It is common practice to have standby redundant units in mechanical and electrical systems so as to attain a high degree of reliability. Suppose two machines are available, one in use and one on a standby basis. The probability that a machine that is in use fails during a unit period is p(q=1-q). It takes three units of time to repair a failed machine. Define a process with the states identified by different combinations of two elements, number of machines in working condition; expended repair time. Thus, the states are 20, 10, 11, 12, 01, and 02. Show that this process is a Markov chain, and determine its transition probability matrix.
I am having difficulty in deciding how to define the states 0,1,2 because of the two elements requirements. Please help me! Thank you! :)