# Recalculate control limits for every lot?

Discussion in 'SPC - Statistical Process Control' started by Jennie, Jan 21, 2016.

1. ### JennieMember

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I'm really embarrassed to be asking this question but are control limits generally recalculated every time you run a lot of the same product? We'll run a lot of let's say product A every month or so. We're going to implement SPC in our tabletting process (we manufacture dietary supplements) and we'll be monitoring tablet weights among other things. The weights from one lot to the next can be highly variable (although in spec). When we start up a new lot of product A, do we just start with the control limits we used last time we ran it or do we recalculate after some initial samples?

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2. ### ncwalkerWell-Known Member

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And you get the award for the coveted Start the Heated Debate in January .....

I will go first: Totally minimizing the math, let me attempt to appeal to your logic. I am going to assume that on a given run of pills, every time you set up the run, it's a tad different. Today, you might be towards the lower limit. Next week, the upper. To throw some numbers in there, let's assume the pills can be between 20 and 30 grams. And when you set the machine up and start running, your average pill is 22 gram with very little variation. You do a capability study correctly and figure out your control limits and lets say for arguments sake that winds up being +/- .5 grams. Imagine now a run chart with spec limits and these control limits. It would be a pretty wide band at 20 to 30 for spec, with a pretty tight band shoved down at the bottom from 21.5 to 22.5. You make your production run and stay within this band. Runs over, and you send your tooling to be serviced. (I've never actually seen a pill made. I am assuming it is very much like a powdered metal tool, however). Anyway, your tool gets serviced/cleaned and your are all ready to go for the next run. With such a small product, even a few microns different in assembly would affect the weight of the thing. So you start up next week and your are making pills on average at, say 26 grams. And you monitor this, and find that you still stay within a band of +/- 0.5 grams. But now, the centerline of this spread is no longer within the old control limits. It is, however, still well within specification. In fact, at 26 grams on average, it is closer to nominal that the first run which you used to set your control limits. What do you think you should do? You could:

a) stop the process, you're out of control
b) move the upper control limit up so that it was 0.5 grams above the new mean.
c) move the entire band up so they were at 26 +/- 0.5 grams
d) do another capability study keeping this batch on hold until you calculated new control limits and moved on from there.

Think about what you are trying to do with the control chart, what makes sense?

3. ### Eric TwinameWell-Known Member

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I think I may be saying the same thing as ncwalker, but not sure...

In this case, the control limits may be use for two different things, and depending on what you're using them for, they may be different.

1. Within the run (using ncwalker's hypthetical data), you don't really care what the last 22gram run data was...there was a significant event in between the runs (refinishing tool)...and the control limits within the run are what you want to look at.

2. Overall process including lot to lot data: Your control limits can be calculated from the 22gram run AND the 26 gram run...and all of the other runs before these...to see if your overall process is staying in control.

For #1, assuming that you are looking at the data after the run, you have a single set of data with control limits from that set.
If you are looking at the live updates as the run is going on, the control limits may change with each new data point.
Me, personally, I would want the last run's control limits overlayed and mean-adjusted so I knew if I had similar data spread around the mean as last time.

For #2, the control limits would, indeed, change with each new lot since you are adding in new data.
The data chain would quickly point out that your lot to lot variation is larger than your within-run variation and the control chart would have given you valuable info on where to pay the most attention (ignore the within-lot causes (feed hopper, dispense shoe), spend your time on the lot-to-lot causes (tooling change, setup parameters, humidity)).

Bottom line I guess...control limits are tools to use. What you are trying to use the tool for may affect how the tool looks and operates.

4. ### ncwalkerWell-Known Member

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That's where my head is at. I don't know what "canon" says about it. I have read (can't cite it) that you can recalculate your control limits as you go. But if you didn't "restart" the chart between the assignable cause events (tool refurbishment), that jump in data would affect your control limits. On run number two, your original limits would immediately show "out of control". When the reality is you have a mean shift. And one you could not correct with a setting. You'd have to pull the tool again. You don't want to just widen the control limits to capture both levels, because you know that wherever the mean winds up from the refurbishment, it will be real stable from that point. To me, what makes sense is to slide the limits "new mean" and use that to monitor the process, looking for sudden process drifting.

DANGER: Remember what the control limit DOES. It is part of a statistical model the removes the need for 100% inspection. If I grab a sample, the probability of the sample being in the tail of the population distribution is low. It is far more likely near the mean. With that said, I need some sense of how close I can let a sample get to the spec limit, knowing that in all likelihood it is NOT at the limit, before probability tells me that because it is unlikely I have a "tail" and I am so close to the limit, my tails are in fact out.

So you can't slide the UCL/LCL bands around willy-nilly. And that's why I don't like the normal way of calculating control limits.

The bigger question in my mind - 100% inspection for weight is pretty easy to pull off, even high speed. Not sure why you wouldn't just do that and be done with it. Even making different shaped pills wouldn't require anything other than a transducer limit. A scales a scale, after all. (He says without actually knowing what the process looks like ...)

5. ### Eric TwinameWell-Known Member

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Well, sure I can...if it is useful to do so...it's just math.

The reason I might want to shift the previous run's control limits to the new mean is to have historical perspective on variation around the mean...it isn't a process control step, it's a way of getting my head around what's important.

I know the mean shift is there, I know why it's there...but did variation change? Overlaying previous runs control limits is just an easy, visual way to do a reality check...it has no statistical significance at all.

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6. ### ncwalkerWell-Known Member

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If you are involving math to move the limits, that's not willy-nilly. Sticking with the numbers above: LSL = 20g, USL=30g. My initial study says my control limit band width is 1 g.

If I refurbish my tool, start the process and it is running at 20.5 g, I would be wrong to just slide down my control limits to the new mean and put them at 20 to 21 g. My LCL is on my LSL. That means statistically I am making bad pills. And quite a lot of them. I will statistically start making bad pills before they become colinear. You need the math (and the acceptable failure rate) to tell you how close you could move them to your spec limit.

7. ### JennieMember

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Thanks for your replies. By the way, I had to laugh about the 20-30 gram tablet-you'd need a shoehorn for that one. However, I got the gist of what you were conveying though. Good insight.

8. ### WCHornMember

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I'm curious about your statement. I'd be interested in knowing more about "high speed part weighing." I have done a few Internet searches and been unsuccessful in finding anything "high speed." For the purposes of this post, I define "high speed" as one per second or faster. Do you have any information you can share with me, either on this forum or in a private message?

9. ### Bev DModeratorStaff Member

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Great question! and you are to be commended for asking it.

OK here comes not only the canon but the theory and the common sense. It's a free country and you can do anything you want but that doesn't make it SPC, nor does it make it the right thing to do from a quality standpoint.

Canon: SPC is independent of capability.
- calculate your control limits based on several lots and/or subgroups of data to capture the full range of variation.
- once your control limits are set DO NOT CHANGE THEM, until you have made a deliberate improvement to the process.
- Do not confuse acceptance sampling with process control - they are independent of each other.

If you recalculate your limits for every lot you will be cancelling out the very purpose of SPC, which is to detect when 'assignable' causes occur. You have a huge opportunity for changes between lots and by recalculating the limits you are ignoring some of the most valuable signals your process is giving you. (and I do know how pills are made.)

Control charts are tests of homogeneity. homogeneity occurs when the factors that control the mean (location) are the same as those that control the within lot or within subgroup variation. in pill making you probably are not homogenous. and so a standard Xbar R chart will have narrow limits and many lot means outside of those limits. This often drives the behavior of recalculating the limits for every lot. (Or someone has confused control limits with capability and they are trying to determine the capability of each lot separately) The answer tot eh non-homogeneity - I fit exists is to change your subgrouping scheme.

I suggest taking a look at the attached excerpt from some of my training materials. Then read some of the references by Wheeler. Then come back and ask some more questions...

#### Attached File(s): 1. Scan for viruses before using. 2. Report any 'bad' files by reporting this post. 3. Use at your own Risk.:

• ###### SPC Summary for QFOL.docx
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1.2 MB
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10. ### ncwalkerWell-Known Member

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You high speed is higher than my high speed. To me, high speed is on every 10 seconds. I would like to see someone weigh faster than 1 a second as well.

Only way I could see that happening would be split the flow in parallel over multiple paths. The initial question was about pills. I know what a pill looks like, so I assume it is made with tooling very much like powdered metal presses. But I have no idea how fast such a thing would run making pills.

Editted to add: This looks fast ....

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11. ### JennieMember

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There's no in-line scale that I know of that can weigh individuals tablets/capsules/sofgels as they come off a machine. It can be 3000-9000 tablets a minute.

12. ### JennieMember

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This is great. Thank you.

13. ### ncwalkerWell-Known Member

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Hi Bev,

I the document you supply .....
-----

Not all process streams are homogenous. Many have systemic patterns and will require special charts. The common charts are designed for homogenous process streams.

Do NOT recalculate control limits to accommodate process degradation unless the process cannot be restored to previous stable levels in a short period of time AND you need to monitor for additional assignable causes.

-----

I am thinking if my "pill mold" is running (using the hypotheticals above) at say 23 g today with tight variation. Then I have to service it (for whatever reason) and I reassemble it and it is now making nominal pills at 27 g with tight variation, I am going to want to move my LCL/UCL to the "new" nominal. If I made them wide enough to capture both "levels" I believe I would miss it if it went out of control. OR definitely violate the "n" readings on one side of the centerline rule. Clearly we don't have a homogenous process stream. There's a mean shift with every tool rebuild (actually quite common in the molding process). Why would this approach not work? And am I asking the question clearly enough?

14. ### ncwalkerWell-Known Member

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WOW !!! That's like a week of production for the kind of units that I am used to. I cannot imaging a piece of equipment running that fast that would not just be flinging pills everywhere. Also - at that rate, WHO IS BUYING ALL THE PILLS?????

15. ### Bev DModeratorStaff Member

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As with every rule there are appropriate exceptions. IF the mean shift occurs due to a change that is technologically difficult to impossible to control and the mean shifts are well within specification then we will have modify our control scheme in two ways. (this doesn't just happen with tooling maintenance but it can happen when you change presses, different lots of certain types of chemicals or reagents, assays, etc.). First determine inner limits fro the allowable range of lot to lot or event to event variation. This is a true guardband, related to capability and not control. the limits should be inside the specifications a sufficient amount to ensure that the no parts will be outside the limits. This amount is usually 3*within lot or within event variation or more. This sets the maximum and minimum level of the mean. Then I apply the control limits using the historical stable within lot, event or subgroup variation. So the mean of the control limits will shift but the range of the limits about the mean does not. Does that make sense?

16. ### JennieMember

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We're a pill popping society! Google how a tablet press runs. It's really not that exciting. We make that many because people normally buy them in bottles which hold 30 to 300.

17. ### Eric TwinameWell-Known Member

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If it helps...
B4 Tablet Press
Bosch Packaging Technology, Inc.
• Catalog Number: B4
• Press Force: 65 kN
• Tablet Output: 48,000 to 90,000 /hr
Wonder how many 84mg aspirin are taken in the US every day...

As for high speed weighing....weigh the full bottles, there's no way a scale is gonna keep up with a rotary press.

18. ### ncwalkerWell-Known Member

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Makes perfect sense. And the phenomena does happen in a lot of other molding processes. You take a mold apart, clean it, put it back together and it doesn't lock up the same way. Depending on how tight you net shape tolerances are, it has an impact.

Also - the document is good.

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19. ### ncwalkerWell-Known Member

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Is the pill weight purely from a quality control standpoint regarding size, or is it controlling dosage as well?

What I mean is, I can't believe the entire pill is "active ingredient." But you set the dosage by active ingredient. So I make my morning batch and the "mix" that gets pressed into the pill has some analysis done saying that it is 15% active ingredient. So I set the pill weight so the math works out to 100 mg of this per pill. Then, my afternoon batch chemistry says it is 10% active ingredient. Which would mean overall the pills would have to be heavier to get me 100 mg per pill because the concentration is less.

Is it like that? Or is the concentration itself crazy controlled?

20. ### ncwalkerWell-Known Member

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OK!

So here is a "medium volume" tablet press.

My thoughts on this are:
1) Based on the background music, y'all are a funky bunch.
2) I was totally surprised by them calling out dust suction specifically. Once they did that, I was like "Yeah, it WOULD be dusty." And it must be wonderful fun to be breathing in the dust all the time.
3) Had my "doh" moment when I realized it would be configured like a turret press. Of course it would. I was expecting a linear punch press type of configuration. But the turret press would give you quite a bit more speed. It would be fun to optimize it. Smaller diameter, less stations, but faster rpm. Larger diameter, more stations, but slower rpm.....

Here's a typical powdered metal press. I was expecting the pill press to be more like this. Obviously much slower.