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

There must be a math explanation, could you please help me?

Thank you

Wally