# Weighted average of a production line OEE

#### wallyak

##### New member
Hi all,

I hope this is the right category, since I'm not sure where to post this topic.

I have been trying to understand what's wrong with a formula I'm using for a while and I've ended in this website to get some help.

The general OEE formula (Overall Equipment Effectiveness) is
OEE = Quality * Performance * Availability.
Don't need to specify the logic behind that, just think it like a simple multiplication of 3 percentages.
here's an example
When Quality = 99% Performance = 90% Availability = 80%, the OEE value would be 71.28%

What I'm trying to do is a weighed average of several OEE values.
The formula would be something like this.
weightedOEE = (OEE1 * weight1) + (OEE2 * weight2) / (weight1 + weight2)

Now when I calculate the weighted Quality , weighted Performance and weighted Availability according the same formula and multiply the 3 values I get a slightly different number (assume that I use Excel for this).

 Weight Quality Performance Availability OEE 100​ 99.50​ 90.50​ 60.00​ 54.03​ 200​ 98.50​ 88.00​ 75.00​ 65.01​ 700​ 99.90​ 95.00​ 80.00​ 75.92​ SUM = 1000​ weighted =99.58​ weighted = 93.15​ weighted 77.00​ weighted = 71.55​ 71.42​ multiplication of 3 weighted averages

I thought it was related to some kind of approximation, but I'm not totally sure about that, since it's a fair difference