P+Q or dual parity in detail

[Frank1940]

 

Further, the issue isn't another complete disk failure -- it's a simple uncorrectable bit error in another disk during the rebuild.  And the probability of an uncorrectable bit error is FAR higher than that of a complete failure of the disk.

 

Be careful when talking about a 'single bit' error.  There are multiple single bit errors everyday on a hard drive.  These are called 'raw read errors'.  The manufacturers realize this and provide error correcting algorithms to correct them and then (as I recall) even longer error correcting algorithms to handle those errors that the primary correcting can't handle.  When you get a true read error, you probably have a massive block of bits that can't be read.  (See this article for a basic introduction to this whole issue:    https://www.quora.com/What-causes-hard-drives-to-have-high-raw-read-error-rate  ) 

 

Remember that (a) real life can often "bite" you r.e. probabilities.    We bought our current home in 1998.  Three weeks later there was a major "100 year" flood.  (Fortunately we had minimal damage -- all exterior)    Three years later, in 2001, we had another ever worse "100 year" flood.    So much for the probabilities !

 

Statistics and Probability predict the outcome of a large number of events.  They predict nothing about single events. In your case of having two hundred year floods in three year period means that these two events have to be added into the database of flood height data to construct a new 100 year graph!  (In fact, the current data of all the floods at that location may not even cover a hundred years!  Statistics is a complex environment that is as difficult to understand as Modern Physics is.) 

[garycase]

I'm not talking about corrected bit errors -- there are hundreds/thousands of those in normal operation.  But there are a predictable number of uncorrected bit errors ... in consumer drives they tend to have about 1 in 10^14 of those.  Sounds like a very large number until you realize just how many bits there are in multi-TB drives      [Enterprise class drives are an order of magnitude better]

 

... and yes, I'm reasonably familiar with the statistical details (did a PhD in math)