
Expanded uncertainty and coverage factor Expanded uncertainty Although the combined standard uncertainty u_{c }is used to express the uncertainty of many measurement results, for some commercial, industrial, and regulatory applications (e.g., when health and safety are concerned), what is often required is a measure of uncertainty that defines an interval about the measurement result y within which the value of the measurand Y can be confidently asserted to lie. The measure of uncertainty intended to meet this requirement is termed expanded uncertainty, suggested symbol U, and is obtained by multiplying u_{c}(y) by a coverage factor, suggested symbol k. Thus U = ku_{c}(y) and it is confidently believed that Y is greater than or equal to y  U, and is less than or equal to y + U, which is commonly written as Y = y ± U. Coverage factor In general, the value of the coverage factor k is chosen on the basis of the desired level of confidence to be
associated with the interval defined by U = ku_{c}. Typically, k is in the range 2 to 3. When the normal distribution applies and
u_{c }is a reliable estimate of the standard deviation of y, Relative expanded uncertainty In analogy with relative standard uncertainty u_{r }and relative combined standard uncertainty u_{c,r} defined above in connection with simplified forms of equation (6), the relative expanded uncertainty of a measurement result y is U_{r }= U/y, y not equal to zero.
