Instead of replacing estimation, I would say that you should embrace the problem in estimates - uncertainty.
Convey the uncertainty you have about a task to those you work with, and then you can start to factor in the risks of uncertain tasks.
I build project management software for a living at LiquidPlanner. Everything we do be it development, design, or marketing is based on ranged estimates. We don't always get the estimate right, but that's the beauty of a range, I it takes into account the fact that you will miss it some of the time.
The other thing that can replace an estimate is... lots of estimates. If you're planning something, update your estimates as you gain more knowledge about the problem.
I used to work for big oil, and they would have 100-200 million dollar projects. Not software projects, actually building plants. Similar to software development, these were basically prototypes. Yes a lot of the technology was known, but they weren't exactly building cookie-cutter houses.
So the first round of estimates would be something crazy like +/- 80%, both money and timeframe.
If that seemed good, then they'ed fork over the money to get more specifications and more details, and come up with a new estimate. Maybe +/- 50%. Then they'd re-evaluate the viability of the project. And do that a few more times, spending more money and time each iteration, before they actually committed to the project or dumped it. At that point, the estimates were quite accurate.
So basically, the software version. How long will that feature take?
An experienced developer can spitball an answer. About a week. Then they start working on it. After a day-and-a-half, they're going to have a better idea if that's actually a three day project or a two-weeker or if it ain't gonna happen.
Or maybe they need a day-or-two or a week to do a spike to be able to provide that estimate. All well and good if you let them do the spike. Not so good if you demand an estimate when the developer has clearly said he has no idea.
I absolutely agree that interval arithmetic is the best way to deal with this, accountants and their budget systems always require estimates to be reduced to fix figures.
Convey the uncertainty you have about a task to those you work with, and then you can start to factor in the risks of uncertain tasks.
I build project management software for a living at LiquidPlanner. Everything we do be it development, design, or marketing is based on ranged estimates. We don't always get the estimate right, but that's the beauty of a range, I it takes into account the fact that you will miss it some of the time.
The other thing that can replace an estimate is... lots of estimates. If you're planning something, update your estimates as you gain more knowledge about the problem.