Tony,
It is a semicunductor industry-wide standard to life-test all new products for an equivalent 10-year operation at 25C and there are many industry standards like this that are not specifically mentioned in TI's or our competitors' datasheets.
I am not sure where you get that a significant number of units will fail PDS limits after 10-years. Since most TI's datasheet max/min specifications are based on 4-sigma Normal Guassian distrubution, only 1 out of 15,000 units may be initially close to the max/min limit - see below output voltage initial accuracy distribution for REF50xx (thus 1-sigma = 0.05%/4 = ~0.0125%).
If you consider 2-sigma distribution (+/-0.025%), statistically only 1 out of 22 units may be outside such limit and only such units after 10-years may at most shift by another 2-sigma (+/-0.025%) and thus get beyond the PDS limit of +/-0.05%. If the initial accuracy and long-term shift were correlated with each other, the probability of this happening would be: P = 1/22*1/22 and therefore 1 out of 484 units could be outside PDS limit after 10 years.
However, since there is no correlation between the initial accuracy and the subsequent long-term shift (meaning worst initial accuracy units typically will NOT shift the most), one must use a vector addition (sum of squares) to calculate the overall long-term shift: since (0.05%)/sq-rt(2) = 0.0355%, therefore, only the units outside of approximately +/-3-sigma initial accuracy distribution (0.0355/0.0125) AFTER 10 years may shift beyond 0.05% [sq-rt(0.0355^2+0.0355^2)] PDS limit. Thus probability of finding REF50xx units outside of PDS limit 0.05% after 10 years of constant operation is: P = 1/370*1/370 = 0.0000073 or 0.00073% or ~ 1 out of 136,900 units - see below Gaussian Distribution table for details.
