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Material Unaccounted For (MUF)

Uranium oxide pellets. (Source: Areva)
Uranium oxide pellets. (Source: Areva) 

Material Unaccounted For (MUF) refers to the difference between the book inventory of material and the physical inventory of material for an MBA over a material balance period.  The following equation is used to calculate MUF:

MUF = (PB + X - Y) - PE

Where, PB is the beginning physical inventory, X is the sum of increases to inventory, Y is the sum of decreases from inventory, and PE is the ending physical inventory.

The book inventory is the algebraic sum of PB, X and Y, which implies that:

MUF = BI - PE

For item MBAs, MUF should be zero, and a non-zero MUF is an indication of a problem (e.g. accounting mistakes).  For bulk handling MBAs, a non-zero MUF is expected for three main reasons: 1) the measurement uncertainty; 2) the nature of processing; and 3) operator's measurement uncertainties associated with PB, X, Y, and PE.  These quantities are combined to determine the uncertainty of the material balance σMUF.

The cumulative MUF is simply the algebraic sum of the MUFs for an MBA over time:

 CumulativeMUFEquationCumulativeMUFEquation

We expect that the Nuclear Material accountancy systems will be able to verify that the MUF is less than three times the standard deviation in the MUF measurements:

|MUF| < 3σMUF

and that the MUFc is less than 1 Significant Quantity (SQ) for the time specified in the IAEA timeliness goal for the facility (usually corresponds to the material balance period).

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