Special examinations exist for many chronic diseases, which can diagnose the disease while it is asymptomatic, with no signs or symptoms. The earlier detection of disease may lead to more cures or longer survival. This possibility has led to public health programs which recommend populations to have periodic screening examinations for detecting specific chronic diseases, for example, cancer, diabetes, cardiovascular disease and so on. Such examination schedules when embedded in a public health program are invariably costly and are ordinarily not chosen on the basis of possible trade-offs in costs and benefits for different screening schedules. The possible candidate number of examination schedules is so large that it is not feasible to carry out clinical trials to compare different schedules. Instead, this problem can be investigated by developing a theoretical model which can predict the eventual disease specific mortality for different examination schedules. We have developed such a model. It is a stochastic model which assumes that i) the natural history of the disease is progressive and ii) any benefit from earlier diagnosis is due to a change in the distribution of disease stages at diagnosis (stage shift). The model is general and can be applied to any chronic disease which satisfies our two basic assumptions. We discuss the basic ideas of schedule sensitivity and lifetime schedule sensitivity and its relation to the reduction in disease specific mortality. Our theory is illustrated by applications to breast cancer screening. The investigation of schedules compares not only examination schedules with equal intervals between examinations but also staggered schedules using the threshold method. (Examinations are carried out when an individual's risk status reaches a preassigned threshold value.).