Now that the Galaxy Note 7 has been officially discontinued, I’m not sure it’s worth worrying about the failure rate of this device. But there’s something that really bothered me about the coverage of the device’s various recalls and eventual discontinuation (is that a word?), which was that almost nobody seemed to be running the numbers on the actual failure rates.
If you do the arithmetic on the device failure rates, you end up looking at the situation rather differently. This is not to say that the device being discontinued was the wrong decision — all it takes is one person being horribly burned to create a panic and do serious damage to the company, not to mention that person!
Rather, I think it’s interesting to do the arithmetic as a way of exploring how humans think about risk. It may not surprise you to hear that I think we are really bad at this. And oftentimes it’s because we don’t run the numbers.
With that said, let’s look at some numbers.
According to this article on the Galaxy Note 7 recall, there were about 2.5 million devices sold in the initial batch, and, at least in early September, there had been 35 handsets discovered with the issue. A later report said that over 70 devices had overheated.
The best final count I could find is the one from the Consumer Product Safety Commission. According to the CPSC, there have been 92 reports of the batteries overheating.
How much danger was I really in? (I just returned my Galaxy Note 7 yesterday, which I LOVED, which is part of why I’m writing this.)
- 2.5 million phones
- 92 incidents of overheating
Turning to my trusty calculator, that looks like a 1 in 26,000 chance of the device overheating:
CL-USER> (/ 2.4e6 92) 26086.957
Expressed as a percentage, there is approximately a 0.004% chance that your device would have been one of the ones to overheat:
CL-USER> (format t "~6$" (* (/ 92 2.4e6) 100)) 0.003833
However, let’s make a more conservative assumption that 1000 devices (over 10x as many) would eventually overheat. That’s still 0.04%, far less than one tenth of one percent. Of course, that number “less than one tenth of one percent” was quoted by Samsung themselves during the initial recall:
CL-USER> (format t "~6$" (* (/ 1000 2.4e6) 100)) 0.041667
Eventually, the bad PR due to overheating devices grew to be too much, and Samsung discontinued the model.
One lesson of this incident seems to be that you can make a product that is nearly perfect, with a 0.0038% failure rate, but if the failure mode is bad enough (it probably is), and if the media exposure is widespread enough to create a public outcry (it definitely was), you’re fucked. With lines like this one appearing in the Verge, it’s not hard to understand why Samsung realized they had to just kill it:
It’s easy to imagine how terrifying it would be to have a phone begin smoking like this on a plane or on your bedside table. No thanks.
The mobile device hardware industry is brutal. You can’t have a failure that occurs even in 0.0038% of devices. And even if you maintain that near-perfect safety record you still have to compete on price, features, and time-to-market. I really don’t envy those folks.
What I find most interesting, as I mentioned above, is what this reflects about how humans assess risk. For example, in 2012, 92 people died in car accidents every day, and nobody has ever considered doing a recall of all automobiles sold in the United States for being fundamentally unsafe!
According to the chart linked above, in 2012 there were 10.691 auto accident deaths per 100,000 people, which means that you had a 0.001% chance of literally dying in a horrible car crash:
CL-USER> (format t "~6$" (* (/ 10.691 10e5) 100)) 0.001069
Compare this to the 0.004% chance of your phone overheating that we calculated above (based on the 92 incidents figure). Given the rather imprecise way we’ve been slinging these numbers around, let’s just assume there’s a lot of error there, and that the figures are roughly equal.
That’s how we arrive at our conclusion:
You have as much chance of your Samsung Galaxy Note 7 overheating as you did of dying in a car crash in 2012.
(Note: this article and its headline do not constitute a claim that the Note 7 is “safe”, or that you should not return it as recommended, etc. This article is not advice on how to live your life, it’s just an exploration of how humans think about risk.)