How to Get the LSC and USC

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    Miguel Hernandez

    Hello all!

    I need to get the process capacity and I want to know how the get the LSC and USC, and this is my scenario:
    – They are not determine by any norm.
    – They are not defined by the customer (the only customer requirement is a yield of 97% +/- 3%).
    – According to data, I’m using a U-chart (thus the LSC limit varies, and as far I know, I could use the control chart limits if they are constant -unless I got it wrong-).

    Is it posible to get them from the yield? If so, how?
    In other case, can I set them up? in which basis or based on what?

    Hope you can help me!

    Thanks a lot in advance! (sorry if I posted this on the incorrect forum)
    B.R – JM


    Chris Seider

    You need to explain your situation a bit more. Are you saying your customers accept 3% defective on some attribute (which I have a hard time believing). Or is this an internal customer that has to process the results downstream (e.g. chemical or oil)? Don’t confuse control limits with spec limits. U charts won’t give you spec limits.


    Miguel Hernandez


    First of all, I made a mistake, I confuse LCL and ULC from control charts with the LSL and LSL (sorry by that).

    I want to measure the Process capability index, where C_p = (USL – LSL)/6s, thus I need to get USL and LSL.
    They do not exist, as I told you. 97% +/-3% is the only datum I have from the customer.

    My yield is calculated as follows:

    DPO = defects / (numbers of units processed * Number of opportunities per unit) = 36/(259*2) = 0.06950

    Yield = (1 – DPO)*100 = 93.050% (actual yield)

    -where one defect on the product or a delay AND the product is considered totally defective-
    The number of products generated per week is a variable number (in the formula 259 is a sample taken from 25 weeks, as well as 36 defects).

    As you can see, in order to apply the formula of Process capability index, I need these spec limits. I can get standar deviation and average from my sampled data of 25 weeks.
    And also, the Ppk (long term capability). Finally, this is the question:

    Is it posible to get them (LSL and LSL) from the yield? If so, how?
    In other case, can I set them up? in which basis or based on what?

    Mass: Hope the explanation lightens the question.
    Kevin: I do not know ImR charts, I will look for them.
    Chris: Thanks for clarifying my error.

    Thanks for you support and answers, guys!
    Let me know if you need more details, please.


    Prabhu V

    Hi Miguel,

    From your explanation, I would like to state the following points

    A) Specification limits for Process capability:
    As you have stated you have the customer voice of 97% average yield (with +/-3% tolerance), hence your USL =100% and LSL=94%.

    Based on the above you may calculate the Process capability.

    B) Yield calculation:
    You have mentioned that the yield has been calculated on the based on DPO, pls find the formula for classical yield.

    Classical Yield or First pass Yield = 1-(Total no of rejections/Total no of production from the process).

    I hope your phenomenon need to be modified since you have mentioned that you have used defective concept for yield calculation. (DPO study is irrelevant for yield calc.)

    Based on your information, your classical yield =1-(36/259)% = 86.1%

    Since your customer may accept only min 94% yield, the gap to target is 7.9% (likely gap to target will vary for mean and upper limit).

    Kindly consider the above.

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