Data Science is Festive: Christmas Light Reliability by Colour

This past weekend was a balmy 5 degrees Celsius which was lucky for me as I had to once again climb onto the roof of my house to deal with my Christmas lights. The middle two strings had failed bulbs somewhere along their length and I had a decent expectation that it was the Blue ones. Again.

Two years ago was our first autumn at our new house. The house needed Christmas lights so we bought four strings of them. Over the course of their December tour they suffered devastating bulb failures rendering alternating strings inoperable. (The bulbs are wired in a single parallel strand making a single bulb failure take down the whole string. However, connectivity is maintained so power flows through the circuit.)

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Last year I tested the four strings and found them all faulty. We bought two replacement strings and I scavenged all the working bulbs from one of the strings to make three working strings out of the old four. All five (four in use, one in reserve) survived the season in working order.

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This year in performing my sanity check before climbing the ladder I had to replace lamps in all three of the original strings to get them back to operating condition. Again.

And then I had an idea. A nerdy idea.

I had myself a wonderful nerdy idea!

“I know just what to do!” I laughed like an old miser.

I’ll gather some data and then visualize’er!

The strings are penta-colour: Red, Orange, Yellow, Green, and Blue. Each string has about an equal number of each colour of bulb and an extra Red and Yellow replacement bulb. Each bulb is made up of an internal LED lamp and an external plastic globe.

The LED lamps are the things that fail either from corrosion on the contacts or from something internal to the diode.

So I started with 6N+12 lamps and 6N+12 globes in total: N of each colour with an extra 1 Red and 1 Yellow per string. Whenever a lamp died I kept its globe. So the losses over time should manifest themselves as a surplus of globes and a defecit of lamps.

If the losses were equal amongst the colours we’d see a equal surplus of Green, Orange, and Blue globes and a slightly lower surplus of Red and Yellow globes (because of the extras). This is not what I saw when I lined them all up, though:

An image of christmas lightbulb globes and LED lamps in a histogram fashion. The blue globes are the most populous followed by yellow, green, then red. Yellow LED lamps are the most populous followed by red and green.

Instead we find ourselves with no oranges (I fitted all the extra oranges into empty blue spots when consolidating), an equal number of lamps and globes of yellow (yellow being one of the colours adjacent to most broken bulbs and, thus, less likely to be chosen for replacement), a mild surplus of red (one red lamp had evidently failed at one point), a larger surplus of green globes (four failed green lamps isn’t great but isn’t bad)…

And 14 excess blue globes.

Now, my sampling frequency isn’t all that high. And my knowledge of confidence intervals is a little rusty. But that’s what I think I can safely call a statistical outlier. I’m pretty sure we can conclude that, on my original set of strings of Christmas lights, Blue LEDs are more likely to fail than any other colour. But why?

I know from my LED history that high-luminance blue LEDs took the longest to be invented (patents filed in 1993 over 30 years after the first red LED). I learned from my friend who works at a display company that blue LEDs are more expensive. If I take those together I can suppose that perhaps the manufacturers of my light strings cheaped out on their lot of blue LEDs one year and stuck me, the consumer, with substandard lamps.

Instead of bringing joy, it brought frustration. But also predictive power because, you know what? On those two broken strings I had to climb up to retrieve this past, unseasonably-warm Saturday two of the four failed bulbs were indeed, as I said at the top, the Blue ones. Again.

 

:chutten