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    • Thread Starter


    i am having a bit of trouble with this question
    i have attached the question. please could u have a look at the question

    my answer: control limits (3.05, 135)
    is that correct? :confused:

    thanks in advance for your help
    Attached Images

    (sum from i = 1 to 5) (X(i) - Xbar)^2 ~ 10 chi^2(4)

    [chi^2(4) is the chi-squared distribution with 4 degrees of freedom]

    From statistical tables,

    P(chi^2(4) <= 0.2971) = 0.01
    P(chi^2(4) >= 13.28) = 0.99

    So the control limits are 10*0.2971 = 2.971 and 10*13.28 = 132.8.


    If the actual stable variance is v then the probability of a false alarm (ie, the probability of an alarm when the process is stable) is

    P(v*chi^2(4) <= 2.971 or v*chi^2(4) >= 132.8)
    = F(2.971/v) + 1 - F(132.8/v)

    where F is the CDF of chi^2(4). The attached graph shows that

    - if v is more than 10 then the probability of a false alarm is more than 0.02,
    - if v is less than 10, but more than about 7, then the probability of a false alarm is less than 0.02.
    Attached Images
    • Thread Starter

    thanks for your help Jonny

    u seem to always help me
    but i still can't rep u again - so i'll just say thanks
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Updated: January 31, 2006

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