This is the first in a series of posts about a calculation that worried me for years – about fifteen years. The question occurred to me when my car, a newish company car, broke. It stopped going along. Eventually it started again and I took it to the garage. They changed some parts, presented a big bill, and I drove away. Next week, the car stopped again. After a few minutes, it started. I took it back to the garage, they changed some more parts, and I paid another big bill. Next week… you get the idea. It was driving away from the garage for the third time that I wondered, “How do I work out whether the car is really repaired?” How much testing do I have to do before I trust the car again?

It took me 15 years to work out the answer. I tried collaborating with four different people, and couldn’t solve it. Then, one day, Eureka.

This all happened when I was working for Sun Microsystems, so if there is any intellectual property in the idea, it belongs to them, or now to Oracle. I don’t think a patent was ever applied for – it was in a chaotic time close to when I left Sun, and it’s not in this list. But, it’s old enough now that I don’t think anyone will mind if I publish it. I’ve never seen the result anywhere else, although I’m a bit out of touch with the field now.

The eventual result is applicable to things that break, and also new products with design flaws. It seems quite general.

Future posts here will explain the idea and (if I get my act together) present an online calculator for working out the chance that a problem has been fixed by a repair, given a pattern of test failures and passes both before and after the repair. But I haven’t written that yet.