Given the following state diagram of a pump system. This pump system can be in g

Question

Given the following state diagram of a pump system. This pump system can be in good working order and deliver full output (state '0'). Under certain conditions the pump may only be able to deliver partial output (state '1), and when failed it delivers no output (state '2'). The state transition diagram for this pump system is given below.All numbers in this diagram are either failure or repair rates in failures/repairs per hour. 0.01 0.5 0.5 0.01 2 0.01 Answer the following questions: a. Set up the set of differential equations that describe this system. b. Given an update time of At 0.1 hr, draw the discrete Markov chain. c. Provide the state transition matrix for the discrete Markov chain found under (b).

Explanation / Answer

states are 0 , 1 and 2

just concentrate on outgoing probability not incoming

from 0 to 1 = 0.01

0 to 2 = 0.01

hence 0 to 0 will be 1 - 0.01-0.01 = 0.98

similarly 1 to 1 will be 0.49

2 to 2 will 0.5

hence

transition matrix will be

P =

    0.9800    0.0100    0.0100
    0.5000    0.4900    0.0100
    0.5000         0 0.5000

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