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Topic Control Limits VS Cpk

Control Limits VS Cpk

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This topic contains 8 replies, has 9 voices, and was last updated by  SickSigma 10 years, 3 months ago.

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    Could someone tell me if there is any relation between Control Limits & Process capability ?
    A scenerio:
    Process is biased towards to the Upper Specification Limits (USL). But the process happens to be within the control limits & it is withing the Specifications.
    i) Will my Cpk be affected due to the shift away from my design  center ? (Or is there no relationship at all ?)


    A process that is ‘within control limits’ is not the same as a process ‘under control’. For a process to be ‘under control’ it is not just enough if all data points are within the control limits. There are various other points need to be met too.
    Any of the below is a indicator of an ‘out of control’ process. Even if one of the below characteristics is present in your process, it means the process is ‘out of control’ and needs tuning.
    A single point outside 3s control limits
    2 out of 3 successive points beyond than 2s on the same side of the centerline
    4 out of 5 successive points beyond 1s on the same side of the centerline
    6 points in a row either increasing or decreasing
    8 points in a row, none between 1s on either side of the centerline
    9 points in a row on the same side of the centreline
    14 points in a row alternating up and down
    15 points in a row within 1s on either side of the centerline
    Manikanda Mariappan


    Morning Luthaniel,
    Am not sure do you mean control limits or specification limits.  Control limits define the area three standard deviations on either side of the centerline, or mean, of data plotted on a control chart. Control limits implies variation.
    Specification limits are not, those are limits specified from customers or else, they are fixed and don’t change unless advised by customer
    So I’ll assume that you mean specification limits.
    first of all you should know how we would calculate the Cpk
    Cpk = (USL – Avegage) / (3*St.Dev)  –  USL = Upper Specs Limits
    Or  Cpk= (Average – LSL)/(3*St.Dev)  – LSL = Lower Specs Limits
    we take the min value as a result
    while Cp = (USL – LSL) / (6*St.Dev)
    So as you can see that the Cpk does look to where is the process average and how it’s related to the Specification limits  and thus will change (decrease) if the process is not centered. you get max Cpk value if average is ceneterd.
    Of course lower Cpk indicates more defects from the process and thus low capability.


    Hi Luthaniel
    Control limits & specification limits are totally different
    Any process should have both control limits & specification limits and Cpk  tells us how process is in center (target).
    Control limits are voice of the process
    Specification limits are voice of customer.
    Just my opinion


    If you characterize your process and find that the mean is biased towards the USL, you  might elect to lock in your control limits around the mean as it is (the better thing to do is to center your process).
    In the above case you have accepted the fact that Zmin will be (USL-mean)/3.  The location and dipersion of the data are used to calulate control limits, and also to calculate capability.   The only difference is that spec limits are used in the capability analysis but not in the control limit derivation.


    Remember not  to  record (or  draw) the SL on  the  control  chart.


    Cpk is a measure of how closely the process is centered by definition. Therefore if your Cpk is excellent your process is targeted on nominal.
    Your control limits are a funtion of the theoretical standard (not actual) deviation as calculated by the specific control chart you are using.
    i.e. in an Xbar&R chart the theoretical Standard deviation is a function of the average range.
    So basically the answer is their is no mathematical relationship between the two.


    Cpk is a measure of how closely the process is centered by definition. Therefore if your Cpk is excellent your process is targeted on nominal.
    This is not true.
    Consider a process witrh spec limits 0 and 100, mean at 90 and std deviation of 0.25. Cpk is enormous and we are nowhere near center.


    Control limits focuses on process behavior and what the process can achieve (Voice Of the Process/Stability) while Cpk focuses on the capability relative to spec limits (Voice Of the Customer/Capability). In order to become capable, a process should be stable first.
    You need to identify first if your spec limits are one-sided or two-sided and what kind of requirement will you be measuring (e.g. time — the lower the better, quality — the higher the better). Bias depending if its one or two-sided can be either beneficial or not.
    If basing on your spec limits interpretation, the more the point reaches the upper spec, the more risky it is to have defects, then your Cpk might be affected.

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