The ultraviolet spectrophotometric determination of vanadium by the molybdovanadophosphoric acid method

A New Conception of Measurement Uncertainty Calculation

“…Having given error denition (15), one can introduce it to expression (16) which after that takes the form P r [|e| ≤ U ] = p. (17) If the error is described by symmetrical probability density function g(e) with the expected value equal to 0, one can write relation (17) as the functional U −U g(e) de = p. (18) Example 2. Let us calculate uncertainty caused by the error described by probability density function shown in Fig.…”

“…Possibility of taking into account correlations between partial errors is important property of this method [18].…”

“…where g i (e i ) is probability density function of i-th error and * is symbol of convolution. Hawing determined g c (e c ), one can use (18) to calculate the combined uncertainty.…”

“…Application of the second way needs knowledge about values of expanded uncertainties of the partial errors. Having it, one can calculate the composed uncertainty using reductive interval arithmetic described in[17,18].…”

“…Histogram of the combined error obtained in Example 5. Uncertainty calculated from this histogram for condence level p = 0.95 is U = 1.8 × 10 −3 .On the base of this histogram, the uncertainty calculated accordingly with(18) for condence level p = 0.95 has value 10 −3 V.Let us assume now that a single measurement has been performed and the obtained value of the evaluation is for example:x = 0.8577 V. The measurement result can be written then as interval:x = 0.8577 + −1.8 × 10 −3 , 1.8 × 10 −3 = [0.8559, 0.8595] V. Procedure 1a. This procedure is performed in the same steps as procedure 1 with this dierence that the error sources are divided into types A and B.…”