4.2.3 Suppose that a production process changes state according to a Markov process whose transition probability matrix is given by

(a) Determine the limiting distribution for the process.

(b) Suppose that states 0 and 1 are “In-Control,” while states 2 and 3 are deemed “Out-of-Control.” In the long run, what fraction of time is the process Outof-
Control?

(c) In the long run, what fraction of transitions are from an In-Control state to an Out-of-Control state?

P= 0 1 2 0 0.2 0.2 0.4 3 0.2| 1 0.5 0.2 0.2 0.1 2 0.2 0.3 0.4 0.1 3 0.1 0.2 0.4 0.3