A general probabilistic solution of randomized radioactive decay chain (RDC) model using RVT technique

This article develops a complete solution of the randomized nuclear radioactive decay chain model based on Bateman master equations. A multidimensional version of the random variable transformation technique is adapted to derive a full probabilistic description for this model. To present general and more realistic physical situation, the initial number of the parent radionuclides and the decay parameters are considered to be random variables. The first probability density functions for the solution processes and the time until a given number of parent radionuclides remains in its state before decaying are constructed and used to calculate the mean, the variance and the confidence intervals. To test the efficiency of the theoretical findings, some numerical results are graphically presented and found to be consistent with the observations.