My numbersense class for Principal Analytics Prep has passed the midway point, and we covered probabilistic thinking. Yesterday, the idea came to me that the surge protector is a good example to use in teaching probability. I just need to find some statistics - which turns out to be hard to come by... so if you know some sources, please let me know!
Appliances in the U.S. are rated 110 (or is it 120) volts. Anyone who have lived elsewhere (say, Europe or parts of Asia) may know that in some countries, appliances use 240 volts. If we take an American appliance to Europe, the 240 volts of electricity will immediately kill the device. The 110V or 240V standard is an average value, and we should expect fluctuations around those values (which are peaks of a sine curve). There is a natural variability in the voltage.
Then there are surges. Statistically, we can define surges as rare events - maybe voltage that is at least three standard deviations above the normal value. (There may be an official definition but I wasn't able to find it on a quick Google search.) Surges are apparently caused by lightning or switching. (Here is a somewhat useful NIST document, which may have been partly or wholly written by suppliers of surge protection equipment.)
I would like to find some data on the statistical distribution of voltage delivered. Then, students can figure out if the data resemble a normal distribution or some other probability model. We can estimate the frequency of surges. This can lead to a quantitative assessment of expected loss due to power surges.
Further, we must account for an asymmetrical cost structure. Having too low a voltage is also a problem. However, it is a much lesser problem compared to having a too high a voltage. There also does not appear to be such a thing as a "negative power surge".
The above lays the groundwork for making a decision about whether one should buy a surge protector. There are different types of surge protectors providing different levels of protection at different prices. How can we decide whether to invest in the next better surge protector?
The NIST document referenced above makes this non-quantified assertion: "A large stack of dollar bills and some change to replace your unprotected computer, if and when a lightning or some other surge destroyed it ..... or use a small number of bills to purchase a 'surge protector' for peace of mind and effective protection." How can we quantify such a statement?