Ageing concepts for discrete data — A relook

Many a times a product lifetime can be described through a nonnegative integer valued random variable. For example, a piece of equipment operates in cycles and the experimenter observes the number of cycles successfully completed prior to failure. A frequently referred example is a Xerox machine whose life length would be the total number of copies it produces before the failure. Another example is the length of the hospital stay of patients who were hospitalized due to an accident. We review ageing concepts like ILR, IHR, IHRA, NBU, NBUE, MRL, etc for discrete random variables and look at stochastic orderings between two discrete random variables.