Suggested method for estimating door counter stats when data is lost I'm wondering if you have any advice about a methodology to use to estimate "door counter" stats (i.e., an automated count of visitors to our organisation, based on "break beam" door counters installed at each branch) when there are outages and data is lost.
For example, let's say we had 1055 visitors last  Friday and this Friday the door counter didn't work so we need to make an estimate of numbers. I assume getting an average of the past x number of Fridays is one approach, but I'm just wondering what the most rigorous and transparent approach to estimating would be?
 A: Typically a good approach will rely on some kind of model for the process, and should be accompanied by some assessment of the degree to which the model might be 'close enough' for your purposes. 
Looking at the previous Friday implies some aspects of a model; specifically it suggests that you think: 1) last Friday is more like this Friday than other days of the week; and 2) recency matters: the most recent Friday is more like this Friday that Fridays from long ago. You have a time series of counts, which suggests modelling the conditional distribution of counts in some way, taking into account the dependence over time. 
Here are some points to consider:
Are there other sources of information that might act as predictors - promotions, for example? 
Do you expect time of year (season, for example), or calendar effects like holidays to matter? 
Time series models tend to rely on having a good amount of information -- do you have data going back a fair number of days?
Do you also have data after the missing day (next Friday might be at least as informative as last Friday)? 
Are visitor numbers tending to grow (or shrink) over time, even slowly?
It might help to look at a good book on time series models, and also something on models for counts (such as GLMs) before trying to tackle count-data time series models. If you have lost only the most recent day (or days), you basically have a forecasting problem, in which case a book like this is probably a good place to start learning (it doesn't really deal with count data issues); if the missing day is in the past, you have something much close to a smoothing problem in time-series terms.
You may also find the literature on missing value imputation useful, though a lot of it tends to focus more or the regression side.
There are many posts here on time series models for count data, Poisson time series (the Poisson being a fairly common distributional model for counts) and a number of other relevant searches. Also see a search on missing-data count time-series
If your typical counts are large, you might even be reasonably well served by standard time series and forecasting/smoothing methods applied to the square roots of counts, or in some occasional situations, a log-count might work better. For example, here's a (famous) data set (monthly airline passengers [1]) where a suitable model for the log of counts works quite well at predicting a missing value:

[1]  Box, G. E. P., Jenkins, G. M. and Reinsel, G. C. (1976)
Time Series Analysis, Forecasting and Control, Third Edition.
   Holden-Day. Series G.
