iSixSigma

z score

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  • #47083

    chhabra
    Participant

    I have a set of 20 data point mean of it is coming to 16.75 and standard deviation is 6.5 , company has givan predefined target of 20 , my z score is coming 0.5, pl. let me know how to explainΒ what isΒ z score in an understandable manner to the lay man.and how it is different with six sigma capability.

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    #156525

    Rupesh
    Member

    Hey.. the easiest way for a layman to understand Z score is that ” How many ‘Standard deviations’ away the target is from the mean” in other words hom many standard deviations can be fitted between the target and the mean. Hope the group will throw more light on this.

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    #156528

    BritW
    Participant

    Need to know if you have an upper or lower boundary.Β  Target is 20+/- X, or is it just 20.Β  Can it be between 0 and 20, but not greater than 20?
    If you calculated yoru Z score correctly at .5, then it indicates that about 69% of your product is at or below 20 (your target).Β  This is foundΒ from the standard normal z table – that is assuming your data is nrmally distributed.Β  If it is not normal, then you are using the wrong probability distribution and need more help.

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    #156534

    newbie
    Participant

    Go to the Dictionary section here under Z and you should find some quick, helpful pointers. But remember this:
    For any process capability metric that uses mean and std dev in its calculations, your first step is to determine if your data is continuous, stable and normal…if you do not have these three things, i believe you will need to take another course of action.
    I would not explain the statistical side of Z score (X – Xbar / std dev), rather focus on how it is used to determine the forecastedΒ yield of the process…that is much easier to comprehend….you can always dive deep if they ask.
    And I dont understand your last question.
    Good luck.

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    #156536

    Snow
    Participant

    How do you answer the question of CI / CL in terms of a process capability metric and its extrapolated yield prediction?Β 
    You calculate the Z score, use the Z table to determine yield, and then the boss asks you:Β  Β¨24% of the product outside spec?Β  How sure are you about this?Β¨ How do you answer?Β 
    Thank you for your time.

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    #156540

    Darth
    Participant

    Without getting into specifics, I never provide point values when predicting.Β  The best approach is to provide a statistical statement such as, ” Based on historical data, I am 95% confident that the % of stuff that is out of spec may range from X% to Y%”.

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    #156542

    Snow
    Participant

    Darth,
    Thank you!Β  But how do you create such a statement when you are dealing with a capability metric?Β 
    Say a Z score is calculated and then a % out of spec determined…..how do youΒ bracket it like you said with a CI and CL?

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    #156545

    Darth
    Participant

    For example, JMP provides UCI and LCI for Pp, Ppk, CPM etc. in it’s capability analysis.Β  Or you can get creative and calculate extremes for Z using the uci and lci for the mean and s.d. of the data.

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    #156547

    Snow
    Participant

    Excellent….thanks again Darth for the help…the site has gone to hell a bit, but having experts like you stick around and give quality advice (no pun intended) isΒ invaluable to us beginners….thanks again for taking the time.

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    #156562

    BritW
    Participant

    dude:Β 
    An additional option via JMP is to do a control chart and select capability. It will ask for LSL, USL and Target and give you a capability (with Confidence limits) as well as the resulting control chart of your choice.
    Need to make sure you understand the potentials with using Z and assuming normality.Β  If not normal, you can fit the distribution to a few optionsΒ and run capability on that data in JMP as well.Β  I think it can be done in Minitab too without transforming the data, but it’s been awhile since I’ve used minitab, so someone else might provide better advice.Β  I have found a few limitations with JMP in this manner, but nothing too serious.

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    #156578

    Snow
    Participant

    BritW,
    Thanks so much.Β 

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