When closing a material balance, the material unaccounted for (MUF) and its standard deviation are calculated. It is common practice to evaluate the MUF for significance by comparing it with the standard deviation. More specifically, if a positive MUF exceeds twice this calculated standard deviation, a quantity that is labeled the MUF limit of error, then the MUF is declared to be significant. That is to say, there is statistical evidence that the true MUF, the quantity estimated by the calculated MUF, is some value greater than zero.
Although the above test is a valid one and is an essential part of the MUF evaluation, there are some considerations that should enter into a more comprehensive evaluation. The calculated standard deviation of MUF normally reflects only the effects of statistical errors of measurement, i.e., those errors that are an inherent part of the measurement process. Mistakes or blunders in measuring, recording, and/ or processing the measurement data do not affect this standard deviation although they do, of course, affect the value of the MUF. Further, such factors as hidden or unmeasured inventories and unmeasured losses also affect the size of MUF, but not its standard deviation as normally defined. It is only when perfection in operation is demanded that it is reasonable to conclude the MUF evaluation with the limit of error test.
How can these other factors be included in the evaluation? This can be accomplished by using past data from a facility judged to be "in-control" in the sense that unmeasured inventories and losses are minimized, as are human mistakes. These data can be used to estimate the parameters of the model that describe MUF behavior and, in turn, these estimates can be used to evaluate a given calculated MUF.
How this can be done is discussed in Chapter 7 of reference [1], This article extends that discussion in several regards with the primary emphasis being an investigation of the conditions under which the special control chart presented in the reference represents an advantage over the somewhat simpler standard control chart.