Computational expressions for point availability and average availability of a system of components each of which is subject to random failures and has random restoration times are determined. Each component is assumed to have a fixed number of spares such that where all spares are exhausted no restoration can take place. These expressions are useful in deciding PL and ASL in the military logistic applications. Given a fixed length of mission duration and finite number of spares, a system may not be available at the end of a mission due to lack of spares. The probability distribution of system down time due to lack of spares is determined as a function of number of spares and mission duration.

The generalized goal decomposition model proposed by Ruefli as a single period decision model is presented for the purpose of a review and extended to make a multiple period planning model. The multiple period planning model in the three level organization is formulated with, linear goal deviations by introducing the goal programming method. Dynamic formulation using the generalized goal decomposition model for each single period problem is also presented. An iterative search algorithm is presented as an appropriate solution method of the dynamic formulation of the multiple period planning model.

A replacement policy for a finite time span is proposed for the cumulative process where an item can fail only when the total amount of deterioration exceeds a prespecified failure level. The optimal deterioration limit level is determined to minimize the total cost expected per unit for a given time span. An illustrative example in case of periodically inspected reformer tubes in ammonia plant is also presented.