A working intensity is one of the important operation process characteristics. Mostly, the working intensity is randomly changeable and it may be modeled to be a finite state space semi-Markov process. Particularly, the working intensity is modeled by a semi-Markov random walk. For this process, lots of interesting characteristics are obtained. A semi-Mafrkov model of a ship engine load allowed us to construct a random research test of the toxicity of exhaust gases.