The example that you have presented occurs often. A common example is that a number of children were under 5 years when the census-based list was created (not using exact birthday) but are now over 5 and not eligible to be included in the survey. The first and most important step is to take the time to update the sampling frame with the village/camp leader before data collection occurs. This will minimize the number of ineligible children included in the sampling frame. Despite your best efforts there will likely be a few ineligible children selected from your sampling frame. If you are using simple random sampling you would NOT measure the ineligible child. Instead you would randomly select another child (common to use a random number table) on the list. If you are using systematic random sampling you would NOT measure the ineligible child. Instead you would select the next U5 child on the list. After this child is measured then you would apply the sampling interval to select the next child.

If I understand correctly, you plan to use a census list of all children less than 5 years of age to select a random sample of children with systematic random sampling. The selected children should then be listed on a separate form and visited to collect the necessary data. The number of children to select should be estimated using sample size calculation, and this calculation should account for non-response, including ineligibility because of mistaken age. In general, it is a bad idea to replace non-respondents; this injects additional bias into the sample. If non-response is higher than predicted during sample size calculation, it is better to sacrifice a bit of precision by not replacing non-respondents in the interest of avoiding bias.

In camp settings the list may include fraudulent children and "dead souls". Fraudulent children are often "created" by HHs sharing children (or borrowing children from the host community for a small fee) during census and registration / re-registration exercises for the purposes of obtaining extra rations or other relief items. "Dead souls" are children who have died but are reported as still being alive in order to maintain a HH's entitlement. There will have been some mortality and emigration so you will need to plan for a larger sample to account for population losses. There will have been new births and immigration and you will have to account for these or your sampel will exclude recent births and incomers (a selection bias). There is also the problem of an "ageing cohort". If (e.g.) the census is one year old then surviving neonates will now be 12-13 months old and 5 year olds will not be 6 years old. Your list will not be a list of children aged under five years but a list of children aged between one and six years. For these reasons I think that your list may not be a good sampling frame to select the standard anthropometric survey sample. You may want to consider updating the list but this can be expensive (compared to the survey). Updating would only be justified if the census is a key planning tool in the camp (even if this were the case I'd consider moving from census to surveys for planning). In this case, I think I would use some form of systematic HH sample. The exact sample design will depend on camp structures. I would tend to use a spatially stratified sample. The SMART manual provides guidance on sampling in camps. The cost of such a sample would probably be lower than a random sample even if the sample size were 50% or 100% larger. WRT has hase been written above. I would use a replacement in a typical cluster type HH sample. For example, if I select a house with no eligibles then I would select the nearest HHs with eligibles. I would not use replacement with a random sample. Instead I would plan to take a larger sample than calculated so as to account for non-response. It is not easy to say how much larger the sample should be. You can only make an informed guess. As an aside ... if all you will do is MUAC measurements and you have a CMAM / OTP service then you may want to consider a well organised mass-screening and referral exercise. I hope this is of some use.