© NMISA 2010 Dissemination of Mass Standards from the National Prototype by Thomas Mautjana

© NMISA 2010 Presentation overview Introduction Method description Traceability Conclusion

© NMISA 2010 Introduction Kg is the only SI unit that is still an artefact Our mandate is to maintain and disseminate the value of the kilogram

© NMISA 2010 How do we disseminate the value of kg? Weighing design is used to calibrate a set of weights using one reference standard Subdivision and multiplication method Calibrate in decades :D 1 500, 200, 200*,100 D 2 50, 20, 20*,10 D 3 5, 2, 2*, 1 etc D 6

© NMISA 2010 Weighings with 5221 structure (10) + d1vs(5) +(2) +(2)* +(1) (10) + d2vs(5) +(2) +(2)* +(1)* (5)vs(2) +(2)* +(1) +d3d3 (5)vs(2) +(2)* +(1)* +d4d4 (2)+(1)vs(2)* +(1)* +d5d5 (2)+(1)*vs(2)* +(1) +d6d6 (2)vs(1) +(1)* +d7d7 (2)*vs(1) +(1)* +d8d8

© NMISA 2010 Method description To determine the values of all the unknown weights the normal equations would have to be orthogonal (i.e. without variances) To ensure orthogonality some of the equations may be omitted and some used more than once Reference standard should be the defining (Head) weight

© NMISA 2010 Orthogonal design: 5221 (10)=(5) +(2) +(2)* +(1)-d1d1 (10)=(5) +(2) +(2)* +(1)* -d2d2 (5)=(2) +(2)* +(1) +d3d3 (5)=(2) +(2)* +(1)* +d4d4 (2)+(1)=(2)* +(1)* +d5d5 (2)+(1)=(2)* +(1)* +d5d5 (2)+(1)*=(2)* +(1) +d6d6 (2)+(1)*=(2)* +(1) +d6d6 (2)=(1) +(1)* +d7d7 (2)=(1) +(1)* +d7d7 (2)*=(1) +(1)* +d8d8 (2)*=(1) +(1)* +d8d8

© NMISA 2010 Calculation: Equations

© NMISA 2010 Calculation: Equations continues

© NMISA 2010 What about weights > 1kg Define:(10) = M =10 u u = (1) thus (10) = 10(1)

© NMISA 2010 Method: Advantages and Disadvantages Advantages:  Less use of reference weights  Use check weights  Produces no variances or co-variances  Lead to higher accuracies Disadvantage:  Placing several weights on a pan

© NMISA 2010 Traceability Copy 56 1kgTransfer Standards E1 set of Transfer Standards E1 Working Standards E2 Working Standards Customer Standards

© NMISA 2010 Conclusion Orthogonal system produces no variances or co- variances The most accurate method with self check Customer standards are compared against the working standards and never and never will be compared against the national standard.

© NMISA 2010 Thank you