Capability study on rate of defect

Six Sigma – iSixSigma Forums Old Forums Europe Capability study on rate of defect

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    Jean Jacques

    Hello all,
    I’m working on capability study and control chart implementation for production of welded components.
    The production is 100% inspected and number of defective and qty produced are recorded.
    There is no more monitoring than record of above mentionned data for each shift.
    To better manage improvement I believe that control chart and capability study could hep me in this way.
    However I meet some difficulties and will appreciate help regarding the following :
    1- How can I calculate a capability (Cpk) regarding rate of defect ?
    2- How to implement control chart when lower limit specified is the same than target (0 defect = 0 percent) ?
    3- How to have a normal distribution when data will never be lower than target and in this case lower specified limit (0% of defect) ?
    Many thanks for your help,


    Arne Buthmann

    Hello JJ:
    ad 1)

    To calculate a Cpk your data have to be continuous and you have to have specification limits (in your case you don’t have spec limits – 0 for defectives is not a specification, it reflects a way of thinking that there is no variation). To calculate Cpk you would need to measure your data continuously, e.g. measuring the weld strength in a destructive test of pull-off force in Newton – and what is the spec here, what force must the weld connection stand?
    ad 2) To display the defect rate (e.g. per shift) you should use the p-control-chart (instead of the individuals control-chart). Since specification (=target)-limits (in your case 0% defect) are not displayed in a control chart, because only statistically calculated control limits are shown, there is no problem if the target and the control limits are the same. (If you decide to measure the components, your control chart will have different control limits, anyway)
    ad 3) For discrete data (what the defect rate actually is) normal distribution is not assumed and, moreover, cannot even be expected. The p-chart makes no assumption of normal distribution but requires binomially distributed data.  
    Summarized: The best would be if you could measure the components instead of just counting defective parts. If this is not possible, use a p-chart to display the defect rate.
    If you have any further questions, please ask!


    Jean Jacques

    Dear Arne,
    Thank you for your answer and advices.
    I well understand that it could not be possible to calculate a Cpk without specification limits. Indeed considering Cpk is the evaluation of the centering of the distribution compared to the limits, it’s mandatory to have limits. However is budgeted scrap level could be consider as a upper limit and 0 as the lower ? With this consideration we will  have the same case than for a perpendicularity or a flatness (no value under zero and only a maximum limit) ?
    I also agree with your conclusion that it should be easiest to perform capability study on data issued from measurement. Unfortunatelly most of the defects come from visual inspection.



    Dear JJ,
    Arne is right, visual inspection is just a part of  “M” of  DMAIC  process.
    Before you discuss about defects % or ppm, a target must be defined (could be zero = 100% of yields, no problem),  your visual inspection is giving you how you are far from you target and the variation of yields, at visual inspection, give you indications about stability of your process around the target, no more. You have to put in place D,,AIC steps to have a full picture of what is happening (the root causes of what you see at visual inspection happen before, so there you must put in place a the corrective actions).  
    Hope this help.



    Dear Peppe,
    I agree that  root causes occur before the visual inspection, and there seems to be quality problem of 100% visual inspection itself.
    Can our inspectors  screen out all defective units with false alarms as low as possible?  how good are they at this?
    Any suggestion to evaluate the inspection quality?

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