A Markov chain is a series of events in which the probability of an event depends on the immediately preceding event. An example is the game of blackjack in which the probability of certain cards being dealt is dependent upon what cards have already been dealt. In the analysis of bad debts, preceding events, such as collections, credit policy changes, and write offs, affect the probabilities of future losses.

Prevention costs are incurred to prevent defects. Appraisal costs are incurred to detect defective output during and after the production process. Internal failure costs are associated with defective output discovered before shipping. External failure costs are associated with defective output discovered after it has reached the customer.