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Which Control Chart to use?

invtanofmark

Just joined the community today and had a question about control charts. I am collecting data that consists of 120 measurements taken once a minute. My goal is to understand the variation between the measurements (between 1 and 2, 2 and 3, etc.) and I have the measurements in groups for each minute of time (120 measurements for 12:01, 120 measurements for 12:02, 120 measurements for 12:03, etc.). Based on what I am trying to understand and the way in which the data is collected, which control chart would be best to use? I tried searching a few discussions on this, but was still confused whether my data is continuous or is actually divided into sub groups.

Accepted answers

Peter_Bartell

invtanofmark: Lots if issues to consider, in no particular order;

1. When you say, 'measurements' I'm presuming some type of continuous variable vs. attribute or count variable? The answer matters wrt to chart type.

2. Can you create rational subgroups of observations? If no, then a chart of individuals is required. If yes, then some kind of variables chart (xbar/R perhaps?) with subgroups is called for.

3. Are your observations independent of each other or do you think there may be correlation among successive observations of some lag? I might check with JMP's Time Series platform to see if there is some autocorrelation among observations? With independence assumption, then the variables chart approach might work. With correlation, you'll want to consider some type of time series oriented chart such as an EWMA.

4. Is this a Phase I or Phase II type investigation? From your first post, it looks like Phase I? So I might just start with an I/mR chart and see what it tells you?

5. Lastly, how stable is your measurement system? Do you have control charts in place there? If not...how do you know the data you've collected is due to process vs. measurement system variability?

For some 'how to in JMP' and thought provokers I suggest taking a look at the Mastering JMP event I host:

Evaluating & Monitoring Your Process Using MSA and SPC | JMP

All comments

Peter_Bartell

invtanofmark: Lots if issues to consider, in no particular order;

1. When you say, 'measurements' I'm presuming some type of continuous variable vs. attribute or count variable? The answer matters wrt to chart type.

2. Can you create rational subgroups of observations? If no, then a chart of individuals is required. If yes, then some kind of variables chart (xbar/R perhaps?) with subgroups is called for.

4. Is this a Phase I or Phase II type investigation? From your first post, it looks like Phase I? So I might just start with an I/mR chart and see what it tells you?

5. Lastly, how stable is your measurement system? Do you have control charts in place there? If not...how do you know the data you've collected is due to process vs. measurement system variability?

For some 'how to in JMP' and thought provokers I suggest taking a look at the Mastering JMP event I host:

Evaluating & Monitoring Your Process Using MSA and SPC | JMP

invtanofmark

Peter,

Thank you for responding. Based on what I understand here are a few answers:

1) The measurements are being taken continuously by a scanner. The

measurements are taken by a scanner across a width of 200" on a sheet of

paper. A total of 120 measurements are taken over the course of 1 minute.

The measurements are taken to see how much variation exists across the

sheet of paper. So, 120 measurements are taken of the same feature within a

minute.

2) In regards to the sub groups, this is where I am confused. I would think

that each minute of time would represent a subgroup of measurements. Say at

12:01 120 measurements are taken, then at 12:02 another 120 measurements

are taken and so on. I am not interested in the changes between the

measurements as time goes on, but instead interested in the changes between

two measurements at the same time. I don't care if there is a difference

between the measurement taken at 12:01 at point (1) and the measurement

taken at 12:02 at point (1). I do want to understand the difference between

the measurements taken at 12:01 between point (1) and point (2),

3) All the measurements are taking the same reading, just at different

points across the width of the sheet.

4)This is a phase 1 analysis. Just trying to get an idea of where we

currently stand.

5) Control charts are in place, but it is uncertain how often they are

actually used to manage the process.

On Mon, Aug 31, 2015 at 10:19 AM, peter.bartell@jmp.com <

Peter_Bartell

invtanofmark:

Thanks for the additional information. In the interest of full disclosure, for many years I worked for a major photographic materials manufacturing company..."You Push the Button...We Do the Rest" was one of the company's marketing slogans many, many years ago. So I have some background in process monitoring on a moving web at high speed for various continuous (coating thickness for example) and attribute (lines and streaks) data types. Sometimes the data was captured real time via optical scanning systems...other times off line via product testing.

Here are some more thoughts;

1. The idea behind forming rational subgroups is that by setting up a subgrouping strategy, you should endeavor to create a subgrouping strategy that captures process common cause variation within subgroups, with a goal of giving you a fighting chance of finding assignable cause variation between subgroups. Quite frankly I'd be hesitant to use one minute time intervals as a basis for forming rational subgroups. That's what I'd call a convenience subgroup...not a rational subgroup. I really think you are in single measurement in time land.

2. Variation across the sheet of paper SCREAMS at correlation among the positions from across the sheet AND down the sheet, especially if there is some kind of extrusion or coating going on, and I'm presuming the sheets are being cut from a web...Have you checked for that? It sounds like you are gathering data at specific widthwise locations? If there is evidence of correlation among the locations, maybe some kind of multivariate chart approach in JMP might be appropriate? Indeed in my On Demand Webinar I offer just such an example.

3. In phase I I'd take a univariate and multivariate distributional (shape, outliers, anything else suspicious?) and second by second (run chart) view and see what you can discover...this should help you lead to the appropriate control charting method.

Steven_Moore

I have been in the paper industry for many years and have struggled to understand the use of Process Behavior Charts (Control Charts) for data generated by continuous scanners that move back and forth across the sheet as the sheet is moving perpendicularly to the travel of the scanner. One of the biggest problems with continuous measurement by any on-line intstrument is the issue of autocorrelation. If the measurement frequency is faster than the ability of the sheet properties to actually change in a meaningful (practical) manner, the autocorrelation is going to KILL you. This is evidenced by very narrow control limits on your Control Chart compared to the ups and downs of the individual data. The reason is because the average moving range is very small due to the autocorrelation. Thus, very tight upper and lower control limits are calculated. I worked with a Black Belt candidate a few years ago on this very type of problem. The answer was to randomly sample the autocorrelated data at some reasonable frequency in order to construct useful Process Behavior Charts. As alluded to already, there is also the issue of cross-machine variation.

If I can be of further help to you, please feel free to contact me. (smoore@wausaupaper.com)

invtanofmark

Peter,

Regarding 1) it sounds like you are saying that the reasoning behind forming subgroups is to understand variation between batches of things. Such as to compare one batch of paint to another made at a different time? In my case, would it be better to look at one set of 120 measurements taken at a 1 second interval? Looking back, I think my reasoning for dividing the scan collections into groups was to try to see if the variation between measurements is increasing with each cross-direction scan. I don't know if this is the correct way to approach this type of variation.

2) I agree with you, there is certainty a correlation between the measurements in both the machine direction and cross direction of the web. For this particular process the sheets are being cut from a web. Could you explain more about the multivariate charts or if possible provide a link to your webinar?

3) In regards to the run chart, I am struggling with understanding how large of a sample size should I plan to collect. Would I first need to use the Sample Size and Power Tool? In the mean time I will collect some more data in the range of one second over 30 seconds to build the run chart.

invtanofmark

The suggestion to use random samples sounds like it would be the way to go . I have found out that although the scan is measuring at 120 points across the sheet; the output number that the operators see is actually the average value of the scan (for all 120 measurements at one time interval). However, it is the amount of variation between the points that is the concern. Say at one edge of the sheet the measurement is 55, it is not an issue if the next measurement is 55.5 or 56. However, if the measurements jump from 55 to 68, this is a problem. It is even acceptable to start with 55 at one end of the sheet edge and finish with a measurement of 70 at the opposite end; as long as the measurements have a small amount of change between them such as 55, 56, 57, 57.5 and so on.

Also, I would like to complete a capability analysis to see how effective the current process is in staying within customer specification levels. Are there any problems I should watch out for with using this kind of data for a capability analysis?

Peter_Bartell

You'll want to insure process stability (or at least assume it?) by control charts before assessing process capability. Then check for normality of the individual observations...JMP can calculate process capability indices for select non-normal distributional forms so just make sure you check for the appropriate non-normal distribution if needed.

Steven_Moore

Do you have a scanner that is moving back and forth across the sheet as the sheet is moving through the equipment, or are you measuring 120 points across the sheet at the same time? If the former is the case, can you stop the scanner and test one place across the sheet multiple times? This kind of information is needed to be able to help you the best way I can.

Steven_Moore

Peter,

In order to use Process Behavior Charts such as the X-mR or I-mR charts for individuals and/or subgroups, normality of the data is NOT required nor assumed. This is one of the great myths regarding Control Charts. You can find this in Shewhart's original work (Shewhart invented the control chart) or in many articles written by Dr. Donald Wheeler. W. Edwards Deming had a lot to say on this subject as well.

That said, some Attributes control Charts DO require certain distributions: NP-charts for counts and P-charts for proportions require the binomial distribution. The C-chart for counts and U-chart for rates require the Poisson distribution.

to paraphrase Dr. Shewhart: "The normal distribution is neither a prerequisite for, nor a consequence of a process being in statistical control." I have confirmed this many times in my 30+ years of utilizing statistical tools.

"Normal distribution? I've never seen one." - W. Edwards Deming (May, 1991 4-day seminar in Cincinnatti, which I attended)

invtanofmark

smoore,

Yes it is the first situation you are describing. The scanner is moving back and forth across the sheet as the sheet is moving through the scanner. I have recently found out that the raw data from the scanner is actually measuring 600 points and that the 120 points are an average from the 600. Also I cannot access the raw data, I am only able to examine the 120 points. Is there different criteria if I am dealing with average values instead of individual measurements? I have attached picture that shows what the sample points actually look like. This is a pretty crude drawing, but I just wanted to describe how the measurement points are "landing" on the sheet.

9730_scanner example.jpg

jvillaumie

How you define the group depends to a large extent on what you are trying to detect:

- If you suspect there is a strip of the sheet that is consistently different (always thicker, or always darker) (e.g. 18" to 20" on your 200" sheet), it would be sensible to use and XBar and R chart with the sampling location as Group. You would have 100 groups/100 locations, and Group 10 would show up as out of control on the XBar chart.

- If you suspect there is a strip of the sheet that is more variable (thickness or color varies too much) (e.g. 18" to 20" on your 200" sheet), it would be sensible to use and XBar and R chart with the sampling location as Group. You would have 100 groups/100 locations, and Group 10 would show up as out of control on the Range chart

- a XBar and R chart with Minute as the group will tell you if the roll is changing over time (not what you are interested in, if I understood you correctly)

- since you have group, Individual Range chart or Run chart would not be my first choice.

invtanofmark

Ok, I think I am starting to understand regarding the charts. I have also been reading some of Thomas Pyzdek's coverage of control chart concepts. According to Thomas, IM-R charts are used in the case when you are really only taking one measurement. So if I wanted to look at the variation between readings of Box 1, I could use an IM-R chart to compare measurements taken over time. Instead, I am really wanting to look at how to measurements vary in the cross direction (as you said 18" in to the sheet, 20" in to the sheet and so forth). I think for this case I will use the Box locations (1-120) as the sub groups and then use 6-10 random sample times as the data seen in each group. Did you pick 100 groups as a general number or do any specific calculations to arrive at this?

invtanofmark

Looking back, I think I have the cart before the horse. My original goal in trying to determine what control chart to use is really to see if the process is in control. The reason for this is that I would like to complete a process capability study to determine if our process can consistently meet customer specifications. Now, even through 120 measurements are taken, and it can be seen that there is variation between the measurements; these 120 measurements are averaged to a single value and this value is used to make adjustments. The process is not actually controlled based on the variation between the individual measurements across the sheet, but rather the average of the 120 measurements.However, to improve the process I need to reduce the variation between the measurements....would the following through process be correct:

1) First plot the Xbar-R chart to see if there are measurements from the sub groups which are out of the control limits (using data taken each minute over a half hour)

2) For those sub groups that are outside of the upper and lower control limits, use an IM-R charts to look for special cause variation.

Does this sound reasonable?

MikeD_Anderson

If you aren't sure if your process is in control, you probably want to do a variability study first. This would allow you to look at all the sources of variability and see if the assumptions required for an effective implementation of SPC are being met. This study can be found under Analyze > Quality and Process > Variability / Attribute Gauge Chart. You can do a components of variance analysis among other useful analyses before you "throw the switch" on an SPC implementation.

Best,

Steven_Moore

Michael,

The only way to understand if your process is in control is to construct a control chart first!!! Your statement seems to follow the old myth that a process has to be in control before a control chart can be used. The real question: Is the process homogeneous? The only way to answer is to start with a properly constructed control chart. Almost any study in which tiime-ordered data is available should START with control chart(s) before doing anything else. I know this idea flies in the face of "Six Sigma", but the failings of "Sick Sigma" is another topic for another time. Please see the wotk of Donald Wheeler and Davis Balestracci to understand further what I am saying here. They both have published plenty of great information on the internet (esp., www.qualitydigest.com).

MikeD_Anderson

Dude! Why you gotta' hate on L6s? Lets keep it friendly in the community.

I also appear to have hit a nerve here... let me say that I like Wheeler's work. I have 4 of his texts and draw from them extensively. Since you mentioned L6S, I should also mention our trainer drew from his works extensively for our SPC training. But most of my thoughts on this issue predated my BB certification by a few years. I also think that my industry bias might have made it hard to understand my point.

My personal bias is that, while the world won't stop turning if I just dump my data into a run chart and calculate some limits, I absolutely need to check that my components of variance and variability charts support any decisions I make from the data. It doesn't cost anything to do this any more than just generating the run chart does. This is primarily because, for semiconductor manufacturing - particularly at the newer technology nodes, we can not make the assumption our measurement error is negligible relative to our signal of interest. So, doing the sanity check of gauge and MSA studies is industry best practice.

The gauge studies and CoV analyses (particularly the graphics that are part of the JMP platform) are also useful in determining where the point of homogeneity is and identifying correlations in the data. This second point is a very serious issue for semiconductor due to some of the physics in the manufacturing process. These points are quite important, as you and others on this thread have made abundantly clear, as some of the assumptions required for good SPC are invalid if the rational subgroup is not chosen correctly. SO, rather than saying invtanofmark should prefer one over the other, I propose that invtanofmark should never look at one without the other - that they are complementary. In my workflow I would do the gauge and CoV first to determine where my rational subgroup size is so that my control chart makes sense right out of the gate and I didn't have to go back and make adjustments - when you're managing several thousand metrology SPC charts every second saved counts!

rabelardo

HI everyone.

This is what I gathered from the control chart types documentation.

* My understanding of the control chart process based on the documentation may be wrong, please correct it.

- Randy, JMP newbie

Steven_Moore

Randolph,

With proper rational sub-groups, you will be able to effectively utilize the Individuals/Moving Range chart about 95% of the time. Most of the other types of charts assume/require a certain distribution of the data in order to be effective. For example, the C Chart requires the Poisson distribution. Dr. Donald Wheeler has published a great deal on this subject that I suggest you read. Much of this can be found at QualityDigest.com. Just do a search of Wheeler's content on the site.

Best regards,

Steve

rabelardo

Thanks for the tips, Steve.

I will definitely search the archives of Quality Digest on Dr. Wheeler and control charts.

And in doing so, I hope to understand how the Control Chart Builder is influenced by the methods and thinking of Dr. Wheeler - as indicated in the deck below from the article An Integrated Process Improvement Approach Using the Second-Generation Quality Tools in JMP® posted 3 months ago.

Much appreciated.

- Randy, JMP newbie