When do you change your oil?

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It has always amazed me why people drain perfectly good oil from their engine, just to replace with perfectly good oil. It should be quite easy for people to rationalize that a set mileage for oil changes is and always will be ludicrous. Just think about the different conditions the engine was run under that same number of miles.
Was the engine started up in sub-freezing weather everyday, versus being started up at 70 degrees F? Was the engine run for five minutes or six hours? Was it a constant speed or a stop and go condition?
I have had people tell me that they religiously change their oil every three thousand miles, all year long. Well, up here in the cold north, if the oil was wasted at three thousand miles of summer driving, it was destroyed at 2000 miles of winter driving, so why not change it at 2000 miles.
In other words, what I am trying to say is that miles mean nothing to the engine oil; it is the time the engine is running and the conditions that the engine is run at during this time span. The reason we use miles is the simple fact we have odometers; not engine hour meters on our vehicles.
Sensors monitor different engine conditions and temperatures as well as mileage while the engine is running and upon immediate startup. It is a well know fact, that short trips in the winter will destroy oil faster than long trips in the summer. So, the computer looks at the engine temp upon startup, along with the ambient temperatures, it clocks how long the engine runs to get up to operating temp, then how long it is at operating temp. These are the main factors in determining the oil life.
The algorithm talked about in the article posted by NewHummerGuy, looks at the sensors? readings from the PCM, and compares all this to its built-in charts. It does assume that you are using oil that is specified by General Motors (or better oil such as a synthetic in the case of the H3). If you use oil that does not meet the spec required, the output from the algorithms will be incorrect also, and your oil life monitor will not turn on the light when required.
In other words, oil that does not meet the spec, could breakdown earlier, but the computer does not know this, so it will keep the light on after the non-spec oil has degraded. Thus, your engine could be damaged. In turn, if the oil is better than spec (dyno versus synthetic), the oil life indicator system will turn on before the engine oil has degraded to a point where it requires changing. Thus, no harm to the engine.
If people are worried about their oil, and were wondering if the oil still had some life after the change, they can always send a sample off to an independent testing lab and get the results back in a week or two. I have done this many times, even when going on the oil life monitor to the big zero, the oil still had a TBN (total base number) above minimum, and the adaptives were still present.
I will add that if people are using an aftermarket foam type air filter, than it might be best to change earlier. How early, I cannot say. Foam type filters allow more dirt into the engine than the paper filters recommended, and the oil life system assumes the intake system is sealed correctly and has a paper filter.