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Probability vector from a Markov Transition Matrix

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Can somebody tell me how to calculate the probability matrix from a Markov Transition Matrix which values are known? I'm not familiar with this calulations in Matlab.
This is the Markov Transition Matrix:
Note: All transition rates of the matrix are known values except for the variable "θpm"
Which script lines should I enter into Matlab to find the values of the P vector for a given "θpm"? And how can I plot a graphic "AbUn" vs. "θpm"? knowing that AbUn=P4+P8 and "P4" and P8" are variables from the probability vector (P).
Thanks a lot in advance
William Rose
William Rose on 14 May 2021
In the PDF document which I posted last night, I specifically did not define , because I did not need it to derive the matrix A. is the derived the rate per unit time of going from state i to j. Therefore is the "rate of going from state i to i", i.e. rate of doing nothing. Is it possible to define or measure the rate of doing nothing? I don't know. But I don't need to define A, so I am OK with not knowing.

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Accepted Answer

William Rose
William Rose on 19 Apr 2021
Edited: William Rose on 19 Apr 2021
@Daniel Caballero, I used the code and ideas I posted in the earlier answer, with appropriate constants for your particular model, to try to reproduce Fig.2 of the paper you posted. It worked. Remember that Fig. 2 was Ab.Un. verus test interval, for a relay with no self test capability, i.e. ST=0. The red trace in the attached figure shows the result from the code, and it is an excellent or perfect match to Fig.2. of the paper.
I also calculated the results for a relay with 50% self test effectiveness and 100% self test effectiveness. Those results are also plotted. The results show that if a relay has 100% self test efficiency, then one should not inspect it at all, because inspecting it takes it out of service for about 2 hours, and does not cause more rapid fault detection.

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