I hope you will be patient with the inarticulate question of a non-mathematician. It's hard to get an answer when you don't even know how to ask the question.
Here the contest: Let's say that I have a kind of Tamagotchi that has the following needs (just to simplify):
Eating a quantity A1 of oranges TA1 times a day (e.g. 2 oranges 3 times a day).
Drink a quantity B1 of water TB1 times a day (e.g. 100 ml of water 10 times a day). While the Tamagotchi grows A1 and TA1 might change becoming A2 and TA2 (e.g. now on eat 4 strawberries once a week). The same might happen (or not) same for B1, TB1.
Who is taking care of it can be careful (sticking with the the diet plan to follow) or distract (forgetting to feed for days, giving less food or 300 times more the planned dose of water).
What I want to achieve is to find a way (an index maybe?) to measure how much the caretaker is compliant with the plan where 1 means totally compliant.
Question 1: a) How to express with a formula the compliance for a single need (A1, TA1) during a certain period of time? (i.e. 1 day, 1 week). b) How to express the same considering that for example in a month I had (A1, TA1) to follow for 1 week and (A2,TA2) as plan for the next 3 weeks.
I guess the compliance for (B1, TB1) can be derived in the same way as above, so the question is if I'd like to calculate the Total compliance (daily, weekly, monthly) how do I match them? It's the average of the two?
Here my failures: Average inside a period for (A1_taken/A1) works for 0 <= A1_taken <= A1 but I don't know how to approach for overdose (A1_taken higher than A1).
Question 1B average of averages doesn't sounds wrong to me. Summation of averages in different periods divided by the periods sounds wrong too and I'm not sure if it would work for higher taken values.
