> You're implicitly assuming a normal distribution I'm not really making that assumption. Instead, I'm pointing out that learning this particular bulb survived

> You're implicitly assuming a normal distribution I'm not really making that assumption. Instead, I'm pointing out that learning this particular bulb survived due to "unusually think or smooth filament compared with other bulbs" is indeed something interesting you can learn by inspecting the survivor, and that might be something you can apply for process quality improvement. Basically, I'm advocating the point of view that if you are trying to improve lightbulb, or say, ball bearing quality (rather than just model it), then it's useful to look beyond the fact that the Weibull distribution is long-tailed. A wide distribution is a reflection of ignorance and thus a learning opportunity; the long tails are still caused by something. Yes, from a given batch of ball bearings, some might last 10x or 100x longer than others under the same loading conditions. But if you put those super-long-lasting bearings under a microscope, you might observe real, important differences compared with others from the same batch. The balls might all be rounder or more identically-sized compared with their cousins. (You can do the inspection before the lifetime test if you want to be extra fair). But it's even more important when you don't expect a long-tailed distribution to begin with; for example, if you have a linear damage model. In this case, if you control for filament diameter, resistance, or brightness, and still see that one bulb is a mysterious outlier, you might want to inspect the joints or run the gas in the bulb through an analyzer to see if there are any other surprises.