A Sokhotski–Plemelj problem related to a renewable T-cell

We analyse the long-run availability of a technical device subjected to inspections and repair. All statistical distributions involved are general. In order to describe the random behaviour of the system, we employ a stochastic process endowed with stationary measures satisfying coupled Hokstad-type differential equations. The solution procedure is based on the theory of sectionally holomorphic functions. As an example, we consider the particular case of Coxian inspections.