To take into account the tool wear during calculating control limits

[Star18]

To take into account the tool wear during calculating control limits we use a coefficient representing the evolution of the mean of the mean.
Someone can give some comments?
In advance thanks.

 

[Star18]

Re: To fit control limits.

Another question about the control limits formulas: what represent the coefficients: d2, d3, A2,...?

 

[Tim Folkerts]

I have certainly heard of such approaches and think they are quite logical. "In control" is supposed to represent the best that the process can do under present circumstance. Given that tool wear is inevitable, then adding a slope to the X-bar chart would better tell you how the process is actually performing. It may not fit the letter of the law, but it certainly fits the spirits of the law.

As for the various constants, they are basically just efforts to estimate the apropriate +/- 3 sigma control limits based on other measurements. For example, if you measure ranges, you need some way to convert from average range to standard deviation.


Tim F

 

[martin elliott]

Using a slope to the X-bar chart can be seen as logical to maximise tool use however beware of the goods inwards trap.

If your customer uses short ppk studies as a goods inwards inspection release, then by selecting at random through the full run, then your product might be caught as apparently non-compliant.

 

[bobdoering]

To take into account the tool wear during calculating control limits we use a coefficient representing the evolution of the mean of the mean.
Someone can give some comments?
In advance thanks.

Actually, calculating control limits that account for tool wear should be easy, if tool wear is the significant portion of your variation. They should be approximately 75% of the tolerance. Why? Because the true distribution for a process that has all of the special causes removed, and has only tool wear remaining, is the uniform or rectangular distribution - not the normal distribution. You can tell if your process meets this distribution by performing a capability study. If, for example, you are machining a OD, set the process at the lower control limit [nominal - .75(tolerance/2)]. If - without operator intervention - the process increases to the upper control limit [nominal + .75(tolerance/2)], then adjust back down to the lower control limit. If this continues (until a tool breaks, or surface finish deteriorates - special causes), then you have the "sawtooth" curve, and it is the uniform distribution. Some normal-centric statisticians like to try to 'normalize' the data with transformations, but that is unnecessary, as well as a useless effort. The sawtooth curve is more meaningful as is to an operator - they understand tool wear. The control limits really never need to be adjusted. Compressing the control limits actually increases overcontrol - and therefore increasing variation. The slope of the line is the tool wear rate - which is meaningful information that would be masked by transformation. Notice the mean has no use whatsoever in the sawtooth curve - only the control limits. Don't forget, most of the Western Electric rules - especially the one concerning runs, do not apply - they are for the normal curve.

Since the probability of the uniform distribution is straight forward, 75% of the tolerance gives you well below the probability of +/- 3 std dev of a true normal distribution. You could use a higher percentage of the tolerance, but it is better to play it safe due to hysteresis concerns (you can never land exactly on the control limits). This follows AIAG SPC Chapter III Non-Normal Charts, last bullet point: use control limits based on the native non-normal form. (Also, AIAG PPAP section 2.2.11.5 states that the Cpk calculation are not applicable, since the uniform distribution is non-normal and the calculations are for bilateral normal distributions).

I must add that X-bar-R charts are the worst for true uniform distributions. X-MR would be a little better. Again, the mean means nothing in the uniform distribution - both for the population or the sample, and there should be virtually no discernable variation between 5 consecutive parts, unless you are shredding up tools. The variation you might see is measurement error, typically because of out-of round or parallelism issues - depending on the process. There is a simple way to deal with that - but that is another lecture.

Sounds as though the approach you are taking is just a little too complicated for the real need of the control. But, you were thinking!

Bob Doering

 

[Bill Ryan - 2007]

Welcome to the Cove Bob

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[Marc]

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