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Math Help - Out of Control probability Questions

  1. #1
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    Out of Control probability Questions

    I need help finding these probabilities. I have no idea where to start. I have no idea which equations to use. If it helps i included the data i used at the bottom.

    The xbar = 31.30, the UCL = 54.66, and the LCL = 7.95

    Find the probability of each of these types of "out-of-control" signals, when the process is really under control:

    1 point > 3 SD from center line (either side)

    9 points in a row on same side of center line

    2 out of 3 points > 2 SD from center line (same side)

    4 out of 5 points > 1 SD from center (same side)

    15 points in a row within 1 SD of center (either side)

    8 points in a row > 1 SD from center line (either side)

    Tim Thomas Saves Per Game 2/11 - 5/14
    15
    36
    28
    29
    28
    28
    39
    45
    41
    22
    31
    24
    28
    32
    31
    25
    32
    32
    20
    26
    36
    38
    45
    27
    37
    34
    54
    38
    23
    33

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  2. #2
    Grand Panjandrum
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    Quote Originally Posted by ChrisYee08 View Post
    I need help finding these probabilities. I have no idea where to start. I have no idea which equations to use. If it helps i included the data i used at the bottom.

    The xbar = 31.30, the UCL = 54.66, and the LCL = 7.95

    Find the probability of each of these types of "out-of-control" signals, when the process is really under control:

    1 point > 3 SD from center line (either side)

    9 points in a row on same side of center line

    2 out of 3 points > 2 SD from center line (same side)

    4 out of 5 points > 1 SD from center (same side)

    15 points in a row within 1 SD of center (either side)

    8 points in a row > 1 SD from center line (either side)

    Tim Thomas Saves Per Game 2/11 - 5/14
    15
    36
    28
    29
    28
    28
    39
    45
    41
    22
    31
    24
    28
    32
    31
    25
    32
    32
    20
    26
    36
    38
    45
    27
    37
    34
    54
    38
    23
    33

    In order to answer this we need a whole bunch of assumptions that are not in general valid. The most significant of these is that if the process is under control the values are uncorrelated and Gaussian (under control of course implies constant mean and variance).

    So your first task is to show that your data are not inconsistent with the hypothesis of being uncorrelated (Gaussian) white noise.

    CB
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