Destruction and productive systems: the incompatibility of the two types of models of the processes of birth and death

In the paper the models of the processes of destruction two types are considered. It is assumed that the destruction associated with the theories of programmed aging and death has the finite support of the function of the distribution of times of death. Destruction with the distribution function with infinite support corresponds to the well-known Gompertz distribution, its analogues and generalizations. A theorem on the incompatibility of models for the processes of performing operations in a random environment in the case of nondegenerate smooth density is formulated and proved. Applications for analyzing productive systems are considered.