Mathematical Optimization Techniques for the Simultaneous Apportionments of Reliability and Maintainability

This paper sets forth mathematical means for optimizing the simultaneous apportionments of reliability and maintainability by means of two techniques. Lagrange multipliers and dynamic programming. Since one of the constraint equations involves allocating both variables, this simultaneous apportionment problem differs from the usual two-dimensional dynamic programming problems. Two cost problems are treated the first minimizes cost while satisfying availability requirements under the assumption that an unlimited ceiling exists for the cost, and the second maximizes reliability and maintainability given a fixed budget. Although these problems appear closely related, step functions usually preclude considering them together. The paper also considers two numerical examples, an interesting cost model for maintainability, and using computers with its models.