Quite often the quantity under measurement (measurand) Y is not measured directly, but is the result of measurement of several independent quantities X1, X2, X3, …,
Xn. The measurand Y is also called the output quantity and X1, X2, X3,…, Xn asinput quantities. The quantity Y is related to output quantities through some welldefined relation. That is Y is expressed in terms of X1, X2, X3,…, Xn a
Notations:
For economy of notation, the same symbol is used for the physical quantity and for the random variable that represent the possible outcome of an observation of that quantity. When it is stated that an input quantity Xp has a particular probability distribution then Xp is a random variable. The physical quantity itself is invariant and has a unique, fixed value.
In a series of observations, the qth observed value of Xp is denoted as xp;q . The estimate of the Xp is denoted by xp, which in fact is the expected value of Xp. Quantities, in general, are expressed in capital letters, while their numerical values by the corresponding small case letters. The value of the quantity Xn is expressed as xn for all integral values of n. Hence y the estimated value of thequantity Y is expressed as
where x1, x2, x3, …, xn are the measured estimates of the physical quantities X1, X2, X3,…, Xn, respectively.
It is assumed that each input estimate is corrected for all known systematic effects, which are likely to influence significantly.
