Basic considerations on the calculation of the trippage number for returnable containers
Authors: Bojkow E. 
Published: November 2006

AbstractThe trippage number of returnable containers has a central position in economic, calculations and in comparing the environmental impacts of disposable and returnable container systems. Extremely varying trippage numbers are frequently reported for the same type of container, usually without any reference to the method of calculation. Only a few authors have published basic considerations on the calculation of the trippage number. Different methods of calculation have been recommended and different definitions of what should be understood by the ‘trippage number’ have been given.To investigate what is really achieved by these kinds of calculation, a model system, performing all the functions of a returnable container system in practice, for system analysis by computer simulation was established. By means of this model system it was found that in the lifetime of a container population one can differentiate between three kinds of populations, each one with an individual mean trippage number:
the average trippage number of all containers put into circulation
the average trippage number of all lost containers
the average trippage number of all existing containers, representing the total stock of circulating containers
Emanating from these basic considerations, it was found that the actual average trippage number of all containers put into circulation after ‘x’ fillings (Ux) can be calculated exactly by the quotientof the sum of all filled containers (ΣN) and the sum of all containers put into circulation (ΣE) since the first day of use of a container type according to the following expression

It must be stated that correct results can only be achieved by taking into account all containers filled or put into circulation from the very first day of use. Despite this drawback, this kind of calculation has the advantage of being based on figures that are available and easily retraceable for almost all filling‐plants.After the first circulation, the average trippage number (Ux) is equal to 1.0, rising with each circulation because of its tendency to approximate to a constant final value after an infinite number of fillings (Ux→∞), which can be calculated by the quotient of the sum of all filled containers (ΣN) and the sum of all lost containers (ΣA) since the first day of use of a container type, represented by the inverse value of the proportion of lost containers (a) or its complement, the share of refillable containers (r), according to

This (theoretical) final value is approximated by each partial population (the population of all input new containers, of all lost and all existing containers) but with a different velocity, dependent on the parameters a=1−r (the loss rate) and rz =1−b (the rate of containers returning to the filling‐plant from the total stock of existing containers). The number of circulations needed to approach this final value rises with a decreasing share of lost containers (a) and with a decreasing share of containers returning to the filling plant (rz) from the total container stock. The calculation by the inverse value of the share of lost containers (l/a ) is therefore not relevant to the calculation of the actual average trippage number of any partial population (number of new containers put into circulation, lost containers or stock of all existing containers). To receive correct results, also for this calculation, it is necessary to take into account all containers filled or lost from the very first day of use. This may be troublesome with a container type used by many filling‐plants and with traditional old containers, where the necessary figures are no longer available. A further drawback of this kind of calculation is that the number of lost containers cannot be calculated exactly, because of the uncertainty of whether all containers, for which the plant holds the deposit, exist or not. Therefore the share of lost containers is mostly set too low, which results in the calculation of too high a trippage number.