Calculate its MTBF assuming 2000 FITS for each DRAM

COMPUTER ORGANIZATION AND ARCHITECTURE DESIGNING FOR PERFORMANCE NINTH EDITION

A common unit of measure for failure rates of electronic components is the Failure
un IT (FIT), expressed as a rate of failures per billion device hours. Another well
known but less used measure is mean time between failures (MTBF), which is the
average time of operation of a particular component until it fails. Consider a 1 MB
memory of a 16-bit microprocessor with 256K
*
1 DRAMs. Calculate its MTBF
assuming 2000 FITS for each DRAM.

Total memory is 1 megabyte = 8 megabits. It will take 32 DRAMs to construct the
memory (32
×
256 Kb = 8 Mb). The composite failure rate is 2000
×
32 = 64,000 FITS.
From this, we get a MTBF = 10
9
/64,000 = 15625 hours = 22 months. Source:
[PROT88].

https://en.wikipedia.org/wiki/Failure_rate

Failure rates can be expressed using any measure of time, but hours is the most common unit in practice. Other units, such as miles, revolutions, etc., can also be used in place of "time" units.

Failure rates are often expressed in engineering notation as failures per million, or 10⁻⁶, especially for individual components, since their failure rates are often very low.

The Failures In Time (FIT) rate of a device is the number of failures that can be expected in one billion (10⁹) device-hours of operation.^[11] (E.g. 1000 devices for 1 million hours, or 1 million devices for 1000 hours each, or some other combination.) This term is used particularly by the semiconductor industry.

The relationship of FIT to MTBF may be expressed as: MTBF = 1,000,000,000 x 1/FIT.