Need help / feedback on Xbar/R charts and Cpk/Ppk applicability - Assemblies

I am conducting SPC studies (using Xbar/R charts) on a grinding process, using variable data from three characteristics:

(1) assembly thickness after grind
(2) parallelism of surface to backing plate after grind
(3) flatness of surface after grind

To make charting easier, I am coding the other words 0.001" will be 1, 0.010" will be 10, 0.007" will be 7, etc...

I am also setting the nominal as zero (0), and then will chart the difference from actual target. For example, if a part thickness target is 0.650", and the measurement taken is 0.652", then I record "2"...if a measurement is 0.647", then I record "3". What this does is it allows me to use one standard set of charts, regardless of the actual part thickness.

That's just a little background on what I am on to the question.

Ok, for THICKNESS, the specification is bi-lateral, however, for PARALLELISM and FLATNESS, the specifications are uni-lateral. Thickness is typically 0.650" +/- 0.005" (ie: in my case, 0 +/- 5). Parallelism and flatness are typically 0 + 0.010" max (ie: in my case, 0 + 10 max).

Ok, for calculating Cpk and Ppk, the formulae are as follows:

(I know that there is no PPU or PPL, I just used those terms for the sake of this question...)

That being said, I realize that these formulae work fine for my thickness studies, since they are bi-lateral, but what about for the uni-lateral tolerances (parallelism and flatness)??

For parallelism and flatness couldn't I just say that Cpk = CPU and Ppk = PPU (since there is no lower specification)?

Does anyone have any ideas on a better way to monitor these two uni-lateral characteristics (are Xbar/R charts even appropriate for these)???

:bonk: (I need a vacation!) :truce:
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Craig H.

Good morning, Xman.

Yes, this is what you should do.

The use of xbar should take care of any "normalcy" issues, and the use of the USL is entirely appropriate - the farther you are from the upper spec, (i.e. closer to zero) the better, right?

Just curious, but how did you determine your subgroup (n) size?
the farther you are from the upper spec, (i.e. closer to zero) the better, right?
Yes, that's correct. The ground surface, ideally, would be perfectly flat/parallel (ie: 0), however since we all know that's virtually impossible, I have a tolerance of a maximum of +0.010" deviation from 0. So, the closer to 0, the better.

Just curious, but how did you determine your subgroup (n) size?[
I am using charts with 25 subgroups of 4 (for a total of 100 readings.) I chose 4 because it is the best "fit" for 100 readings, as well as the fact that our grinder runs 4 jigs/fixtures, so I can also track the variation from jig to jig by watching the charts as well.

Thanks for your reply! :)

Ravi Khare

As Craig rightly pointed out, X-bar should take care of Normalcy issues. X-bar R Charts would give you a good indication of the stability of the process.

Your evaluation of Cpk = Cpk(U) and Ppk = Ppk(U) is also would give you the right picture of the Process Capability. Cp and Pp are undefined in such cases.

Since you have parameters of parallelism and flatness that have one sided specification, the approach you need to take for an out of control situation will difer slightly from that for parameters with two sided specs.

If you find that you have an out of control situation that takes the X-bar below the lower control limit, your process has drifted lower, but actually improved. You should then investigate what you have done right ( assignable cause of the right kind) to get this out of control. If you are able to replicate the assignable cause setting, and maintain the out of control below LCL, you could consider reapplying the Control Limits based on the new improved process study data. You could then maintain the process stable with reference to the new limits.

With the parallelism and flatness characteristics, since there is no lower spec, wouldn't it make sense to say that there should also be no lower control limit (in other words the LCL should be 0), like the R chart (since range can only be =/< 0 as well)?

For example, one set of data I analyzed for flatness gave me a LCL of -0.12. However, since I have no negative (-) readings, and can have no readings less than 0, shouldn't the LCL be 0?

Craig H.

Well said Ravi! A much more complete answer than mine. However, one warning.

I got in hot water with a VP recently for pointing out that a chart drifted "out of control" when the process improved. He waited until we were alone in his office to point out to me that we were in better control now than we were a month ago. He was more than a little unhappy.

The lesson: be careful when talking to "non-practioners"!!!

Ravi Khare

The lower control limit is only meant to draw the line beyond which you know that the drift is significant. That way you will be able to differentiate random variations from assignable cause ones. The lower control limit is going to tell you when there is going to be a 'significant' (real) process drift towards improvement.

As for Craig's comments, I wholeheartedly agree with you Craig... We all have gone through this sometime or the other I guess. I have spent hours trying to argue with smug people who look at Control Charts and be happy that they are producing quality; when the Cpk is all the time flashing the disaster warning!


If there is only one spec, I feel that you should try Cpmk or its equivalent using ds_total, as othe other posts said, you could get better Cpmk if the process is farther from the target and the variation is lower, than a process that is closer to the target and with higher variation, with the definition of quality improvement as "reduce variation centered on the target" that doen't make any sense.:confused:

look at

:truce: Be careful of wich control chart to use, I feel that there could be autocorrelation if this is a continuos process, you may need an X/MR chart.

Thanks for the input (and the link Darius)! :bigwave:

I think I will look further into this and re-evaluate how I am monitoring the uni-lateral toleranced characteristics.
The formula loks acceptable tome and as Darius indicated there are other methods. However, I am curious about the tolerance. +/-0.005 on thickness, +/- 0.010 on flatness & perp.
Typically the Flatness & Perp should be less than the size tolerance. preferably 1/2 the size tolerance.
Just a thought.
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