(This is just a brief overview. For more information, see the book

__CorrectSPC: When 'Normal' Is Not Typical. A Practical Guide For The Statistical Control Of Precision Machining Processes.)__

*It will provide all the statistical support necessary to show why X bar-R charts are the worst charts to use for precision machining - bar none!*

**STATISTICAL PROCESS CONTROL FOR PRECISION MACHINING**

Many folks have attempted to implement X-barR charts for years in precision machining applications, only to be frustrated by tightly compressed control limits or unexpected bimodal distributions. The problem turns out to be that the X-barR charts are the wrong charts for precision machining. They utilize the wrong statistical distribution, and they promote overcontrol. Precision machining is non-normal. There is a better way.

**What Is A Normal Process?**

A good starting point is to ponder whether a distribution can be expected to be normal. Normal distributions are a result of normal processes - and there is an emphasis on natural variation. One of Shewart's examples was tensile strength. Random natural variation caused by a myriad of influences - chemistry, crystalline structure, surface flaws, etc. Sure, I'd buy that. The example I like to use is a processing line of loaves of bread. The height of the loaves of bread is controlled by so many variables - proofing, yeast quality, humidity, accuracy of ingredient ratios, etc. The net result is a natural variation -most a particular height, some less, some more. If a process can be expected to stay at a particular "level", with some variation above and below that level - with NO operator intervention - until a special cause appears, it's normal. That is the "voice of the process". But, if you have to have someone adjust is to keep it there, then it is not normal - and you might as well start investigating what the distribution truly is.

The problem is how many people assume normality, because they are attempting plug-and-chug statistics. Notonly that, the statistics for Shewhart charts work on a wide variety of distributions - if the data is

**independent**and

**random**-

**The other problem is people performing transformations because they only understand normal data (barely), since transformations tend to mask valuable information. It is not so much their fault, they have likely not been trained well. All transformations will do is mask the true data.**

*which they are not in precision machining!**Even Shewhart recommended against them!*

**What Is Precision Machining?**

First of all, it is sensible to define “precision machining”. For this discussion, it is a process where the most statistically significant variation originates from tool wear. So, any variations from worn bearings, measurement, etc., are all controlled to a level that is statistically insignificant.

**The Correct Distribution For Precision Machining**

The true distribution for precision machining as defined above is the

**- 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.**

*continuous uniform or rectangular distribution***Calculating Control Limits**

They should be approximately 75% of the tolerance, centered within the tolerance. 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 calculations are not applicable, since the uniform distribution is non-normal and the calculations are for bilateral normal distributions).

**What Chart Works With Precision Machining?**

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 first problem people run into when running a machine capability is they measure one of the resulting part diameters. The emphasis is on 'one'. How many diameters are there in a circle? There are an infinite number. So, how can you describe or predict an infinite number of diameters with one measurement? You can not. So, to resolve that problem, you need to pick a specific diameter - such as 24.000 mm from the end of the part (so that taper does not affect your data). You need to measure around the diameter, and determine the largest and smallest diameter measurements. Then, plot both of those dimensions on a X hi/lo -R chart, with UCL and LCL at 75% of the tolerance for X and 30% of the tolerance for R. The range is the difference - or the roundness. Continue that for about 100 pcs. (Make sure your gage R&R is less than 10%! Try to use the same material lot, if possible, operator, etc.) Is that enough pieces? Usually. If the process is 'in control' you should see the diameter increase as the tool wears (for an OD, opposite for an ID). You might see some fluctuation at the beginning as the machine warms up. That is a special cause that you cannot remove, but need to consider. If the tool wears until the X hi data is up to the upper control limit, then adjust until the X lo reaches the lower control limit. (Adjust during a capability study?? Yes.) If you get two cycles, you will have a real good idea of how the 'machine system' is going to perform. If the machine runs 100 pieces with no need for adjustment, but the data is gradually increasing at a steady rate, then you can likely extrapolate when the adjustment would need to be made. If you have the luxury to find out how long you can run before adjustment with more pieces, then all the better. There are occasions where the tool will wear to the point of breaking or poor finish prior to need for adjustment - and that information is good to know too. But, as long as you can keep the process between 75% of the tolerance, and you are capable to at least 1.33 [capability=(USL-LSL)/(UCL-LCL)].

The next thing to review from the run is roundness (R chart). If the roundness is less than 10% of the tolerance, you have no worries. If it is greater than 30%, then you will have to watch that process like a hawk with frequent SPC checks. I would vote to resolve the roundness issue (which is most likely a machine or machine set-up issue, particularly in chucking or bearings). If it can not be improved, I suggest passing on that process and finding one that can maintain the roundness better.

Now you have some real data on whether that 'machining process' will work for you! This is the short and sweet lesson, but I hope it corrects some of the misconceptions on the topic.

See the SPC Actual Machining Process Data attachment for a good benchmark of how a controlled precision machining process should appear (it is OD dimension.)

**The X Hi/Lo –R Chart Sounds Like More Work**

No, not really more measurements. Right now, most people measure a diameter on 5 parts. One diameter out of an infinite number of diameters. That would be statistically insignificant. Then they take the average of statistically insignificant data. Great... The range of those measurements more closely represents measurement error. All I ask is to measure 1 part 5 times, and report the highest and lowest diameter. After all, if you are really doing precision machining, 5 parts in a row really should not vary significantly. So, do not measure more parts, spend quality time with one part. As a quality professional, even if it were true that it was more work, one should recognize that less work does not trump correct.

When I walk into a plant that is doing precision machining, they are so frustrated with X-bar - R SPC charts that they may be doing them, but they ignore them. I do not blame them. After training them on the correct method, they are relieved, they have a clearer idea of what the process is doing, how to control it, and how to improve it. No wonder SPC gets a bad rap - people are trying to rubber stamp the wrong charting methodology creating havoc.

**Continued at Statistical process control for precision machining Part 2**

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