5.3 Comparison of Uncertainty Budgets
Comparing unceriainty budgets is gencrally the firststep in resolving discrepancies that are deemed signifi-canL.Such cormparisons consist of verifying that theunIcerlainly budgel includles,and properly accounts for,all significant sources of uncerlainly.
5.3.1 Accounting for Uncertainty Sources5.3.1.1 influence Quantities. The factors thataffeci measurement results are known as influencequantities (GUM 3.1. and GUM B.2.10). All significantinfluence quantities shouid be lisiedi and a comparisonmade toensure that both uncerlainty budgeis haveconsidere tese effects. If an influence quantity isaccounted for in one budgci but omitted in te other,discussion regarding the significance of the quantityshould be conducted. Unless the unccrlainty budgctis primarily composed of numcrous small uncertaintysourccs,individual sourecs that have a standard uncer-tainty less than 10% of thc largcst standard unccrtaintysourec in the budgct can usually bc omittcd withoutsignificance.
The list of influencc quantitics also depends on thctime period over which the uncertainty budget is valid.For cxample,if an unccrtainty budget is developed fora single measurement then only thosc influence quanti-ties that affect that mcasurement need be considered.However,if an uncertainty budget is to be used formany measurements (of the same measurand)thenall influencequantities over the entirc period whenmeasurements will be taken must be considered. Forcxample,seasonal temperature changes might be arelcvant uncertainty source for an uncerrainry hudgetintcnded to be valid for product measurements madeover the course of a year. lnput Quantities. Various uncerlainlysources known as input quantities conuprisc an uncer-tainty budget. These quantitics are listed and combinedusing the mcthods dcscribed in the GUM. Each inpuiquantity is composcd of onc or morc influcnce quantitics.Mctrologists choosc how diffcrent influencc quantitieswill be combined into input quantitics and this is whytwo uncertainty budgets,both of which arc corrcctlyconstructed,can appear to be very different in theirtreatment of the influence quantities. For cxamplc,oncbudget might list each influence quantity as an inputquantity and have a long list of unceriainty sourcesthat need to be combined. Another budge: might haveonly a few input quantities,choasing to cambinc manyinfluence quantitics into a single input quantity,suchas a Type A uncertainty evalualed from a long-term reproducibility study. The important point is that all
iniuence quantities of the measurement are accounled for in some input quantity. In certain cases. e.g.. uncertainty evaluated by computer simuiation, input quantities are represented as parameters that are allowed 10 vary between simulation cycles.
5.3.2 Magnitudes of Uncertainty
Components (Standard Uncertainties of input Quantities). Aftcr ascertaining that cach significant infuence quantity is present in the uncertainty budgct In some input quantity, the input quantitics must be evaluated. The magnitudes of uncertainty componcnts are quantified by standard dcviations, known as standard
uncertaintics (GUM 4.1). Each input quantity has an associated standard uneertainty. The value of the standard uncertainty must account for the range of values that could reasonably be atributed to the input quantity over the time period that the measurements are performed. Some uncertainty budgets pertain to a single measurement that occurs in a short period of time. Other
uncertainty budgets might pertain to many subsequent measurements, (as is typical of production workpieccs), here the measurement conditions, while being :bounded, change from measurement to mcasurement.
The time scale over which the measurements are performed must he considered. An uIncertainty budget designed for a large numher of measurements, eg, production workpieces that are continuously produced and inspected over a long time scale (days. weeks, months, or years). will have greater variation in the input quantities than measurements performed in a short time period. Consequently, when determining the standard uncertainties of the input quantities it is essential 10 consider the full range of possible variations that may occur during the measuremenis. in addition, for uncertainty budgets that will apply Io many subsequent
measurements, the bounds on the permissible variation of the inpul quantities under which the uneertainty budgel is valid should be clearly staled.