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Cpk >2.5, data is normal, but SPC is totally out of control

Discussion in 'SPC - Statistical Process Control' started by Chris Halbower, Jul 7, 2022.

  1. Chris Halbower

    Chris Halbower Member

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    I am trying to roll out an SPC program at my company. We have the software. We have the hardware. We just need to implement the training. In order to get buy-in, I picked a part that has both variable data collected on it and also has a strong history of quality conformance. I don't want to roll out the SPC program and have everyone over adjusting.

    The variable data we collect is normally distributed.
    • The skew and kurtosis are with +/-2.
    • The mean equals the median.
    • The χ2 test also confirms normally distributed data.
    The Cpk is over 2.5. We have fairly wide tolerances and can hold the feature robustly.

    The GR&R is robust. This is in part because the tolerances are fairly wide.

    However, the SPC is out of statistical control. About 2/3 of the readings are out of control. The major cause is centering: the subgroup x̄ is outside the control limits. I verified the software's formula. They are correct. The UCL and LCL are indeed X̿ ± A2*r̄.

    We are measuring subgroups of 5 parts. The range of these 5 parts is quite small, creating a small A2*r̄ (and thus narrow UCL and LCL). However, the x̄ jumps around, many times outside the control limits. This is my dilemma.

    Is there something I am missing? Why would a centerline jump around but the subgroup range remain tight?
     
  2. Bev D

    Bev D Moderator Staff Member

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    There is NO need to understand - or achieve - Normality of the data for SPC. Normality has some meaning for Cpk but only if you want to (incorrectly) conflate the process variation with the number of defects. But this only applies when the process is clearly producing parts out of specification.

    From your description of rather small variation within the subgroups relative to larger variation between the subgroups I would say that you have an irrational subgroup scheme. But we would need to know more about the process and how you are subgrouping as well as seeing your data…

    The descriptions of SPC in most mainstream literature relies on ideal situations which rarely occur in real life. You probably need to understand how to create rational subgroups. I recommend the collective writings of Donald Wheeler. I have posted a list of SPC references before and will try to find it and post later…
     
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  3. Bev D

    Bev D Moderator Staff Member

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    ...and here it is. I have included relevant articles regarding the misuse of Cpk. links are to FREE articles and there are a lot of them...
    I have also included a paper I wrote that you might find thought provoking. (it too includes references)
     

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  4. RonR Quality Pro

    RonR Quality Pro Active Member

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    Bev is much more knowledgable than I in this matter, however I do have a suggestion on how to evaluate your data.

    Rather than use the generated control limits from your data, try setting ARTIFICIAL control limits (± 2/3 of your tolerance) and see if there is any change. Not sure how well it will work for you, but I have used this method (precontrol limits) in the past without any issue.
     
  5. Chris Halbower

    Chris Halbower Member

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    Thank you for the input.

    We are using 5 pieces in each subgroup. We are measuring parts twice a shift (so every 4 hours). This helps us understand the process at start up and at mid-shift.
     
  6. Bev D

    Bev D Moderator Staff Member

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    PreControl can work IF you have a lot of knowledge about what creates out of spec product AND you have the ability to adjust those inputs. Plus you have to follow the PreControl rules for adjustment…the limits are not “control limits” like in SPC and the SPC rules do not apply.

    PreControl is intended to ensure the production of in spec product.
    SPC is intended to indicate when a process has changed.

    These are very different things and are based on different statistics and physics. They seem similar but they are not.
     
  7. Bev D

    Bev D Moderator Staff Member

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    This doesn’t mean you have a rational subgroup. A rational subgroup is one where the variation to be ‘controlled’ is included in the subgroup. The variation to be controlled is the largest component of variation. Piece to piece variation is the ideal used by most SPC ‘hacks’ but it is far from common. Lot to lot, within piece, time to time, material lot to lot, etc. all can be larger components of variation.

    We would have to see your data to understand how to subgroup properly. A multi-vari chart will show the components of variation and enable rational subgrouping…
     
  8. Miner

    Miner Moderator Staff Member

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    It would help us if you can provide some general information about the process, so we can understand the various sources of variation.
     
  9. Chris Halbower

    Chris Halbower Member

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    We are stamping out a steel bracket. The press operates quite quickly: we have coil changes about every 2.5 to 3.0 hours. However, we are doing SPC checks every 4 hours (or twice a shift). So when we measure 5 parts every 4 hours, we see little variation in those five parts. However, the variation between groups is large. That is, in four hours, the x̄ of subgroup at 10AM is out of control compared to the x̄ of the 6AM subgroup.

    After reading and rereading Bev's comments about rational subgroups in an attempt to really understand, I reviewed the literature on the subject. The subgroups we are using are likely irrational. We are comparing 5 pieces all in a row on one coil (getting one x̄) to another 5 pieces all in a row to another coil. The difference in material properties varies from coil to coil, especially yield strength. This could introduce variation that I hadn't considered. Furthermore, the point in time when the measurements are taken (at the outer coil vs. the inner coil) could introduce variation. The inner coil is more work-hardened than the outer. Also, the coil change operation itself could introduce a small amount of variation because the spool could be located a bit differently from change to change.

    Instead of measuring 5 parts every 4 hours, I am reviewing a different subgrouping. SPC shall be done at every coil change. Perhaps 4 parts: 2 from the last coil and 2 from the incoming coil. This will capture the variation from the inner coil to the outer coil, the differences in coil set up to coil set up and the differences in coil mechanical/chemical properties.
     
  10. Miner

    Miner Moderator Staff Member

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    I agree with your thinking on the irrational subgrouping. Given your process and the sources of variation, I would recommend using an individuals/moving range (IMR) chart. You could take your historical data, select one measurement from each subgroup plot that on an IMR chart and see how that works. You may even keep the 4 hour frequency.
     
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  11. Bev D

    Bev D Moderator Staff Member

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    Miner is correct - try the 3-way chart (it’s covered in one of the articles by Donald Wheeler that I posted…)
    I’ve used it many many times in the type of situation you describe quite successfully.
     
  12. Chris Halbower

    Chris Halbower Member

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    After reading Donald Wheeler's ideas about 3-way charts, I agree that this is very applicable to my process.

    However, I cannot seem to find how UCL/LCL are determined in 3-way charts. Did I somehow miss this somewhere? I believe I have looked at everything.
     
  13. Bev D

    Bev D Moderator Staff Member

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    You calculate the limit for the subgroup to subgroup mean using the I, MR chart formulas. The subgroup mean is the individual value, I. This gives you 2 charts. The I chart and the MR (moving range) chart. The third chart is either an R Chart or S chart of the within subgroup variation. Does that help?
     
  14. Chris Halbower

    Chris Halbower Member

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    Thanks. I was struggling with the d2 constant. It is equal to the 1.128 if you are calculating a M̅R̅ from the last two readings.
     
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