Sampling Plan on a Centerless Grinding Process

M

MinorNuisance

#1
I need some advice on developing an effective sampling plan on a centerless grinding process of shaft journals. The process automatically feeds and grinds several ODs on the shaft. After a set amount of grind cycles, the machine automatically dress the grinding wheel and continues. There is no integrated size control in the machine (in-process gauging). The shafts are sampled on an external gage and the machine is comensated based on the average of the subgroups if required.

The current sampling is to measure the 1st 3 parts after the dress and calculate a subgroup, measure 3 parts in the middle of the cycle and calculate a subgroup, then measure 3 right before the dress cycle. As you could see we tend to have a saw-tooth shaped control charts with the ranges being fairly tight. When attempting to recalculate the exsiting control limits based on the process data, the lines become tighter than the avg of the start & end of cycle subgroups, thus showing out of control.

No being an expert of any sort, my first impression is that the sampling plan is not approprate for this process and sample ranges don't show true variablility of the process spread... and that a better sample would include parts throughout the whole dress cycle and not neccesarily the 'consecutive' samples.

Any advice or information would be helpful...
 
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Tim Folkerts

Super Moderator
#2
Re: Advice for Sampling Plan on a Centerless Grinding Process

There have been one or two other discussions on this topic. You might look in this thread.

Control charts where the center line is a trend or slope?
Tool Wear Control Charts

At the simplest level, the process is NOT in control. There is a clear non-random element that contributes to variation in the part (i.e. tool wear). Thus, a basic control chart SHOULD tell you it is out of control.

You can come up with charts to track the CHANGE in the size of the parts, or the deviation of the parts from the expected drift due to tool wear.


Tim F
 
S

sauhiew

#3
Re: Advice for Sampling Plan on a Centerless Grinding Process

I had similar problem in high speed progressive stamping due to tooling wear out. In the measurement of the 3 parts within subgroup, there is relatively low variation because all 3 parts are sampled at the same time. However, in between subgroup measurements, the variation appears more because it picks up the tooling wear out aspect along time.

When you said you attempted to re-calculate the control limits, you could have calculated the variation with the range within the subgroup of 3. (Can you confirm?) This will give you out of control to your start and end cycle because your control limit width doesn't take into account of tool wear.

The following was I did, not sure how right I was. I calculated the control limits by using moving range, after taking average of the subgroup. The idea was to capture the actual tooling wear variation along time against the control limit, which was the major part of the variation. Otherwise, you would have to increase your sample size or frequency of checking to a very unacceptable level, thus cost, just to match the tooling wear variation to part variation within subgroup.
 

Bev D

Heretical Statistician
Staff member
Super Moderator
#4
Re: Advice for Sampling Plan on a Centerless Grinding Process

there are other threads in this forum that cover this issue nicely. Check out an article by Donald Wheeler "Can I Have Sloping Limits" in Quality Magazine 1999.
 
M

MinorNuisance

#5
Re: Advice for Sampling Plan on a Centerless Grinding Process

Thanks to those who responded...

I'm not sure if sloping limits are what i'm looking for here... We are still trying to keep the process centered as possible through out the day and the dress cycle occurs every ~15 minutes... so the saw-tooth is very frequent event.
My problem is like sauhiew said... the variation in the subgroups is such that when calculating the control limits they become tight such that some of the 1st and last subgroups exceed these limits showing that the process is not in control. Would it be better (and valid) to incorperate all the measurements from a dress cycle (begining, middle, end) into 1 subgroup or is having consecutive samples to calculate the range critical to SPC?
 

Bev D

Heretical Statistician
Staff member
Super Moderator
#6
Re: Advice for Sampling Plan on a Centerless Grinding Process

if you post your data we can give you a much better and useful answer
 
S

sauhiew

#7
Re: Advice for Sampling Plan on a Centerless Grinding Process

In my opinion, you don't want to subgroup the entire dress cycle. You don't want to lose critical information about the measurement in the cycle, especially the last reading. For example, you may have good looking control chart, but your product at the end of the dress cycle may be approaching the low end of the spec or out of spec, and you can't detect it.

One additional thought. Have your ever verified if you data is normally distributed? Control chart is used under the assumption of normal distribution. If it's not, you could be spinning your wheel to achieve good control chart and minimize cost.
 

Bev D

Heretical Statistician
Staff member
Super Moderator
#8
Re: Advice for Sampling Plan on a Centerless Grinding Process

One additional thought. Have your ever verified if you data is normally distributed? Control chart is used under the assumption of normal distribution. If it's not, you could be spinning your wheel to achieve good control chart and minimize cost.
OK control charts are not based on the assumption of Normality of the individual values. On the contrary the Central Limit Theorem says that regardless of the distribution of individuals the sample averages will be roughly Normally Distributed - close enough for the chart to be useful.
HOWEVER, there is an assumption of homogeneity that drives rational subgrouping.

Tool wear will typically have a Uniform distribution. and from the description of the OP's situation he has a uniform distribution and a SYSTEMIC drift (tool wear). The variation between a few sequential pieces will be very small in comparison to the overall variation caused by the tool. Since the limits on the averages is derived from the within sample variation, he'll have very narrow limits for his averages.

again if the OP can post his data we can answer using facts instead of conjecture.
 
M

MinorNuisance

#9
Re: Advice for Sampling Plan on a Centerless Grinding Process

Here is some data my an analysis.

I haven't checked for the 'normality' of the data. I would assume it isn't, based on the artifical limits of the dress cycle and wheel wear. Also, I'm sure the existing control limits we arbitarily set inside the spec limit... but basing it on the data makes them too tight for the current control method.

Any more opinions on the best way to monitor this process?

Thanks
 

Attachments

Tim Folkerts

Super Moderator
#10
Re: Advice for Sampling Plan on a Centerless Grinding Process

The challenge (IMHO) is to choose an appropriate rational subgroup for the process of interest with the ultimate goal being to keep all parts within spec.

SPC should be chosen for the process at hand. The standard Xbar/R doesn't seem to apply here, for reasons mentioned in previous posts.

As I see it, the process that you want to control is the dressing processes. If this is done correctly, then it almost guarantees the actual parts will be good. Hmmmm ... the following idea I just made up ... but it seems logical.

Measure the first part off after each dressing. Make an I/MR chart of these points. These will presumably be the smallest part (or almost the smallest) in the whole batch. If the dressing process is done consistently, then SPC on this chart will be in control. If you find a reading out of control ... redress!

Then measure the last part before teh next dressing. Make an I/MR chart of these points. These will presumably be the largest parts in the whole batch. If the processes for deciding when to dress is done consistenly, then this data will be in control. (The variation will probably be be greater than for the first part, because variation from the dressing AND from wear during the 15 min cycle will show up). If you find a reading out of control ... check the output for the last 15 min and watch the next dressing!

If each of these is consistent and in control, then the overall process would be in control. Further, I would calculate the Cpk for each of these two halves. The worse of these two Cpk calculations would be a good estimate for the overall Cpk.


OK ... that is my brainstorm for a logical solution for this situation. Any comments???

Tim F
 
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