1. Consider two machines, operating simultaneously and independently, where both machines have an exponentially distributed time to failure with mean 20 hours. There is a single repair facility, and the repair times are exponentially distributed with rate 0.5 per hour.

State variable definition:

State space:

Transition rate matrix:

2. We now assume that at most one machine can operate at any time. Namely, while one machine is working, the other one may be either under repair or already fixed and waiting to take over.

Revised state space:

Revised state definitions:

Revised transition rate matrix: