I have 95% confidence intervals for a figure that represents the higher-than expected number of failures for a particular machine where the expected number comes from using data for months 0 - 13 to predict the number of failures for months 14, 15 and 16. The observed number of failures is for months 14, 15 and 16.
At the moment, I have the difference between expected and observed for months 14, 15 and 16 individually.
However, I would like to aggregate months 14, 15 and 16 together to assess whether the number of failures was higher-than-expected for the entire 14-16 month period rather than each month individually.
Can I just add the confidence intervals for months 14, 15 and 16 to eachother for this?
NOTE: I have read a previous and related question but I don't think it quite covers mine.