There is perhaps no beguilement more insidious and dangerous than an elaborate and elegant mathematical process built upon unfortified premises." - Chamberlain 1899b:224Following the discovery of radioactivity by Becquerel (1896), the possibility of using this phenomenon as a means for determining the age of uranium-bearing minerals was demonstrated by Rutherford (1906).
One year later Boltwood (1907) developed the chemical U-Pb method. By combining Von Weizsacker’s argon abundance arguments with Kohlhorster’s observation that potassium emitted gamma-radiation, Bramley (1937) presented strong evidence that potassium underwent dual decay.
There are some circumstances that can affect this rate such as magnetic fluctuations etc...
In short, the assumption that decay rates are immune to outside influences isn't as solid as it once appeared to be.
However, if one does assume a constant decay rate, and if one starts with an originally pure sample of “parent element,” then the proportion of parent to daughter tells us the number of half-lives, which has been used to find the supposed age of igneous rocks. The conclusions of Renne and his team read as follows: Ar can be identified in volcanic sanidine, and while perhaps negligible in pre-Holocene rocks, it has important consequences for sample at the limit of the method’s applicability.
Chamberlain (1899) pointed out that Kelvin's calculations were only as good as the assumptions on which they were based.
"The fascinating impressiveness of rigorous mathematical analyses, with its atmosphere of precision and elegance, should not blind us to the defects of the premises that condition the whole process.