Snapshot 1: a product having a long shelf life that becomes perishable after package opening (log-linear plot with a time scale of days)
Snapshot 2: a product having a long shelf life that is also fairly stable after package opening (linear plot with a time scale of days)
Snapshot 3: a product having a short shelf life that becomes even more perishable after package opening (linear plot with a time scale of days)
Snapshot 4: a very stable pharmaceutical product having a long shelf life that is also fairly stable after package opening (log-linear plot with a time scale of months)
The shelf life of perishable food and pharmaceutical products is principally of concern to their manufacturers and can become a safety issue to the consumer. Usually, the term "shelf life" is associated with the expiration date, which indicates how long the product can be stored before being sold or consumed.
According to Nicoli and Calligaris , both the manufacturer and consumer ought to be more attentive to the fact that most if not all food and pharmaceutical products have two shelf lives, one in the sealed package or container, which they call primary, and another after it has been opened by the consumer, which they call secondary. Both shelf lives depend on several factors (e.g., whether the opened container is kept refrigerated), many of them difficult to control, and they vary dramatically between different kinds of products. For example, rice, pasta or pepper, unless abused, can last quite a long time after their original package has first been opened, and the same can be said about pills such as aspirin. In extreme contrast, canned sardines or wine, which can last for years in the hermetically sealed aluminum can or corked bottle, may spoil in a day or two after the container is opened. The same applies to certain pills, which at least partly for this reason are packaged individually or protected in other ways.
The concept of primary and secondary shelf life has been illustrated by a schematic drawing showing two decay curves; one continuous, showing the quality loss in the sealed package, and the second discontinuous, showing the loss before and then after the package opening. The two shelf lives are indicated by the points where the curves cross the chosen threshold line . This Demonstration expands the plot in  so that it can describe the various types of relationships between the primary and secondary shelf lives, at least qualitatively.
A single-term exponential decay is used in this Demonstration to represent the quality loss before and after the package opening,
, respectively, with two corresponding characteristic times
). The two decay patterns are then described by:
is the time when the package is opened. For simplicity,
are normalized decay functions, that is, with a range from zero to one, and
is in arbitrary units (arb. units), which can be assigned days, weeks or months as appropriate, or in the case of extremely perishable medical products, hours.
The chosen threshold
that determines the two shelf lives is shown as a red horizontal line. The times of its crossing by the
, are the sought primary and secondary shelf lives, respectively. They are extracted by solving the equations
All of the model parameters are entered with sliders.
The calculated values of
are displayed above the plot, whose type can be chosen as "linear" or "log-linear" by clicking the "plot type" setter bar.
The purpose of this Demonstration is to illustrate the concept, not to describe the shelf lives of any particular food or pharmaceutical product, and hence not all parameter combinations must have a counterpart in reality. Nevertheless, it does allow an unlikely scenario in which the package is opened after the primary shelf life has passed but not when the product becomes more stable after the package has been opened.
 M. C. Nicoli and S. Calligaris, "Secondary Shelf Life: An Underestimated Issue," Food Engineering Reviews
(2), 2018 pp. 57–65. doi:10.1007/s12393-018-9173-2