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Charting "sawtooth" data

Discussion in 'SPC - Statistical Process Control' started by _Zeno_, Sep 3, 2015.

  1. _Zeno_

    _Zeno_ Member

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    I'm painfully aware that Xbar and R charting doesn't work in a machining environment that generates "sawtooth" datasets.

    I've seen charting that will handle this type of data (most noteworthy is the control limits were angled with respect to the X axis) but cannot remember where. Can anyone point me in the right direction?

    Also, in a machining center with numerous tools using replaceable inserts (which have an average working tool life of 15-20 minutes), what type of sampling scheme can be devised to account for the constantly changing process. The inserts on the tools are routinely replaced on a schedule programmed directly in the CNC machine or when a tool alert is generated because an insert is exhibiting too much vibration. Depending on the amount of work an individual insert is doing (depends on amount of stock being removed and length of time for the cutting path), all of the tools are replaced at varying intervals of time. Combine this with the sawtooth effects (from tool wear) and logical sub-grouping eludes me.

    Any advice in this arena would also be greatly appreciated.
     
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  2. Bev D

    Bev D Moderator Staff Member

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    Bob Doering (a member here) has some useful information on your first situation. Basically his approach is put the 'control limits' at 75% of the tolerance range centered on the target. he has some info here: Correct SPC

    Donald Wheeler published an article entitled "Can I Have Sloping Limits" in the May 1999 issue of Quality Magazine. I have attached a copy of it (It was free on the internet when I created my copy. Ajit if this is a violation of TOCs or copy write rules please delete the article.

    As for your second issue, I assume you are cutting 'tough' material (e.g. Rene 77, Inconel...) that requires multiple inserts to complete the cut? In this case there are several approaches depending on your intent. I always simply charted the intended final cut result. (I didn't chart any 'additional' cuts to make the final dimension closer to target or whatever) This approach monitored the result of the entire process of making the cut and in my case at least provided the most informative information to know when the process had changed.
     

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  3. _Zeno_

    _Zeno_ Member

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    Thanx, and it's great to know you are still available as my expert source. I only wish we could recover all of the great advise that was on the Cove.
     
  4. _Zeno_

    _Zeno_ Member

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    No, the biggest difference in the inserts is the radius on the end of the tool. Depending on the radius required in the corners, different inserts are required. The issue being the out-of-sync changing of these inserts produce parts where different features are at different points in the "sawtooth" distribution of the data. So what is a "rational" sub-group?
     
  5. Bob Doering

    Bob Doering Member

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    If you follow the technique for the X hi/lo R charting methodology for tool wear the sample is typically one part, measured about the part. It is critical to measure the same same location on the consecutively machine parts, or you will involve taper error. You can control taper with three simultaneous X hi/lo -R charts representing 3 "slices" along a cylinder feature. Probably too much detail to describe in a forum atmoshpere... You will also see variation in roughing/finishing operations due to the difference in wear rates of the tools used to make the feature. This is typical, and its afect on teh sawtooth os to curve it some, rather than generate the perfect sawtooth. As long as you understand why the effect is exhibited, you are still good.

    The best approach is one chart per finish tool at the tightest toleranced dimension in that tool's path.

    Remember this: the "angled chart" or trend chart is useless. It tracks measurement error, not process error. It provides no valuable information back to the operator on what to do with the process based on its control limits. That, and it is painful to maintain for its uselessness. Doesn't matter who wrote the article about it, it is useless and the proof is in the total variation equation.

    The free training video at CorrectSPC.com should be valuable in getting you up to speed on the concept.
     
  6. Mark Paul

    Mark Paul Member

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    I had always used a "saw tooth- staircase" run chart to monitor tool wear, bottom of spec to top of spec. The problem is explaining that to a TS16949 company that is bent on getting either getting Ppk or Cpm. 1. How does one explain this in a machine shop environment?
    2. How can I show Ppk (not Cpk)?
    Thanks!
     
  7. Bev D

    Bev D Moderator Staff Member

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    well. This inability to think isn't limited to Ppk or Cpk. you can try to have a rational discussion with your quality rep. The real dilemma here is that the original intent of the capability index was to provide a quantification of the variation of a process relative to its' specification limits. The idea being that the more parts varied from the target and the further they varied the worse the ultimate quality would be. This is true for parts that wear and for 'visual' perceptions. In this case the underlying distribution is irrelevant. See: "Reducing Variability: A New Approach to Quality", by L. P. Sullivan, Quality Progress, July 1984. ($5 from ASQ if you are a member, $10 if not. well worth it. written by a guy at FORD)

    But then people had to create this whole world of pseudo statistics and conflate the idea of variation of a continuous data characteristic with actual nonconformance to a specification (categorical data: pass/fail)

    I would talk to your quality rep. show him your graphs. show him that you have an approximately uniform distribution and no parts out of spec. ask him whether he cares about variation or defects. they are not the same thing. if he needs a Xpk value then ask him if you can back calculate from your actual defect rate.
     
  8. Bob Doering

    Bob Doering Member

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    It is really not hard to explain it to a TS-16949 company, because the AIAG books actually TELL them Ppk and Cpk DO NOT APPLY! It is a shame they do not read and comprehend the books. The answer: YOU CAN NOT SHOW Ppk OR Cpk. It is in the book!!!

    AIAG PPAP 4th Edition, 2.2.11.5 Processes with One-Sided Specifications or Non-Normal Distributions:

    NOTE: The above mentioned acceptance criteria (2.2.11.3) assume normality and a two-sided specification (target in the center).

    When this is not true, using this analysis may result in unreliable information.

    Sawtooth is non-normal - continuous uniform distribution, so Cpk and Ppk DO NOT APPLY.

    The note continues: These alternate acceptance criteria could require different type of index...

    Yes, with that distribution the capability is (USL-LSL)/(UCL-LCL) If they don't agree, they don't understand the math. If you want 1.33, the UCL-LCL must be 75% of USL-LSL. or (USL-LSL)/.75(USL-LSL)=1.33 (Note, that indicates you cannot use the whole spec. The total variance equation illustrates why that is the case.)

    Again, the explanation is fairly complete on the training video on correctspc.com

    What is not on the video, yet, is that using any Shewhart chart will tell you the exact opposite of the true condition of the process control. If the X-bar/R or IMR chart says it is out of control, it is actually in control, and vice versa. That is how incorrect those charts are for precision machining.
     
    Last edited: Sep 25, 2015
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