Uncertainty in # of Units and Effect on Final Values and Determinations

The number of units required has uncertainty from the uncertainty in the cooling capacity.

We rounded up the number of units to get the value we used for our cost calculations (since obviously there should be an integer amount of units, and we figured there needs to be at least 10kW cooling capacity).

This makes it difficult when it comes to the exact number of units, uncertainty in the costs, etc....

For example, for a number of units = 13.92 +- .12 ... most of the range will require 14 units for 10kW cooling capacity, but some of it would require 15 units. (if rounding the the nearest integer, an example would be number of units = 13.50 +- .13 ... could be either 13 or 14 units)

However, it HAS to be one number of units or the other if we're making recommendations on the number of units to use. And whether or not we specify the number of units, it causes a cost problem: it doesn't cause an uncertainty in the costs, but rather causes 2 possible values (with their own uncertainties), depending on which number of units it is. Which also means we can't make a determination based on the cost unless it is one or the other, or if we combine them somehow.


So I guess my questions are:

-How should we round the number of units? Always up (to ensure at least 10kW cooling capacity) or to the nearest integer (closest to 10kW cooling capacity)?
-Which value should we use when there is uncertainty that would change this rounded value? Should we just always use the rounded value and not worry about it changing with uncertainty?
-(Combining the different values of units and associated costs into 1 value and 1 uncertainty each seems like a bad way of solving this, but if that's what we need to do, in which way should we combine them?)

When you report your cost savings it should be one number with an uncertainty. Part of that uncertainty in savings is based on the number of units that you need to meet the cooling capacity the client requires. Your situation is quite tractable; you will have an upper and lower bound on your cost savings based on whether you are upgrading 14 or 15 units to run (based on your average #units needed and your experimental uncertainty), and of course you could provide an average cost savings simply by averaging the upper and lower limits. In doing it this way you are giving an average savings, as well as providing a best and worst case which is completely reasonable. You will always be rounding up to the nearest whole number of units required, as you can't have fractional units upgraded and you MUST meet the 10kW cooling capacity. In your case:

13.92+-0.12 AC units = 13.8 to 14.04 AC units = either 14 or 15 AC units to upgrade