I think you could use a method like that used in SMART/ENA which uses the collected data to define outliers. SMART uses the mean and standard deviation of anthropometric indices calculated from collected data to decide which observations are more likely to be outliers than true values. In this scheme, we exclude (flag) that lie outside of +/- 3 z-scores from the mean z-score so that values of (e.g.) WHZ that are below:
mean(WHZ) - 3
and:
means(WHZ) + 3
are flagged as as implausible values.
I think this approach may be problematic as it assumes that SD(WHZ) = 1 and it assumes the distribution of WHZ is normal. Work done by members of the SMART team shows that these assumptions are reasonable with WHZ usually normally distributed (with only slight deviations from normality) and SD(WHZ) tending to be limited to between 0.8 and 1.2 z-scores and centered around 1 z-score.
This does not, however, help us much with your problem as we tend to use raw measurment values rather than z-scores with MUAC. An analogous approach woud be to flag MUAC values that lie outside of mean(MUAC) +/- 3 * SD(MUAC). The problem here is that both the mean and the SD are strongly influenced by outlier values. It might be better, therefore, to use more robust summary measures such as the median (as an alternative to using the mean) and the median absolute deviation (multiplied by 1.4826) as an alternative to using the SD).
A common alternative is to use the method used with boxplots. The "box" on boxplots ranges between the upper and lower quartiles of the data.
The “whiskers” on boxplots usually extend to 1.5 times the interquartile range from the ends of the box (i.e. the lower and upper quartiles). This is known as the "inner fence". Data points that are outside the inner fence are considered to be mild outliers. The "1.5" can be increased to 3.0. This defines the "outer fence" which can be used to identify extreme outliers. I tend to think of mild outliers as possible outliers and severe outliers as probable outliers.
See these sections:
Box Plot
What are outliers in the data?
Detection of Outliers
of the NIST/SEMATECH Handbook of Statistical Methods. Links on theses pages lead to tests that can help identify outliers.
You could use the SMART method with MUAC/A z-scores.
I hope this is of some use.