity during test)




               Base Temperature (To)       Constant with suitable units




              MUT Temperature (Tm)         Temperature in MUT(includes variablity during tests)




               Base Temperature (To)       Constant in suitable units




             Referance Volume (Vr) Uc      The uncertainty of the volume calibration of the bell prover (from Vr_Budget)




               MUT Volume (Vm) Uc          Uncorrected volume of MUT (from Vmut_Budget)




                                                                                                      Page 6 of 17
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            Process Repeatability (Ur it)
                                                                            x
                                            Long-term reproducibility of calibration process
                                                                                                   D:\Docstoc\Working\pdf\ee5ee42b-acdf-4bd8-b946-47287df4e7d5.xlsee5ee42b-acdf-4bd8-b946-47287df4e7d5.xls
                                                                                                BUDGET




             MUT correction limit (Urio)    Installation effects for MUT




                                                                                               Page 7 of 17
Printed: 9/10/2011                                                       Sensitivity Coefficients                                File: ee5ee42b-acdf-4bd8-b946-47287df4e7d5.xls
8:29 PM                                                                                                                                                         Sheet: Total_Coef


                                                           Sensitivity Coefficient Computations
             GS-UTP-04-06.2(Manual_Master_Bell)rev4.3.xls                                                                         Linked To:        Total_Bell_Budget
                                                                                                                                                              ='Total_Bell_Budg
                                                                                                                             Expected Value:   0.041829616
                                                                                                                                                              et'!I5
                                                                                                                           Calculated          Calculated
                                                                                Parameter &         Parameter
                                                                                                                           Sensitivity         Sensitivity     Calculated Mean
                                                               Parameter        Uncertainty         Combined
                     Description of Major Variables                                                                        Coefficient         Coefficient        Sensitivity
                                                                 Value            Unit of           Standard
                                                                                                                              (Plus)             (Minus)          Coefficient
                                                                                  Measure           Uncertainty
                                                                                                                           (1 Std Dev)         (1 Std Dev)
       V1              Barometric Pressure (Pb)                    360          in H2O @ 60 °F        1.00E-02            2.29017E-06           2.2903E-06       2.29023E-06
       V2              Pressure Differential (ΔP)                 0.003         in H2O @ 60 °F        5.00E-03            0.276355588          0.276355588       0.276355588
       V3              Reference Pressure (Pr)                    2.001         in H2O @ 60 °F        1.00E-02            2.29017E-06           2.2903E-06       2.29023E-06
       V4             Reference Temperature (Tr)                    21               °C               6.89E-02            0.340104805          0.340104805       0.340104805
       V5               Base Temperature (To)                    273.15              °C               5.77E-10            0.340095181           0.34013364        0.34011441
       V6               MUT Temperature (Tm)                        20               °C               1.41E-01            0.341101249          0.341428864       0.341265057
       V7               Base Temperature (To)                    273.15              °C               5.77E-10            0.341248958          0.341287418       0.341268188
       V8              Referance Volume (Vr)                      10.03              ft³              2.92E-03            9.971356215          9.977165588       9.974260902
       V9                   MUT Volume (Vm)                         10               ft³              1.11E-02            10.00418284          10.00418284       10.00418284
       V10
       V11
       V12
       V13
       V14
       V15
       V16
       V17
       V18
       V19
       V20
       V21
       V22
       V23
       V24
       V25
                                                    (((V9X/V8X)*(1+(V2X/(V3X+V1X)))*(V5X+V4X)/(V7X+V6X)-1)*100)

                                                                 Value              Units        GUM (5.1.4): provides an empirical first-
      "Value" should equal expected process computed                                             order Taylor series expansion method
      nominal value!                                                                             used by this worksheet.
                                                                4.18E-02='Total_Bell_Budget'!I5                                                      Rev. Date: 9 Jan 2008




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                                                                                                                       BUDGET




                                                               Template Version GS-UTP-04-06.2(Manual_Master_Bell)rev4.3.xls
                            Title of Analysis:        MUT. Temperature (Tm)
                                                                                                                                                                                     Normal
                              Analysis Units:                      °C                         Measured Value:                   20 C                k-factor =       2.000          Distribution     2.8E-01             °C
                                            Date:             22-Jun-05                        Performed by:                    Hardock                    MTE:                               Prover - MUT Temperture


                                                                     Parameter                                                                                      Effective                        Computed          Effective
                                                                                                                          Level of    Coverage       Std Dev in                     Sensitivity                                       Relative %
             Description of Uncertainty Contributor    Type A/B      Uncertainty   Parameter Units     Distribution                                                Degrees of                       Uncertainty in   Uncertainty in
                                                                                                                         Confidence   Factor (k)   Parameter Units                  Coefficient                                        of Total
                                                                       Limits                                                                                       Freedom                         Analysis Units   Analysis Units

      A           (Tm) Cal Unc                            B         2.5000E-01           °C          Normal              95.45%        2.000        1.2500E-01        50.0                1         1.2500E-01       1.2500E-01         58.28
      B          (Tm) Resolution                          B         1.0000E-02           °C          Resolution          100.00%       3.464        2.8868E-03        50.0                1         2.8868E-03       2.8868E-03         1.35
      C            (Tm) stablity                          B         1.0000E-01           °C          Rectangular         100.00%       1.732        5.7735E-02        50.0                1         5.7735E-02       5.7735E-02         26.92
      D Total Temperture difference (∆Tr-m)               B            0.05              °C          Rectangular            1          1.732        2.8868E-02         50                 1         2.8868E-02       2.8868E-02         13.46
      E
      F
      G
      H
      I
      J
      K
      L
      M
      N
      O
      P
      Q
      R
      S
      T
      U
      V
      W
      X
      Y
                                                                     Variable 1     Variable 2              Correlation Coefficient from 1.0 to -1.0                  "Percent of Total" takes      Corr Values                          GUM
                                                                                                                                                                    correlations into account via                    Uncertainty
                                                                                                       ρ of 1,2 =                                                       use of the "Effective        0.0000E+00                         Method
                                                                                                                                                                                                                      Toolbox          Calculator
                                                                                                       ρ of 1,2 =                                                       Uncertainty" values.         0.0000E+00
           Bolded Percent of Total Values are > or = to:                25%        of Expanded Uncertainty                   Total Eff. Degrees of Freedom (u)= 76.5864543 Std Unc =                1.4071E-01       1.4071E-01       Std Unc
                                                                   Student's t-           To achieve the stated "Level of Confidence" using t-statistics and                        Expanded                                                   4
                       u2                           95.45%                                                                                                       2.033                          2.8613E-01            °C          
                                                                                                                                                                                                                                              uT
       u1eff  u12    2 1 2  2 1,2u1u2 
                      u u                 
                                                                   Distribution                    Effective Degrees of Freedom, the calculated k-factor =                              Unc =                                               n
                                                                                                                                                                                                                                               u4
                      1    2                      Level of     Normal            To achieve the stated "Level of Confidence" for an assumed "Normal"
                                                                                                                                                                     2.000
                                                                                                                                                                                    Expanded
                                                                                                                                                                                                    2.8143E-01            °C                i
                                                                                                                                                                                                                                           i 1 i
         Where u1 & u2 are correlated                 Confidence   Distribution                                        distribution, the calculated k-factor =                          Unc =




                                                                                                                      Page 9 of 17
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                                                                                                            BUDGET




        Uncertainty Contributors                                                              ANALYSIS DETAILS                                                                             Rev. Date: 9 Jan 07




                    ux 
                                               This is the uncertainty of measurements used to establish traceability of measurement to National, International, or consensus Standards. Basically this is the calibration
                    (Tm) Cal Unc
                                               measurement uncertainty.




                                               The Manufacturers' Specifications are being used as the limits for Instrument "Long Term Stability" uncertainty with respect to time since compared to calibration reference
                  (Tm) Resolution
                                               value.




                    (Tm) stablity              Accounts for the varation during the test run or the test sets




         Total Temperture difference (∆Tr-m)   Accounts for the diferance in a)




                                                                                                         Page 10 of 17
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                                                                                                                      BUDGET




                                                               Template Version GS-UTP-04-06.2(Manual_Master_Bell)rev4.3.xls
                            Title of Analysis:        MUT Volume, Vm
                                                                                                                                                                                   Normal
                              Analysis Units:                                                  Measured Value:              0.04 %                k-factor =       2.000          Distribution     2.2E-02
                                            Date:              7-Jul-06                         Performed by:                 Hardock                    MTE:                                       MUT Meter


                                                                     Parameter                                                                                    Effective                        Computed          Effective
                                                                                                                        Level of    Coverage       Std Dev in                     Sensitivity                                       Relative %
             Description of Uncertainty Contributor    Type A/B      Uncertainty   Parameter Units     Distribution                                              Degrees of                       Uncertainty in   Uncertainty in
                                                                                                                       Confidence   Factor (k)   Parameter Units                  Coefficient                                        of Total
                                                                       Limits                                                                                     Freedom                         Analysis Units   Analysis Units

      A              MUT Resolution                       B         1.0000E-04           ft³         Resolution        100.00%       3.464       2.8868E-05         50.0                1         2.8868E-05       2.8868E-05         0.26
      B              MUT LTS (spec)                       B         0.0000E+00           ft³         Normal             95.45%       2.000       0.0000E+00         50.0                1         0.0000E+00       0.0000E+00         0.00
      C             MUT Repeatability                     A         1.1120E-02           ft³         Std Dev           1 Std Dev       1         1.1120E-02         29.0                1         1.1120E-02       1.1120E-02         99.74
      D
      E
      F
      G
      H
      I
      J
      K
      L
      M
      N
      O
      P
      Q
      R
      S
      T
      U
      V
      W
      X
      Y
                                                                     Variable 1     Variable 2              Correlation Coefficient from 1.0 to -1.0                "Percent of Total" takes      Corr Values                          GUM
                                                                                                                                                                  correlations into account via                    Uncertainty
                                                                                                       ρ of 1,2 =                                                     use of the "Effective        0.0000E+00                         Method
                                                                                                                                                                                                                    Toolbox          Calculator
                                                                                                       ρ of 1,2 =                                                     Uncertainty" values.         0.0000E+00
           Bolded Percent of Total Values are > or = to:                25%        of Expanded Uncertainty                  Total Eff. Degrees of Freedom (u)= 29.0003909 Std Unc =               1.1120E-02       1.1120E-02       Std Unc
                                                                   Student's t-           To achieve the stated "Level of Confidence" using t-statistics and                      Expanded                                                   4
                       u2                           95.45%                                                                                                     2.090                          2.3240E-02                        
                                                                                                                                                                                                                                            uT
       u1eff  u12    2 1 2  2 1,2u1u2 
                      u u                 
                                                                   Distribution                    Effective Degrees of Freedom, the calculated k-factor =                            Unc =                                               n
                                                                                                                                                                                                                                             u4
                      1    2                      Level of     Normal            To achieve the stated "Level of Confidence" for an assumed "Normal"
                                                                                                                                                                   2.000
                                                                                                                                                                                  Expanded
                                                                                                                                                                                                  2.2239E-02                              i
                                                                                                                                                                                                                                         i 1 i
         Where u1 & u2 are correlated                 Confidence   Distribution                                        distribution, the calculated k-factor =                        Unc =




                                                                                                                  Page 11 of 17
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                                                                                             BUDGET




        Uncertainty Contributors                                                ANALYSIS DETAILS                                                                    Rev. Date: 9 Jan 07




                   ux 
                  MUT Resolution




                  MUT LTS (spec)     See attached Type A data worksheet for R&R results.




                 MUT Repeatability




                                                                                           Page 12 of 17
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                                                                                                                      BUDGET




                                                               Template Version GS-UTP-04-06.2(Manual_Master_Bell)rev4.3.xls
                            Title of Analysis:        Bell Temperature (Tr)
                                                                                                                                                                                   Normal
                              Analysis Units:                                                 Measured Value:                 21 °C               k-factor =       2.000          Distribution     1.4E-01
                                            Date:             22-Jun-05                        Performed by:                  Hardock                    MTE:                  Prover - Referance meter temperature


                                                                     Parameter                                                                                    Effective                        Computed          Effective
                                                                                                                        Level of    Coverage       Std Dev in                     Sensitivity                                       Relative %
             Description of Uncertainty Contributor    Type A/B      Uncertainty   Parameter Units     Distribution                                              Degrees of                       Uncertainty in   Uncertainty in
                                                                                                                       Confidence   Factor (k)   Parameter Units                  Coefficient                                        of Total
                                                                       Limits                                                                                     Freedom                         Analysis Units   Analysis Units

      A                (Tr) Cal. Unc.                     B         1.2500E-01           °C          Normal            95.45%        2.000        6.2500E-02        50.0                1         6.2500E-02       6.2500E-02         66.31
      B                  Resolution                       B         1.0000E-02           °C          Resolution        100.00%       3.464        2.8868E-03        50.0                1         2.8868E-03       2.8868E-03         3.06
      C                 (Tr) (stablity)                   B         5.0000E-02           °C          Rectangular       100.00%       1.732        2.8868E-02        50.0                1         2.8868E-02       2.8868E-02         30.63
      D
      E
      F
      G
      H
      I
      J
      K
      L
      M
      N
      O
      P
      Q
      R
      S
      T
      U
      V
      W
      X
      Y
                                                                     Variable 1     Variable 2              Correlation Coefficient from 1.0 to -1.0                "Percent of Total" takes      Corr Values                          GUM
                                                                                                                                                                  correlations into account via                    Uncertainty
                                                                                                       ρ of 1,2 =                                                     use of the "Effective        0.0000E+00                         Method
                                                                                                                                                                                                                    Toolbox          Calculator
                                                                                                       ρ of 1,2 =                                                     Uncertainty" values.         0.0000E+00
           Bolded Percent of Total Values are > or = to:                25%        of Expanded Uncertainty                  Total Eff. Degrees of Freedom (u)= 70.6522263 Std Unc =               6.8905E-02       6.8905E-02       Std Unc
                                                                   Student's t-           To achieve the stated "Level of Confidence" using t-statistics and                      Expanded                                                   4
                       u2                           95.45%                                                                                                     2.036                          1.4031E-01                        
                                                                                                                                                                                                                                            uT
       u1eff  u12    2 1 2  2 1,2u1u2 
                      u u                 
                                                                   Distribution                    Effective Degrees of Freedom, the calculated k-factor =                            Unc =                                               n
                                                                                                                                                                                                                                             u4
                      1    2                      Level of     Normal            To achieve the stated "Level of Confidence" for an assumed "Normal"
                                                                                                                                                                   2.000
                                                                                                                                                                                  Expanded
                                                                                                                                                                                                  1.3781E-01                              i
                                                                                                                                                                                                                                         i 1 i
         Where u1 & u2 are correlated                 Confidence   Distribution                                        distribution, the calculated k-factor =                        Unc =




                                                                                                                  Page 13 of 17
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                                                                                                 BUDGET




        Uncertainty Contributors                                                    ANALYSIS DETAILS                                                                              Rev. Date: 9 Jan 07




                   ux 
                                      This is the uncertainty of measurements used to establish traceability of measurement to National, International, or consensus Standards. Basically this is the calibration
                   (Tr) Cal. Unc.
                                      measurement uncertainty.




                                      The uncertainty due to limited measuring instrument resolution is believed to be 100% contained within a spread equal to the smallest discernable increment value. The
                     Resolution
                                      plus and minus limts are given to equal the half-width of the spread, L=R/2. U=L/root3




                                      The Instrument "Long Term Stability" uncertainty with respect to time since compared to calibration reference value is being contained within limits determined by historical
                    (Tr) (stablity)
                                      observations.




                                                                                               Page 14 of 17
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                                                                                                                      BUDGET




                                               Template Version GS-UTP-04-06.2(Manual_Master_Bell)rev4.3.xls
                  Title of Analysis: Bell Prover volume (Volume Vr)
                                                                                                                                                                                   Normal
                              Analysis Units:                                                  Measured Value:             10.03 ft³              k-factor =       2.000          Distribution     5.8E-03
                                            Date:             27-Jun-07                         Performed by:                 Hardock                    MTE:                               Master Manual Bell prover


                                                                     Parameter                                                                                    Effective                        Computed          Effective
                                                                                                                        Level of    Coverage       Std Dev in                     Sensitivity                                       Relative %
             Description of Uncertainty Contributor    Type A/B      Uncertainty   Parameter Units     Distribution                                              Degrees of                       Uncertainty in   Uncertainty in
                                                                                                                       Confidence   Factor (k)   Parameter Units                  Coefficient                                        of Total
                                                                       Limits                                                                                     Freedom                         Analysis Units   Analysis Units

      A            Bell prover Strapping                  B         4.0120E-03           ft³         Normal             95.45%         2.000      2.0060E-03        50.0                1         2.0060E-03       2.0060E-03         45.27
      B            Scale Reading error                    A         1.0000E-04           ft³         Rectangular       100.00%         1.732      5.7735E-05        50.0                1         5.7735E-05       5.7735E-05         1.30
      C                 Oil film error                    A         2.1063E-03           ft³         Std Dev           1 Std Dev         1        2.1063E-03        50.0                1         2.1063E-03       2.1063E-03         47.53
      D            Bell alignment error                   B         4.5135E-04           ft³         Rectangular       100.00%         1.732      2.6059E-04        50.0                1         2.6059E-04       2.6059E-04         5.88
      E            Bell Cal. Temp. (Tc)                   B         1.5000E-06           ft³         Rectangular       100.00%         1.732      8.6603E-07        50.0                1         8.6603E-07       8.6603E-07         0.02
      F
      G
      H
      I
      J
      K
      L
      M
      N
      O
      P
      Q
      R
      S
      T
      U
      V
      W
      X
      Y
                                                                     Variable 1     Variable 2              Correlation Coefficient from 1.0 to -1.0                "Percent of Total" takes      Corr Values                          GUM
                                                                                                                                                                  correlations into account via                    Uncertainty
                                                                                                       ρ of 1,2 =                                                     use of the "Effective        0.0000E+00                         Method
                                                                                                                                                                                                                    Toolbox          Calculator
                                                                                                       ρ of 1,2 =                                                     Uncertainty" values.         0.0000E+00
           Bolded Percent of Total Values are > or = to:                25%        of Expanded Uncertainty                  Total Eff. Degrees of Freedom (u)= 101.43694          Std Unc =       2.9209E-03       2.9209E-03       Std Unc
                                                                   Student's t-           To achieve the stated "Level of Confidence" using t-statistics and                      Expanded                                                   4
                       u2                           95.45%                                                                                                     2.025                          5.9150E-03                        
                                                                                                                                                                                                                                            uT
       u1eff  u12    2 1 2  2 1,2u1u2 
                      u u                 
                                                                   Distribution                    Effective Degrees of Freedom, the calculated k-factor =                            Unc =                                               n
                                                                                                                                                                                                                                             u4
                      1    2                      Level of     Normal            To achieve the stated "Level of Confidence" for an assumed "Normal"
                                                                                                                                                                   2.000
                                                                                                                                                                                  Expanded
                                                                                                                                                                                                  5.8418E-03                              i
                                                                                                                                                                                                                                         i 1 i
         Where u1 & u2 are correlated                 Confidence   Distribution                                        distribution, the calculated k-factor =                        Unc =




                                                                                                                  Page 15 of 17
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                                                                                                    BUDGET




        Uncertainty Contributors                                                      ANALYSIS DETAILS                                                                              Rev. Date: 9 Jan 07




                    ux 
                                        This is the uncertainty of measurements used to establish traceability of measurement to National, International, or consensus Standards. Basically this is the calibration
                Bell prover Strapping
                                        measurement uncertainty.




                Scale Reading error     Uncertainty from reading scale - usually 1/2 graduation




                    Oil film error      Maximum value assumed to be 0.021% from Appendix E of GS-ENG-04-06




                Bell alignment error    Maximum value assumed to be 0.009% from Appendix C of GS-ENG-04-06




                Bell Cal. Temp. (Tc)    Maximum value assumed to be 0.003% from Appendix B of GS-ENG-04-06




                                                                                                  Page 16 of 17
Spreadsheet Version History
Version #                     Date                                         Validation/details                               By

   1                     2007.06.25   First version - Populated Quametec spreadsheet                                    P.J. Hardock
  1.1                    2007.06.27   Editorials and added password protection. Password is "password"                  P.J. Hardock
   2                     2007.10.17   repaired links                                                                    P.J. Hardock
  2.1                    2007.10.17   Editorials                                                                        P.J. Hardock
                                      File Size = 1.00 MB (1,053,184 bytes)
   3                     2007.10.29   Simplified spreadsheet and re-populated Quametec spreadsheet                      P.J. Hardock
                                      Issued for use; File Size= 722 KB (739,328 bytes)
                                      Added duel Language provisions
  3.1a                   2007.11.19   verified calculations using data set 1)                                           P.J. Hardock
  3.2c                   2008.01.30   conversion to template 2.8 format                                                 P.J. Hardock
  3.3c                   2008.05.06   corrected link                                                                    P.J. Hardock
  3.4c                   2008.05.06   Editorals and prepare for translation                                             P.J. Hardock
  3.4c                   2008.05.12   Name Change to from ENG to UTP                                                    P.J. Hardock
  3.5                    2008.05.12   Corrected links in coeff page                                                     P.J. Hardock
   4                     2008.05.15   Completed translation                                                             P.J. Hardock
  4.1                    2008.05.29   Changed filed name to add control limit value                                     P.J. Hardock
                                      added cross referance to "ENG" name
   4.2                   2008.07.17   Added temperature difference input for IO sheet                                   P.J. Hardock
  4.2.1                  2008.07.24   Editorials and explinations
   4.3                   2009.11.26   corrected Tm,Tp, Bell Cal. Temp. (Tc) inputs from s/(3)^1/2 to s/(2 (3)^1/2) in   P.J. Hardock
                                      Tm_budget, Tr_budget sheets, and Vmut_budget sheets

				
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