Wallace Blischke provided an overview of the analysis of warranties and life-cycle costs. Analysis of life-cycle costs typically is carried out from the point of view of the producer, examining the costs of a system from conception to withdrawal from the marketplace. The earlier life-cycle and associated costs can be estimated, the better it is for the decision maker, though the earlier in development these estimates are attempted, the more difficult they are to produce. Blischke stated his preference for a Bayesian approach in this effort, since that paradigm provides a basis for the use of engineering judgment and information derived from similar systems, as well as a natural method for updating predictions.

It is important not only that reliable estimates of life-cycle costs be produced, but also that reliable estimates of their uncertainty also be developed and communicated to assist in decision making. Further, an understanding of the origin of the uncertainties can help in assessing how best to improve the quality of future predictions. This is especially true for defense systems, which of course can be much more complex than consumer goods. (For example, costs for defense systems sometimes include disposal costs, which can be nontrivial.)

The Bayesian approach is initiated before initial testing with the use of all available information to form a prior distribution describing system reliability. Prototypes are then produced and tested. The data from these tests are employed using Bayes’ theorem to update the prior distribution to form a posterior distribution, and the posterior distribution is used in turn to produce estimates and prediction intervals concerning parameters that govern life-cycle costs, the profitability of warranties, and related constructs.

As an example, Blischke discussed the analysis of life-cycle costs for a propulsion system in development. To achieve a required level of reliability, preliminary reliability levels are specified for the basic subsystems and components. Some of the standard tools used for this purpose are fault trees; reliability block diagrams; and failure modes, effects, and criticality analysis. One important issue is whether reliability problems are due to the design, the process, or the operations. Often, operational errors are more important than design errors. Engineering judgment based, for example, on information on components used in previous propulsion systems, can support a preliminary Bayesian assessment of system reliability (although such information will be very limited when the system involves a new tech-