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Math Help - Reliability Question

  1. #1
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    Reliability Question

    I have a circuit diagram of 5 switches.
    Reliability of switch A and B are 99.5%
    while C,D and E are 98%.

    Reliability Question-screenshot_1.png

    What is the reliability of the circuit working?

    I understand how to do a straight circuit multiplying the percents such as A and B being .995 * .995= .99025 or 99.025% but seeing how this circuit spreads out I am having a hard time finding the equations I must do and put together in order to find the percent if reliability. I do understand with all these switches the percent of reliability must be extremely high and close to 100%.
    Anything will help at this point. Thanks!
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  2. #2
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    Re: Reliability Question

    Quote Originally Posted by Launcher View Post
    I have a circuit diagram of 5 switches.
    Reliability of switch A and B are 99.5%
    while C,D and E are 98%.

    Click image for larger version. 

Name:	Screenshot_1.png 
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ID:	27614

    What is the reliability of the circuit working?

    I understand how to do a straight circuit multiplying the percents such as A and B being .995 * .995= .99025 or 99.025% but seeing how this circuit spreads out I am having a hard time finding the equations I must do and put together in order to find the percent if reliability. I do understand with all these switches the percent of reliability must be extremely high and close to 100%.
    Anything will help at this point. Thanks!
    The probability of a parallel circuit working is the same as 1 - P(all branches not working). Hence, the probability of E/D working is: 1-(1-0.98)(1-0.98) = 0.9996. Now C/D/E is parallel to A/B, and since you know how to calculate the probability components in series, apply the parallel reasoning as above to compute the total prob (I get 99%).
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  3. #3
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    Re: Reliability Question

    Thanks for that.
    With what you gave me I did this for all 3 combinations and multiplied them together giving me
    .9995670
    or 99.9% does that sound correct?
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  4. #4
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    Re: Reliability Question

    Quote Originally Posted by Launcher View Post
    Thanks for that.
    With what you gave me I did this for all 3 combinations and multiplied them together giving me
    .9995670
    or 99.9% does that sound correct?
    I punched the numbers into excel and used the wrong cell in the final calculation! Here's the corrected version. I get 99.98%:

    Here's what I got:

    P(A & B) = (0.995)(0.995) = 0.990025
    P(D||E)=1-(1-0.98)(1-0.98) = 0.9996
    P(C&D||E)= 0.98(0.9996) = 0.979608
    P(A & B || C & D|| E) = 1-(1-0.990025)(1-0.979608)=0.9998
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