![\"\"](\"https:\/\/research.reading.ac.uk\/fiduceo\/wp-content\/uploads\/sites\/129\/2019\/07\/tutorial-1-pt3-fig1-1-1024x388.png\")
<\/figure>\r\n\r\n\r\n\r\nAs can be seen from the diagram above, this uncertainty analysis tree is centred on the hypothetical measurement function:<\/p>\r\n\r\n\r\n\r\n
y=f(x_1,x_2,x_3) + 0<\/span><\/p>\r\n\r\n\r\n\r\n Notice from the diagram that there are three effects that contribute to the uncertainty in the first term, u(x_1)<\/span>, and that this uncertainty in x_1<\/span> is propagated to an uncertainty in the measurand\u00a0( y <\/span>) using a \u2018sensitivity coefficient\u2019,c_1<\/span> . We\u2019ll examine sensitivity coefficients in detail in the next recipe of this series.<\/p>\r\n\r\n\r\n\r\n Moving on, we can see that the second term has its own measurement function:<\/p>\r\n\r\n\r\n\r\n x_2=x_2(X_a,X_b)<\/span><\/p>\r\n\r\n\r\n\r\n The uncertainty in the terms in this measurement function, u(X_a) <\/span> and u(X_b) <\/span> , is again propagated to an uncertainty in the measurand (in this case x_2 <\/span> ) via a sensitivity coefficient, and the uncertainty in x_2 <\/span> , u(x_2) <\/span> , is propagated to an uncertainty in the measurand (y) <\/span> via the sensitivity coefficient c_2 <\/span> .<\/p>\r\n\r\n\r\n\r\n A number of effects contribute to the uncertainty in the third term, u(x_3) <\/span> , but it is not possible to quantify them separately. Instead, their combined uncertainty has been evaluated and propagated to the measurand using the sensitivity coefficient c_3 <\/span> .<\/p>\r\n\r\n\r\n\r\n