I think the idea of "everything is about half its life" is to account for survivorship bias in longevity. The only units that make it to the 95th percentile lifetimes clearly got luckier with parts and can reasonably be expected to last longer.
Reliability of most complicated devices (cars, electronics) is usually thought to follow a “bathtub curve.” Some early mortality due to defective parts or manufacturing defects, a long trough of reliability from say, 1-10 years, then a rapid rise in failures due to aging. “Everything at half life” is a pretty bad approximation of this.
Not just electronics, go read the print quality of some of your paper receipts from three years ago and see if you can make heads or tails or where you purchased the item. Ever see photos from photo albums long ago?
Right, correcting for survivorship bias is very important. If an object lasts one year, its expected life isn't now $average_use_life - 1; that's too low an estimate.
The problem with the "half life" rule is that it corrects for this in the dumbest possible way, not only providing an inaccurate estimate for most of the object's life, but even getting the first derivative wrong for most objects. Usually, lasting longer does not make the expected remaining years of service go up, but the rule implies it does!
Take people for example. At birth, a woman in the United States has a life expectancy of 81. If she makes it to 60, she can now expect to make it to ... 85. Not a big change! Every year she lived (even her first), her remaining life expectancy went down, not up. See this chart I made comparing the life expectancy of people versus a theoretical "half-lifer": https://0x0.st/otZ_.png
sgerenser|3 years ago
titoCA321|3 years ago
bscphil|3 years ago
The problem with the "half life" rule is that it corrects for this in the dumbest possible way, not only providing an inaccurate estimate for most of the object's life, but even getting the first derivative wrong for most objects. Usually, lasting longer does not make the expected remaining years of service go up, but the rule implies it does!
Take people for example. At birth, a woman in the United States has a life expectancy of 81. If she makes it to 60, she can now expect to make it to ... 85. Not a big change! Every year she lived (even her first), her remaining life expectancy went down, not up. See this chart I made comparing the life expectancy of people versus a theoretical "half-lifer": https://0x0.st/otZ_.png