A time series analysis of some interrelated logistics performance variables

This paper is a case study. We show how the powerful methods of time series analysis can be used to investigate the interrelationships between Alert Availability, a logistics performance variable, and Flying Hours, an operational requirement, in the presence of a major change in operating procedures and using contaminated data. The system considered is the fleet of C-141 aircraft of the U.S. Air Force. The major change in operating procedures was brought about by what is known as Reliability Centered Maintenance, and the contaminated data were due to anomalies in reporting procedures. The technique used is a combination of transfer function modeling and intervention analysis.     

The class of mifra lifetimes and its relation to other classes

In a previous paper, the authors have introduced a class of multivariate lifetimes (MIFRA) which generalize the univariate lifetimes with increasing failure rate average (IFRA). They have also shown that this class satisfies many fundamental properties. In this paper it is shown that other concepts of multivariate IFRA do not satisfy all of these properties. Relationships between MIFRA and these other concepts are given. Finally, positive dependence implications with respect to these classes are also discussed.     

On nonpreemptive strategies in stochastic scheduling

It is shown that there is an optimal strategy for a class of stochastic scheduling problems which is nonpreemptive. The results which yield this conclusion are generalizations of previous ones due to Glazebrook and Gittins. These new results also lead to an evaluation of the performance of nonpreemptive strategies in a large class of problems of practical interest.     

Postoptimality analysis in nonlinear integer programming: The right-hand side case

An algorithm is presented to gain postoptimality data about the family of nonlinear pure integer programming problems in which the objective function and constraints remain the same except for changes in the right-hand side of the constraints. It is possible to solve such families of problems simultaneously to give a global optimum for each problem in the family, with additional problems solved in under 2 CPU seconds. This represents a small fraction of the time necessary to solve each problem individually.     

The economic effects of inspector error on attribute sampling plans

In this paper the effects of inspector error on a cost-based quality control system are investigated. The system examined is of a single sampling plan design involving several cost components. Both type I and type II inspector errors are considered. The model employs a process distribution, thus assuming that a stochastic process of some kind governs the quality of incoming lots. Optimal plan design is investigated under both error-free and error-prone inspection procedures and some comparisons are made.     

Sequential determination of inspection epochs for reliability systems with general lifetime distributions

The problem of determining the optimal inspection epoch is studied for reliability systems in which N components operate in parallel. Lifetime distribution is arbitrary, but known. The optimization is carried with respect to two cost factors: the cost of inspecting a component and the cost of failure. The inspection epochs are determined so that the expected cost of the whole system per time unit per cycle will be minimized. The optimization process depends in the general case on the whole failure history of the system. This dependence is characterized. The cases of Weibull lifetime distributions are elaborated and illustrated numerically. The characteristics of the optimal inspection intervals are studied theoretically.     

Incremental approximation of optimal allocations

This paper concerns the approximation of optimal allocations by δ allocations. δ allocations are obtained by fixing an increment δ of effort and deciding at each step upon a single cell in which to allocate the entire increment. It is shown that δ allocations may be used as a simple method of approximating optimal allocations of effort resulting from constrained separable optimization problems involving a finite number of cells. The results are applied to find δ allocations (called δ plans) which approximate optimal search plans. δ plans have the property that as δ → 0, the mean time to find the target using a δ plan approaches the mean time when using the optimal plan. δ plans have the advantage that. they are easily computed and more easily realized in practice than optimal plans which tend to be difficult to calculate and to call for spreading impractically small amounts of effort over large areas.     

A defense allocation problem with development costs

In this paper, the mathematical model for the allocation of resources among a general mix of percentage vulnerable and of numerically vulnerable weapon systems is presented and solved. Percentage vulnerable systems consist of mobile weapons which are difficult to locate, but relatively easy to destroy once located; numerically vulnerable systems comprise easily located fixed base weapons which are difficult to destroy. The distinguishing feature of this analysis is the inclusion of development costs. The theory of max-min is extended as necessary to solve this problem. References are provided to a sequence of earlier versions of this problem.     

A convex property of an ordered flow shop sequencing problem

A flow shop sequencing problem with ordered processing time matrices is considered. A convex property for the makespan sequences of such problems is discussed. On the basis of this property an efficient optimizing algorithm is presented. Although the proof of optimality has not been developed, several hundred problems were solved optimally with this procedure.     

Queueing models for spares provisioning

A population of items which break down at random times and require repair is studied (the classic “machine repair problem with spares”). It is desired to determine the number of repair channels and spares required over a multiyear planning horizon in which population size and component reliability varies, and a service level constraint is imposed. When an item fails, a spare (if available) is immediately dispatched to replace the failed item. The failed item is removed, transported to the repair depot, repaired, and then placed in the spares pool (which is constrained to be empty not more than 10% of the time) unless there is a backlog of requests for spares, in which case it is dispatched immediately. The first model considered treats removal, transportation, and repair as one service operation. The second model is a series queue which allows for the separate treatment of removal, transportation, and repair. Breakdowns are assumed Poisson and repair times exponential.