Can we do this? Fill volume average calculations

We have a filling line , it runs circa 4500 bottles per hour, filling a 750mL volume of liquid into bottles. In NZ we have similar rules to the '3 packers' in the form of the Weights and Measures Act 1999. We aim fill to a minimum of 750.0 and a maximum of 753.0mL, but due to the nature of the process and variation in the glass bottles, we experience some variation around this - so far so normal ....

We calculate the average 'run' fill volume by taking the sum of the documented hourly fill volume checks (each hourly check is the average of 6 bottles) and dividing by the number of check instances. This is now where it starts to get interesting:

if the 'run' average volume is < 750.0mL (ie:less than stated label volume) then we are up for a rework, as it fails the '3 Packers/W&M 1999' requirements. So, if the operator does an hourly check and it is <750.0 mL , we retest another 6 bottles and record this also. Typically, variation being what it is, the second check will be in the target band. The second check is completed within 10 mins of the first one.

There has been a request that the 'out of spec' initial volume check be excluded from the average calculation. What are your thoughts on this? My thinking is that it is still a valid measurement and reflects the fill volume at the time of sample. I am concerned that we could be seen to be picking and choosing which data points we include so as to maniplulate the run average to suit our needs.

I have requested also that when volumes are >753.0 that they are retested/recorded also , this removes any bias that you retest to bring up your average only when the fill volume is low.

Hi Mr QA,

I will give this a go but average weights and measures do my head in! I have some questions:
- are you calling a 'lot' what you process in an hour?
- what determined a 6 bottle sample?
- are the bottles sold singly or in a pack?
- do you have any tolerable deficiency's (T1 and T2)?

Dear MrQA,

Welcome to the forum !

I hv no idea what the "3 packers" standard(?) is but it appears to me that you are mixing 2, maybe, incompatible objectives -
(1) to conform to the legal requirements
(2) to "control" yr process by some rigorous, or at least semi-rigorous "statistical" procedure.

If you hope to involve any possibly interested readers in item (1), is the standard available anywhere on the web ? I seem to recall there are 2 basic methods typically involved, the t1/t2 procedure as referred in previous post and the (more empirical) procedure which usually was employed prior to any change to a t1/t2 system. I suspect you are discussing the earlier type system.

In the case of No2 the full approach is of course via SPC however this requires yr testing as to whether the process is in "control".

If you are merely trying to estimate what yr average fill volume is to some intrinsic accuracy, this is textbook statistics. As you probably know data is not discarded unless you can demonstrate the existence of outliers. The usual approach is to define a lot as per previous post and then use book formulae with yr own inputted accuracy requirements / trial guess. The calculation is slightly more involved if sampling is from "boxes" of bottles on a line but not horribly so (from memory). Offhand, the usual crude suggestion to achieve a "reasonably" accurate idea is to take around 30 samples, eg split (timed) uniformly across yr "lot" run, maybe 1 "random" bottle from each box and make the measurement / do the calculation. This is "systematic" sampling. Slightly biased from memory (?) but not bad. If you want more details on internal variations, need to take more bottles per sampling (2-stage / ANOVA etc).

Sorry if you knew all that already.

Offhand, the adjustments you describe look "non-statistically" inspired, ie arbitrary.

Rgds / Charles.C

It looks like you are trying to control your fill to the declaration on the label without any allowances for container variation (tare variability allowance), standard deviation and sampling allowance.
The Packers Guide has a section on control based on sampling and can be followed very easily.
With regard to the set of 6 and resampling, you cannot ignore the low results, nor is the resample as you seem to be doing it a valid method. If you sample 6 bottles, you will have to target a higher fill than if you sample 12 bottles. This is simple averages - the average of 12 will be typically closer to the average of the batch than 6. Statistically you can take an average of the 6+6 but you should still be targetting the properly calculated target fill (not the declared).
You may not be getting across the message that the average of your 6 bottle sample is not the average of the actual fill. It is only the average of the 6. The higher the sample rate (number or frequency) the closer you can run to your declared, up to the point of 100% sampling - a checkweigher, where you could effectively run on the limit.
This is all about sampling from an assumed normal distribution.
If your distribution curve takes you into Packers Rules 2 and 3 (excess T1s and T2s) you target fill must be increased further.

Hi Mr QA,

I will give this a go but average weights and measures do my head in! I have some questions:
- are you calling a 'lot' what you process in an hour?
- what determined a 6 bottle sample?
- are the bottles sold singly or in a pack?
- do you have any tolerable deficiency's (T1 and T2)?

thanks for the response ; )

A 'lot' for us is a run of a particular product. Eg: if we bottled product X all day, that would be a 'lot'. Conversely if we bottled product X for 4 hours and product Y for 4 hours, that would be 2 'lots' .
The 6 bottle hourly 'sample' was determined by the balance and associated printer/control apparatus we purchased many years ago - it requires 6 samples to weigh and calculate volume based on density and weight of sample.
Bottles are sold by us as 6 or 12 packs.
Tolerable deficiencies are defined for us by the Weights and Measures 1999 administered by Consumer Affairs. From memory T1 is 15 mL and T2 is 30 mL for underfills. Overfills we use 753.0 ml as max fill . the system is fairly simple and easy to use, the question is more directed at whether or not you can disregard measurements if you retest, or should you include original AND retest?

Dear MrQA,

Welcome to the forum !
I hv no idea what the "3 packers" standard(?) is but it appears to me that you are mixing 2, maybe, incompatible objectives -
(1) to conform to the legal requirements
(2) to "control" yr process by some rigorous, or at least semi-rigorous "statistical" procedure.
If you hope to involve any possibly interested readers in item (1), is the standard available anywhere on the web ? I seem to recall there are 2 basic methods typically involved, the t1/t2 procedure as referred in previous post and the (more empirical) procedure which usually was employed prior to any change to a t1/t2 system. I suspect you are discussing the earlier type system.
In the case of No2 the full approach is of course via SPC however this requires yr testing as to whether the process is in "control".
If you are merely trying to estimate what yr average fill volume is to some intrinsic accuracy, this is textbook statistics. As you probably know data is not discarded unless you can demonstrate the existence of outliers. The usual approach is to define a lot as per previous post and then use book formulae with yr own inputted accuracy requirements / trial guess. The calculation is slightly more involved if sampling is from "boxes" of bottles on a line but not horribly so (from memory). Offhand, the usual crude suggestion to achieve a "reasonably" accurate idea is to take around 30 samples, eg split (timed) uniformly across yr "lot" run, maybe 1 "random" bottle from each box and make the measurement / do the calculation. This is "systematic" sampling. Slightly biased from memory (?) but not bad. If you want more details on internal variations, need to take more bottles per sampling (2-stage / ANOVA etc).
Sorry if you knew all that already. Offhand, the adjustments you describe look "non-statistically" inspired, ie arbitrary.
Rgds / Charles.C

Definitely trying to conform to the legal requirements first and foremost , but also our own objectives as well. The standard is avail at: http://www.legislati.../DLM301528.html but is very lengthy. Our SOP is this:


To ensure fill levels of all bottles produced meet the requirements of The Average Quantity System-Proposed Amendments to the Weights and Measures Regulations 1999. It is recognised that automated filling processes cannot fill every bottle to an exact amount over a production run, however the AQS aims to ensure that bottles do contain the amount stated on the label ‘on average’. Filling tolerances are proportional to the product size and difficulty of obtaining the correct fill, creating a standard which is fair to both manufacturers and consumers.

PROCEDURE:



The AQS has 3 basic requirements with which a production run must comply. If a sample taken from a production run fails any of these 3 requirements, the sample fails and the production lot fails (ie: does not meet the AQS requirements and must be reworked).



1) The actual contents of the bottles in a production run must not be less, on average, than the quantity

stated on the label.

2) There must not be >2.5% non standard bottles in a run.

3) There must be no inadequate packages.



A non standard bottle contains less than the stated volume where the deficiency is greater than the set tolerance, but not greater than twice that set tolerance.

An inadequate bottle contains less than the stated volume where the deficiency is greater than twice the set tolerance.



The diagram below indicates tolerances for all bottle sizes filled.





187mL------------------------375mL-------------------------750mL-------------------------1000mL-------------



Fill volumes falling within this band are acceptable providing the run passes the average test.



178.6mL----------------------363.75mL---------------------735mL-------------------------985mL--------------



Fill volumes falling within this band are non standard, no more than 2.5% allowed.



170.2mL----------------------352.5mL----------------------720mL--------------------------970mL--------------



Fill volumes falling below here are inadequate, none permitted.



Ok...so our difficulty is at times , point 1) - and this is where the question of disregarding a result came up , if we retest immediately can it be done . My thought is no, but i've been asked to investigate. Agree with the latter half of your post , we are 'systematic sampling' and by and large it seems to work . However production people and QA people have different ideas about how to treat the data obtained, and the validity of such !

Dear Mr!

Beside following 3 basic requirements as above, you can apply SPC to control well

Dear Mr!

Beside following 3 basic requirements as above, you can apply SPC to control well

Dear MrQA,

Thks for link.

Looks like a relic of the Victorian Era.!

I remember seeing the Australian rules some time ago and they were much simpler. Seems that NZFA's standardisation program does not extend to Weights and Measures.

There are bits of the EC procedure (circa 1960s) here and there (eg the 2.5%) but it's basically a mish-mash to me. The EC procedure is statistically quite logically based and one-third the thickness. For weight of supermarket retail packages, i hv observed a system based on x-unit samples (x as mentioned in standard) from a line every 30mins or so and calculated sample / grand average net weights for the day together with the sample-based t1/t2 results. Even easier with a checkweigher/PC of course.
One did occasionally see a "blunder" value but the latitude for outliers is considerable enough to almost guarantee legal non-failure.

In many respects yr problem is the perennial case of how to minimise "how much (money) to give away?", sadly the more inaccurate the filling system, the greater the penalty, if one wishes to avoid legal embarrassment.

Charles.C

There has been a request that the 'out of spec' initial volume check be excluded from the average calculation. What are your thoughts on this? My thinking is that it is still a valid measurement and reflects the fill volume at the time of sample. I am concerned that we could be seen to be picking and choosing which data points we include so as to maniplulate the run average to suit our needs.

My view is that you can exclude the volume check if you exclude the product produced where the result is represented.

For instance if you started up the filler, the check was low and you wanted to discard the out of spec check this would be fine if you discarded the product. Otherwise you should include the check and providing the product was legal up your fill volume to bring your average up.

Some organisations will do this by increasing the sampling rate of in spec samples but this does mean in some way that you have deliberately manipulated your average fill figure.

Dear MrQA,

A few more comments.

IMO, the mathematical answer to yr original question is not to drop data unless statistically justifiable however if the situation is frequently occurring then you have a genuine problem anyway. Increasing sampling rates should allow a more accurate evaluation of the magnitude / cause of the problem (particularly for short runs).

The immediate solution is self-evident of course unless you can simply replace the machine with a known (better) one. The correct solution probably depends on the details.

Theoretically of course, it is not too difficult to predict the number of bottles falling substantially below 750ml by measuring the std.devn. Preferably before and after the problem of course. And for another (good) machine. (The proper analysis, eg ANOVA, does need a bit more statistical acumen and is best avoided if possible IMO unless you enjoy such things ).

If you had no problem before and you now hv a consistent problem, something must hv changed. It may hv been that you were already running close to the edge (yr current range suggests this ) so some small (new machine?) change pushed things negative. Or if results are now swinging much more, some other kind of set-up problem maybe. Only one line with problem ??

The standard is designed to deter people from (accurately / cleverly) producing right on the minimum acceptable level and / or poorly controlling the process. The EC standard has a similar concept but adds a little more statistical flexibility.

Rgds / Charles.C