Statistical Process Control for Precision Machining - Part 2


Stop X-bar/R Madness!!
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Is This Charting Accepted By The Big 3 Automotive OEMs?

I have found that all customers (Big 3 and Japanese transplants) that I have trained on this concept (as a supplier) have accepted the concept, including its use for PPAP submissions. When it is all said and done, its simplicity makes it more understandable to customers and operators. There is no guarantee that every SQE will follow along. After all, we know the automotive industry better than that.... Most importantly, it follows AIAG Blue Books for dealing with capability (which comes up at PPAP time):

AIAG PPAP 4th Edition Acceptance Criteria for Initial Study
The organization shall use the following as acceptance criteria for evaluating initial process study results for processes that appear stable.

Index > 1.67 Meets acceptance criteria

1.33≤ Index ≤ 1.67 May be acceptable

Index ≤ 1.33 Does not meet acceptance criteria Processes with One-Sided Specifications or Non-Normal Distributions

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

When this is not true, using this analysis may result in unreliable information.
NOTE (cont.): These alternate acceptance criteria could require a different type of index or some method of transformation of the data. The focus should be on understanding reasons for the non-normality and managing variation.

This process addresses these issues. Of course, I do not recommend transformations, when using the correct distribution directly - as this process does - is adequate. As Dr. Walter A. Shewhart said: "The total information is given by the observed distribution.” I agree.

One last supporting item is that one of the Big 3’s Six Sigma Master Black Belts is implementing this process internally for their precision machining. It is new, but the sell is not that hard.

How Do You Determine Capability?

Remember, the 1.33 criteria is based on a bilateral normal distribution (as stated above), not the non-normal distribution found in precision machining. If the customer demands 1.67, then set the limits at 60%. According to 4th ed PPAP, it is up to the customer to determine an alternative, although I offer them my system as the alternative. There is no need to "center" the distribution, as it is centered as 75% of the tolerance when you set up the control limits. The use of the smaller of (USL - mean)/3s or (mean - LSL)/3s is specifically for bilateral normal distribution. The normal distribution goes on to some degree forever, but we decide to "call it quits" at +/-3s. The uniform or rectangular distribution - in its perfect state - stops exactly at the control limits. That is why capability=(USL-LSL)/(UCL-LCL)].

What Gage Requirements Are There For SPC?

If you are doing SPC, it is best to have 10:1 to your control limits, not the tolerance. So for precision machining, .001 is the range between your control limits (.00075) would need to read at .000075 After all, if you do not have 10 units of discrimination within your control limits, how can you tell what your process is doing? This is a starting point. Follow the MSA instructions for GR&R, and determine the true statistical discrimination (ndc). ndc>=10 when calculated using the control limits instead of tolerance. MSA says ndc should be >=5. I find that woefully inadequate. That is about as much discrimination as a gas gage.

What About That Darn Central Limit Theorem – Does It Not Make Everything Normal?

I hate to let these little rumors spread. For many distributions, it seems to be handy. For the uniform distribution, the theorem fails miserably. You do not need triple integrals and partial derivatives to show this to be the case. I have attached a data set of a uniform distribution. When correctly sampled (and that is important, we are evaluating the process distribution, not the sampling error distribution) at 5 pcs, and they are averaged, the resulting distribution is also uniform. Any correctly sampled subset of a uniform distribution is also a uniform distribution.

Interesting note: The central limit theorem (CLT) states that the re-averaged sum of a sufficiently large number of identically distributed independent random variables each with finite mean and variance will be approximately normally distributed (Rice 1995).

The continuous uniform distribution that arises from tool wear is neither random nor independent. So, CLT must not be assumed to apply to every distribution.

For more information, an easy to read manual on X hi/lo-R charting for precision machining is available at:
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