The Mathematics of Reliability (When does 99% Approach Zero?)

For a business product like Beam, it’s only useful if it’s reliable. When you start to build your day, your career, and your company around using a device, you need it to work all the time and every time. One dropped call during a big meeting and you’ll quickly start looking for alternatives.

We know this all too well from our experience with Texai, a prototype assembled from a number of existing, fairly reliable off-the-shelf components. But let’s do some math.

A remote presence device has many components that have to work together. For example: Wireless networking with multiple radios, on-board computer, multiple cameras, multiple microphones, multiple motors, wheelbase, stability design, speakers, wiring, video display, custom optic lenses, heat dissipation, videoconferencing software, session management software, logging system, driving software, UI customizations — the list goes on.

For many of those components on their own, a reliability level of, say, 90% might be perfectly fine. For example, how often do you fail to connect on the first try with Skype? Even if it’s 1 in 10 times, that’s probably ok. You can try again quickly.

But what about when you start combining components? In the best case, you’re probably multiplying the reliability numbers — but that assumes there are no adverse interactions. Even so, let’s assume the best case. Here’s a simplistic formula:

Total reliability = Component reliability ^ # of components

It’s simplistic because it assumes each component has the same reliability, which is obviously not true, but close enough for our purposes.

Plugging in some numbers, we see that:

Total reliability of 10 components = .9^10 = 34.9%

Total reliability of 100 components = .9^10 = 0.002%

Even if we increase component reliability to 99%, the total score for 100 components is only 36.6%.

Clearly, this analysis is very simplistic, but it resonates with our experience building Texai. This is why we made the difficult decision to redesign everything from the ground up, from our motor controller, to our computer, to our wireless software, to our audio system, to our custom videoconferencing software, to even our own custom camera lenses.

The result is a business-class product that you can rely on, all the time and every time.