Statistical models for intercepted data.

Consider a population of replaceable items, of different ages, and suppose that for each item there is a certain measurable attribute which is a monotone function (perhaps random) of the item's age. To fix ideas, we refer to this attribute as 'deterioration' and we assume that as items age their level of deterioration increases. We further assume that as the level of deterioration hits a certain (unknown) threshold value, the item dies and disappears from the population, so that it is not available for sampling anymore. Note that since items that deteriorate at a slower rate live longer, any sample which is obtained over a short period of time would over represent slowly deteriorating items. Consequently, under such circumstances longitudinal studies are often needed in order to statistically study deterioration as a function of age.