Monitor Process capability on IMR chart

Hi,

Is it Ok to plot process capability indices (Cpk) on an IMR chart?

I have a part with a uniform thickness requirement. The thickness is measured on 20 different locations within each part. So if I do a Cpk calculation of each part and then plot 30 Cpk values on the IMR chart; does it have any statistical validity and can i prove that the process is under statistical control?

I know about the three-way-control chart but i would like to know the for / against argument for plotting Cpk in a control chart?

Thanks

I don't see what meaning such a chart would have.

Tahirawan77 said:

Hi,

Is it Ok to plot process capability indices (Cpk) on an IMR chart?

I have a part with a uniform thickness requirement. The thickness is measured on 20 different locations within each part. So if I do a Cpk calculation of each part and then plot 30 Cpk values on the IMR chart; does it have any statistical validity and can i prove that the process is under statistical control?

I know about the three-way-control chart but i would like to know the for / against argument for plotting Cpk in a control chart?

Thanks

Click to expand...

You can't calculate Cpk on an individual part. Cpk assumes (1) a statistically stable process and (2) rational subgrouping of samples taken from an active process. Chronological order of sample selection is important.

A lot depends on the operational definition of 'uniform' in the case of your part. Do the 20 different locations on a given part need to be 'uniform' in comparsion with each other? That is - if all locations are say 1/2 inch too thick, but all are uniform with each other, is that okay? Or does a given measurement locations need to be 'uniform' with all other parts at the same location?

You question implies you want to plot some sek values, but the I MR chart itself is the basis for a Cpk calculation, so afraid there is some circular logic at work here.

Can you explain the actual requirement for "uniformity"?

Steve Prevette said:

A lot depends on the operational definition of 'uniform' in the case of your part. Do the 20 different locations on a given part need to be 'uniform' in comparsion with each other? That is - if all locations are say 1/2 inch too thick, but all are uniform with each other, is that okay? Or does a given measurement locations need to be 'uniform' with all other parts at the same location?

You question implies you want to plot some sek values, but the I MR chart itself is the basis for a Cpk calculation, so afraid there is some circular logic at work here.

Can you explain the actual requirement for "uniformity"?

Click to expand...

Hi Steve,

Thanks for your reply. I have attached a simplified image to present the problem. We have a part which has an initial thickness of 'T1'. We use milling operation to reduce it to a thickness of T2. Once the milling process is completed, then the part is measured at various locations (P1 ... p9) to measure the thickness. The deviation between the T2 and the 'actual thickness' is recorded. It is this 'actual thickens' which i want to do a Cpk study and see if it varies from the target value of T2.

So we have two main sources of variation.

Within part variation = mainly due to milling process + part setup
Between part variation = in addition to milling process & part setup there is also extra source of variation which is the variation in the T1 thickness.

So if I mill 10 parts then i can have one Cpk value for each part and if i plot these 10 Cpk values on a SPC chart does it means that my process is in statistical control?

Thanks

OK, that makes sense. We basically have a specification which is applied against several measurements taken on sequental items.

There is a precedent of the "chi square control chart" which is used for counts of items. Since the individual components are poisson, the sum becomes a chi square. But that would not apply here directly since these are normal data. We can make use of the traditional Xbar-R control charts, I believer.

We do want to consolidate the data for a part into one entity since there really is not a time sequence we are looking at for the within part variation. One answer is to do Xbar - R or Xbar - S charts where you plot the sequential average "T2 deviation" (T2 - measurement) and the range of the T2 deviation (max - min for the part) in the traditional Xbar - R chart. Note we are likely more interested in the Range chart than the average chart.

One thing to consider is - are you equally concerned about too high T2 deviation as well as too low, or are we really more concerned about the strength of the milled item, where thinness would be the issue.

There may be some advantage to plotting the Xbar - R of the absolute value of the T2-measurement if we are concerned about both directions.

Another option is to plot the standard deviation of the T2 minus measurement data for each part as the input data to an Xbar-R or Xbar-S set of charts. That would give more complete coverage rather than taking just the max minus min values.

Note that I am considering the "within lot variation" to be based upon the individual part and its nine measurements.

One more thought. Since you would declare a part as "failed" if it exceeded the maxiumum deviation, I would plot a I-mR chart of the max values for each part, and another chart of the min values of each part and check those Cpk's.

Thanks for your valuable input. Here are my comments

Steve Prevette said:

OK, that makes sense. We basically have a specification which is applied against several measurements taken on sequental items.

There is a precedent of the "chi square control chart" which is used for counts of items. Since the individual components are poisson, the sum becomes a chi square. But that would not apply here directly since these are normal data. We can make use of the traditional Xbar-R control charts, I believer.

We do want to consolidate the data for a part into one entity since there really is not a time sequence we are looking at for the within part variation.

Click to expand...

There is a Time sequence within each part. The part is always milled from P1 to P9.

Steve Prevette said:

One answer is to do Xbar - R or Xbar - S charts where you plot the sequential average "T2 deviation" (T2 - measurement) and the range of the T2 deviation (max - min for the part) in the traditional Xbar - R chart. Note we are likely more interested in the Range chart than the average chart.

One thing to consider is - are you equally concerned about too high T2 deviation as well as too low, or are we really more concerned about the strength of the milled item, where thinness would be the issue.

Click to expand...

I am equally concerned for both too high and too low T2 deviation. As it may allow us to see if there is any 'offset' in the milling process.

Steve Prevette said:

There may be some advantage to plotting the Xbar - R of the absolute value of the T2-measurement if we are concerned about both directions.

Another option is to plot the standard deviation of the T2 minus measurement data for each part as the input data to an Xbar-R or Xbar-S set of charts. That would give more complete coverage rather than taking just the max minus min values.

Note that I am considering the "within lot variation" to be based upon the individual part and its nine measurements.

Click to expand...

I think I have the following options

Cpk charts as below

i) Prepare ONE Xbar-S chart for each of the position (P1 .. P9). For e.g i can make 9 Xbar-S charts to monitor each location over time. (to monitor ' part-to-part variation'?)

ii) Prepare ONE Xbar-S chart for each part. For e.g all 9 points are put in one sub group (To monitor 'Within part variation'?)

Individual value chart

iii) Prepare two IMR charts one each to monitor MAX and MIN values (so no Cpk here)

Any comments about the above strategy?

Your plan sounds good. One additional piece of information (which could be plotted on a p-chart) is the percent of measurements that exceeded spec, and if enough data, a Pareto chart by location and whether it was high or low. That could help with troubleshooting if you were having failures.

Steve Prevette said:

Your plan sounds good. One additional piece of information (which could be plotted on a p-chart) is the percent of measurements that exceeded spec, and if enough data, a Pareto chart by location and whether it was high or low. That could help with troubleshooting if you were having failures.

Click to expand...

Thats a good suggestion to setup a P-chart, and i guess there will be one point per part on the P-chart . Once i have collected enough data then I plan to use a 'Heat map' so i can identify any areas where the process is not in control so it can assist us to take action.