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    Six sigma

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    For Statistics for Quality Control

    © BrainMass Inc. brainmass.com June 3, 2020, 5:05 pm ad1c9bdddf
    https://brainmass.com/statistics/conditional-probability-distribution/six-sigma-13304

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    We can describe such design using a tree diagram.
    <br>Here, we define all events that can happen and assign a probability of an individual event for each branch.
    <br>For example, in the first layer (or sample1), there are two probable events:
    <br>- an out-of-control condition is detected, probability=1 - &#946;
    <br>- an out-of-control condition is not detected, probability=&#946;
    <br>Notice that ...

    Solution Summary

    1. A quality characteristic is monitored by a control chart designed so the probability that a certain out-of-control condition will be detected on the first sample following the shift to that state is 1 - &#946;. Find the following:

    a) The probability that the out-of-control condition will be detected on the second sample following the shift.

    b) The probability that the out-of-control condition will be detected on the mth sample following the shift.

    c) The expected number of sub-groups analyzed before the shift is detected.

    d) The probability that the first sample following the shift produces a statistic that plots inside the control limits.

    e) The probability that the first sample following the shift produces a statistic that plot inside the control limits.

    f) The probability that two consecutive samples produce statistics that plot out-side of the control limits.

    g) The probability that at least one of the next m samples yields values of the test statistics that plot out-side the control limits.

    $2.19

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