Exactly right.
1 million hour MTBF means "If you have 5,000 drives in your datacenter, you should expect to RMA 44 drives each year".
It absolutely does not mean that a drive is expected to last for 114 years.
No, this is NOT the definition of MTBF...
But it is what drive manufacturers MEAN when they say MTBF, so they are bastardizing a term. But it just so happens that it is functionally identical. You see, both the math you suggested (which is NOT what they claim or how they test) and the math I suggested work perfectly and give the exact same result for the same figures.
You see, you proved yourself wrong, you calculated a failure rate of 44 / 5000 every year based on an MTBF of 1 million and said "this does not mean they would last 114 years" when such a failure rate absolutely DOES mean they last 114 years on average.
If you have 5000 drives and only 44 fail a year they then your failure rate is 0.88% failed/year.
But in this amazing place called reality failure rates are an order of magnitude higher. If you have a 5000 drive datacenter you can expect close to 500 of them to fail every year (~10%).
This gives you an MTBF closer to 11 years using both my formula AND your formula. Both formula are correct and give identical results if you input identical numbers. The thing is, I am actually inputting numbers and calculating things out while you are just taking the figures from the manufacturers and declare them facts.
Look here:
http://www.pcworld.com/article/1295...e_rates_much_higher_than_makers_estimate.html
The Carnegie Mellon study examined large production systems, including high-performance computing sites and Internet services sites running SCSI, FC and SATA drives. The data sheets for those drives listed MTBF between 1 million to 1.5 million hours, which the study said should mean annual failure rates "of at most 0.88%." However, the study showed typical annual replacement rates of between 2% and 4%, "and up to 13% observed on some systems."
I have no idea whether they used my formula, your formula, or some other formula entirely. But they got the exact same 0.88% yearly failure rate = 1 million hour MTBF. This is because in the amazing world of math you can solve the same problem many different ways and all of them are correct
I would like to point out that I only looked it up after calculating and writing out the rest.