By Nicholas Harris

The 01/01/2014

The 01/01/2014

Regulatory texts tend by nature to make for tedious reading, but when it comes to controlling weights and capacities for prepackaged products, they also call upon mathematical notions of the laws of statistics, which can be quite complex. It was the rise of supermarkets in the 1960s and 1970s that drove the decline in the retail trade, where the required quantity of a product stored in bulk was weighed out in front of the customer. More and more products were presented "prepacked", and "prepackaging" effectively became the most common form for packaging commodities.

Bottled liquid foodstuffs undoubtedly represent the oldest form of prepackaging through the ages, with the trading of wine and olive oil in amphorae on a truly industrial scale in Roman times and probably well before, as witnessed by numerous archaeological remains. There is no doubt that the question of guaranteeing the volumes purchased was already subject to regulations in accordance with the forms - and the punishments - of the time.

Much more recently, it is the expansion of the prepackage markets that led the legislator to examine in greater depth the question of the guarantee of the weights and capacities of prepackaging for the consumer. Indeed, any method of automatic industrial metering inevitably includes a degree of random variability which can be assumed to obey a statistical distribution that is fairly similar to a "normal" distribution centred on a mean value. The legislator has acknowledged that with prepackaging it is necessary to make an exception to the basic principle that the delivered quantity must be at least equal to the stated quantity, resulting from Article L213-1 of the French Consumer Code. The legislator has therefore instituted, through Decree 78-166 and the Order of 20 October 1978 "relative to the metrological controlling of prepackaging", the principle that the delivered quantity can occasionally be slightly less than the stated value, on condition that:

- The quantity delivered is
__on average__at least equal to the stated quantity for a given prepacked product; - That the missing quantity does not exceed a specified limit.

but the operations to verify conformity with such criteria require a slightly more advanced notion of statistics.

The reason for this is that the verifications performed by the government authorities will, in principle, only involve a small number of samples compared with the entire production volume monitored. This is all the more the case with destructive tests, which are necessary if the content cannot be verified without separating it from its packaging. The regulations propose limiting the number of inspected articles in such cases to 20 per commercialised product batch. Products in glass packaging are particularly concerned by this limit because of the relative variability of the tare weight (that is to say the weight of the package itself).

In such cases the probability that the mean measured on a small number of samples could be slightly different from the "true" mean of the entire population should be taken into account. The calculation uses the statistical law known as the Student's t-distribution, developed in the early 20th century by William Gosset ("Student" was his pseudonym), a chemist and mathematician employed by the Guinness brewery in Dublin for selecting varieties of brewing barley.

In such cases the probability that the mean measured on a small number of samples could be slightly different from the "true" mean of the entire population should be taken into account. The calculation uses the statistical law known as the Student's t-distribution, developed in the early 20th century by William Gosset ("Student" was his pseudonym), a chemist and mathematician employed by the Guinness brewery in Dublin for selecting varieties of brewing barley.

in verification, the mean of the capacity measured on the sample may be less than the nominal value within the limit of a statistical uncertainty defined according to the standard deviation of the measurement. This tolerance on the mean observed volume can obviously only be of a statistical nature and does not change the principle that the quantity delivered shall on average equal the stated quantity for all the production batches.

At the time it seems that this incursion of statistics into the regulations gave rise to a degree of suspicion on the part of judges, accustomed to more clear-cut criteria of culpability where assumed fraud was concerned. One must indeed praise the pragmatism of the regulators of that time for the way they took the technical realities into account*.

The bottler should be able to prove, by the records of its own verifications, that the average quantity supplied is indeed at least equal to the nominal quantity. Here again, Student's t-distribution can be usefully applied to calculate the acceptable deviations in nominal volume within the limits of statistical uncertainty according to the number of samples tested, this number being determined according to the rate and observed variability of the bottling process.

Cetie Quality Guidelines No. 9 "Control of filling volumes of product prepacked in glass containers" gives practical advice about the verifications to put in place to comply with the regulations for production processes that are subject to this obligation. This document, due for review by a working group in 2014, is - we hope - much easier to digest than the regulations themselves.

At the time it seems that this incursion of statistics into the regulations gave rise to a degree of suspicion on the part of judges, accustomed to more clear-cut criteria of culpability where assumed fraud was concerned. One must indeed praise the pragmatism of the regulators of that time for the way they took the technical realities into account*.

The bottler should be able to prove, by the records of its own verifications, that the average quantity supplied is indeed at least equal to the nominal quantity. Here again, Student's t-distribution can be usefully applied to calculate the acceptable deviations in nominal volume within the limits of statistical uncertainty according to the number of samples tested, this number being determined according to the rate and observed variability of the bottling process.

Cetie Quality Guidelines No. 9 "Control of filling volumes of product prepacked in glass containers" gives practical advice about the verifications to put in place to comply with the regulations for production processes that are subject to this obligation. This document, due for review by a working group in 2014, is - we hope - much easier to digest than the regulations themselves.

Published in Liquides & Conditionnement N°370 (April 2014)

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