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Math Help - Markov chain transition matrix

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    Markov chain transition matrix

    In a certain production process, items are pass through two manufacturing stages. At the end of each stage, the items are either scrapped with a probability of 0.15, sent through the stage again for rework with a probability of 0.25, or passed on the the next step with a probability of 0.6. Describe this as a Markov chain and set up the transition matrix? What is the expected number of steps to absorption?
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    Moo
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    Hello,

    Introduce a third state : the one where the product goes if it's scrapped. And if it's there, it cannot leave : \mathbb{P}(\textcircled{3}\to \textcircled{3})=1

    And from your text, you have :
    \mathbb{P}(\textcircled{1}\to \textcircled{1})=0.25
    \mathbb{P}(\textcircled{1}\to \textcircled{2})=0.6
    \mathbb{P}(\textcircled{1}\to \textcircled{3})=0.15

    But I don't understand what happens for the second stage... ?

    This gives the following transition matrix :

    \begin{pmatrix} 0.25 & 0.6 & 0.15 \\ ?&?&? \\ 0&0&1 \end{pmatrix}
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    Quote Originally Posted by Moo View Post
    But I don't understand what happens for the second stage... ?
    Probably there should be introduced a fourth state \textcircled{4} for the finished items: after \textcircled{2} , the item either is scrapped (goes to \textcircled{3}), is reworked (stays at \textcircled{2}) or leaves the line (goes to \textcircled{4}).
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    Quote Originally Posted by veronica.white View Post
    In a certain production process, items are pass through two manufacturing stages. At the end of each stage, the items are either scrapped with a probability of 0.15, sent through the stage again for rework with a probability of 0.25, or passed on the the next step with a probability of 0.6. Describe this as a Markov chain and set up the transition matrix? What is the expected number of steps to absorption?
    Also asked here: http://www.mathhelpforum.com/math-he...on-matrix.html

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