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6-Sigma Equates to 3.4 DPMO or 6.8 DPMO?

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  • #28366

    Dewi Lloyd
    Participant

    Am I right to assume that 3.4. DPMO, as for the normally quoted definiiton of 6-Sigma, assumes that any score below the LCL is OK, and that we only above the  UCL?  Thus for a process where being too small is just as bad as being too big (door gaps on cars, most machining applications), 6-Sigma would be 2 x 3.4  equals 6.8
    I’d welcome confirmation on this as I am not sure!
     
     
     

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    #70486

    Erik L
    Participant

    When we talk about the sigma level of a process we take the sigma level to be the relation from the center of the processes dispersion to the closer of either the upper or the lower specification limit.  So if I’ve got 12 sigmas between my mean and the USL, but 1.5 sigma from the mean to the LSL, I have a 1.5 sigma process.  Therefore, a 6 sigma level process, long-term) will have 3.4 defects per million (accounting for the 1.5 sigma shift). 
     
    Regards,
    Erik

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    #70501

    hoon
    Participant

     hello erik,
    when we say that a company has achieve 6 Sigma level,ie. 3.4 DPMO, then we are saying that its spec limits are plus/minus 6 sigma?(instead of the control limits).
    Thank again.

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    #70506

    Erik L
    Participant

    A company that claims a process performance at a six sigma level is basing that information related to the the specifications of a process.  I like to think of sigma levels like the Cp and Cpk metrics.  They are a relation between the VOC and the VOP.  Control limits are created, based on the process information, and are set so that there are 3 standard deviations between the grand average and the upper and lower control limits.  Companies that mature up the scale of sigma levels still keep their control chart limits at the 3 standard deviation norm. 
     
    Regards,
    Erik

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    #70529

    john beaudoin
    Participant

    It was very hard not to laugh after reading your question, and I see that some of the other responses you have received, although correct, may not help you understand.
    Point Blank – 3.4 DPMO (Defects per Million Opportunities) is exactly what it is.  How you define the defect is up to you.  If someone makes a determination that customers say it is ok for a gas pump to be off by 1 gallon in 10 gallons pumped, one could say that gas pumps operate at a 6 sigma level in that for everyone that visits a pump, only 3.4 people in every million visists will have more or less than an extra gallon of gas for 10 gallons pumped on the meter.  We did not say that you could have 3.4 people with an extra gallon and another 3.4 people short more than a gallon.  A defect is either a defect or not a defect.
    When you look at a specification limit, such as the tolerance between 2 mechanical parts, you can define that the pieces need to be between .005 inches and .025 inches.  If you are less than the .005, that would be a defect and if you were greater than .025, that would also be a defect.  If you say that .004 inches is really acceptable, then your lower specification is not set correctly at .005 inches.
    When you look at a control chart, a process that is in control will have most of the points between the upper and lower Control Limits.  These are different from Specification Limits.  A process can be in control, but be at a very low sigma number as the target you consistantly hit does not meet customer expectations.  If you put a rifle on a stand, aim with a scope, and shoot 10 rounds, the process can be very much in control with all 10 shots hitting in a small grouping, but if the grouping is 5 inches to the right of the target, you also have 10 defects out of 10 shots.
    I hope this is in a language you can better understand.

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    #70531

    Bobby
    Participant

    The DPMO that determines your sigma level doesn’t distinguish between under spec or over spec. DPMO only looks at defects, as you specify, compared to the total opportunities to create a defect. ASSUMING your process is normally distributed and is performing at a 6 sigma level, then you would average 1.7 defects above and 1.7 defects below per every million opportunities.

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    #70532

    Dave Strouse
    Participant

    Bobby wrote –
    The DPMO that determines your sigma level doesn’t distinguish between under spec or over spec. DPMO only looks at defects, as you specify, compared to the total opportunities to create a defect.
    I agree with this in general, you can get a measure for sigma in this way that can be used to evaluate the healtha nd later improvement of the process. You must take into account the shift to do so.
    However, when you say –
    ASSUMING your process is normally distributed and is performing at a 6 sigma level, then you would average 1.7 defects above and 1.7 defects below per every million opportunities
    This is not true. A process performing at a six sigma level assumed to be normal AND centered, would produce approximately 1.25 parts per BILLION defective on either spec limit. This is sometimes referred to as Cp of 2 or Z(short term). When we now allow the process to shift by 1.5 sigma toward either spec limit we get a Cpk of 1.5 and a Z(long term) of 4.5. This Z is what is usually referred to as the “sigma” value of a process. It allows for process variation of 1.5 sigma units. This shifted distribution would produce 3.4 ppm defective on the close spec boundary and about 1 part in 10 trillion on the other side, that is obviously of little impact. (last number from only table I have that shows 7.5 sigma , “Measuring Process Capability” Davis Bothe )
     
     
     
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    #70543

    Zimmerman
    Participant

    You were the only one who gave the correct
    response. It’s quite simple, as you said in your
    last paragraph, the 1.5 sigma shift towards
    either limit makes the other limit irrelevant
    because your now 7.5 sigma away from it.

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