Geometry of the total time on test transform

Total time on test (TTT) plots provide a useful graphical method for tentative identification of failure distribution models. Identification is based on properties of the TTT transform. New properties of the TTT transform distribution are obtained. These results are useful to the user of TTT plots. Although IFR (DFR) distributions are particularly easy to identify from TTT plots, the user must exercise caution relative to identification of IFR A (DFRA) distributions.     

A complete importance ranking for components of binary coherent systems,with extensions to multi-state systems

Means of measuring and ranking a system's components relative to their importance to the system reliability have been developed by a number of authors. This paper investigates a new ranking that is based upon minimal cuts and compares it with existing definitions. The new ranking is shown to be easily calculated from readily obtainable information and to be most useful for systems composed of highly reliable components. The paper also discusses extensions of importance measures and rankings to systems in which both the system and its components may be in any of a finite number of states. Many of the results about importance measures and rankings for binary systems are shown to extend to the more sophisticated multi-state systems. Also, the multi-state importance measures and rankings are shown to be decomposable into a number of sub-measures and rankings.     

Coordinated replenishments of items under time-varying demand: Dynamic programming formulation

We consider a group (or family) of items having deterministic, but time-varying, demand patterns. The group is defined by a setup-cost structure that makes coordination attractive (a major setup cost for each group replenishment regardless of how many of the items are involved). The problem is to determine the timing and sizes of the replenishments of all of the items so as to satisfy the demand out to a given horizon in a cost-minimizing fashion. A dynamic programming formulation is illustrated for the case of a two-item family. It is demonstrated that the dynamic programming approach is computationally reasonable, in an operational sense, only for small family sizes. For large families heuristic solution methods appear necessary.     

A partitioning technique for obtaining solutions to the modularization problem

A significant problem in electronic system design is that of partitioning the functional elements of an equipment schematic into subsets which may be regarded as modules. The collection of all such subsets generated by a particular partitioning forms a potential modular design. The specific problem is to determine that partitioning of the schematic that minimizes a cost function defined on the subsets subject to specified hardware, design, packaging, and inventory constraints. This problem is termed the modularization problem. This paper presents a method for obtaining restricted solutions to the modularization problem by employing some recent developments in linear graph theory obtained by one of the coauthors. Numerical results from the solution of several typical problems are presented.     

Optimization in mixed-integer space with a single linear bound

The search for an optimal point in a mixed-integer space with a single linear bound may be significantly reduced by a procedure resembling the Lagrangian technique. This procedure uses the coefficients of the linear bound to generate a set of necessary conditions that may eliminate most of the space from further consideration. Enumerative or other techniques can then locate the optimum with greater efficiency. Several methods are presented for applying this theory to separable and quadratic objectives. In the maximization of a separable concave function, the resulting average range of the variables is approximately equal to the maximum (integer) coefficient of the constraint equation.     

Maintenance policies when failure distribution of equipment is only partially known

An optimal schedule for checking an equipment subject to failure which can be detected by inspection only, is derived. Increasing failure rate and one percentile specify the otherwise unknown life distribution. Dynamic programming methodology yields the solution which minimizes the maximum expected cost. Numerical examples are presented and compared with models employing differing amounts of knowledge.     

On the economic application of airlift to product distribution and its impact on inventory levels

In many resupply situations, the decisionmaker has the option of “purchasing” faster replenishment leadtimes. For example, a premium may be paid for delivery by parcel post rather than slower but less expensive delivery by railway express. It may be economically advantageous to pay shipment premiums for faster leadtimes when considering the possible cost reductions in pipeline (on-order) inventory and safety stock levels. This paper develops a decision rule which, for any given item, will indicate whether it is economically advantageous to purchase a faster leadtime. The general methodology is then applied to a peacetime military resupply operation involving several million items, each requiring a decision as to whether the item should be shipped by air or sea.     

The payment scheduling problem

Large complicated projects with interdependent activities can be described by project networks. Arcs represent activities, nodes represent events, and the network's structure defines the relation between activities and events. A schedule associates an occurrence time with each event: the project can be scheduled in several different ways. We assume that a known amount of cash changes hands at each event. Given any schedule the present value of all cash transactions can be calculated. The payment scheduling problem looks for a schedule that maximizes the present value of all transactions. This problem was first introduced by Russell [2]; it is a nonlinear program with linear constraints and a nonconcave objective. This paper demonstrates that the payment scheduling problem can be transformed into an equivalent linear program. The linear program has the structure of a weighted distribution problem and an efficient procedure is presented for its solution. The algorithm requires the solution of triangular systems of equations with all matrix coefficients equal to ± or 0.