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Math Help - Help to set up a Markov Chain/Transition Matrix Problem.

  1. #1
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    Acolman, Mexico
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    Help to set up a Markov Chain/Transition Matrix Problem.

    Hi,

    I need help to set up a transition matrix for the following problem

    "A video cassette recorder manufacturer is so certain of its quality control that its offering a complete replacement warranty if a recorder fails within 2 years. Based upon compiled data, the company has noted that only 1% of its recorders fail during the first year, whereas 5% of the recorders that survive the first year will fail during the second year. The warranty does not cover replacement orders
    a Formulate the evolution of the status as a Markov Chain whose states include two absorption states that involve needing to honor the warranty or having the recorder survive the warranty period. Then construct the (one-step) transition matrix"

    I am sorry this problem is so wordy, but I have no idea how to set the transition matrix. I'm guessing that there are 4 states, 0 being a new replacement recorder has to be absorbing and 3 being survived the recorder past the warranty has to be also absorbing.
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  2. #2
    Grand Panjandrum
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    Quote Originally Posted by akolman View Post
    Hi,

    I need help to set up a transition matrix for the following problem

    "A video cassette recorder manufacturer is so certain of its quality control that its offering a complete replacement warranty if a recorder fails within 2 years. Based upon compiled data, the company has noted that only 1% of its recorders fail during the first year, whereas 5% of the recorders that survive the first year will fail during the second year. The warranty does not cover replacement orders
    a Formulate the evolution of the status as a Markov Chain whose states include two absorption states that involve needing to honor the warranty or having the recorder survive the warranty period. Then construct the (one-step) transition matrix"

    I am sorry this problem is so wordy, but I have no idea how to set the transition matrix. I'm guessing that there are 4 states, 0 being a new replacement recorder has to be absorbing and 3 being survived the recorder past the warranty has to be also absorbing.
    Let the possible states of a recorder be:

    1: failed warrantee
    2: in first year of warrantee
    3: in second year of warrantee
    4: survived warrantee period.

    Then states 1 and 4 are absorbing.

    RonL
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