Yes, by using another function (SUMPRODUCT). Extending my previous example, say column B then had the different sites:
The way to read this formula is:
the A1:A100 bit is converted to an array (or list) 100 elements long of 0 and 1 values depending on whether the cells contain the value 5 (you can replace this 5 with another fault value or with a cell reference like E2 say to suit), 0 if it doesn't, 1 if it does. The B1:B100 bit does exactly the same thing based on the cells containing "BH" (adjusted to suit). The respective elements of these two arrays (1s and 0s) are then multiplied with the corresponding element in D1:D100 and summed together. The double minus -- is required before the first two arrays, as the 100 elements are actually returned as TRUE/FALSE values, and the -- coerces Excel to convert these to 1s and 0s.
Hope this helped!