DO HARD DISKS AND SSD CONVERGE?

Everyone knows that prices per MB/GB/TB/EB of hard disks and SSD have fallen substantially over time. The data can be explained as exponential decay. With two curved however it gets slightly more advanced and a jump to honors math is needed. No problem!

SSD prices are falling at about 45% annually. Hard disks have also fallen considerable, floods notwithstanding.

In general y(t) = a × ekt for any exponential decay system. Plugging in the values of 100 for a and 365 for one year, its possible to calculate k to then estimated price on any day.

Now with two products to be considered the question becomes one of convergence. Does the SSD fall faster and eventually obsoletes the hard disk. To solve this problem needs to consider the derivative of the a × ekt for each of the commodities being analyzed. Using the chain rule gives us:

k × ekt

This is now possible to consider the slope of each curve. Immediately it will show if the curves intersect. The answer is not likely over [0, ∞) . The reason is simply the curve is always exponential/logarithmic for both items. Given k is a constant its clear no convergence can be done. QED.

Recently some article from Wikibon suggested SSD servers would become cheaper. The honors math major says no. Notice the price per GB for hard disks is artificially flattened while SSD prices are a bit aggressive at above 45% price deflators. The Seagate 18TB hard disk has also fallen 40% since it was added to my NewEgg watchlist.

Flash production capacities will simply remain too low for SSDs to outstrip HDDs. Flash fabs cost billion of dollars and take two years to build. But HDD output can be increased relatively easily “because less cleanroom production is needed than in semiconductor production. MAMR and HAMR costs are high but over time improvements will allow for larger capacity and lower costs per EB. Wikibon believes HDD vendors of HAMR and MAMR are unlikely to drive down the costs below those of the current PMR HDD technology.

Wikibon might want to hire me to check the projection because this is WRONG! False advertising also has serious legal consequences. Stick to facts and do the math.