Transient analysis of multiple-unit reliability systems

A general Markovian model representing several multiple-unit redundant repairable systems is proposed and its transient behavior is studied. Specifically, for multiple-unit reliability system the reliability and availability functions are derived in an explicit form for the transient case. The stationary availability and mean time to system failure are deduced from the main results as special cases.     

Application of dirichlet integrals for curtailment problems in sampling inspection

The standard problem in sampling inspection is to consider plans with and without curtailment. Curtailment causes difficulty and authors rarely give exact results (i.e., exact OC and ASN functions) for curtailed procedures. In this article we regard curtailment as an inverse sampling procedure and use Dirichlet integrals to obtain exact formulas for the OC, the ASN, and also the variance of the number of observations required under three types of plans: no curtailment, semicurtailment (for rejection only) and two-sided curtailment. Different sections of the article deal with the single sample, the two-stage, and the multiple-stage sampling problems. New tables for carrying out the single-sample procedure are included in the article. The authors feel that this article presents new directions and new ways of dealing with problems associated with quality control.     

A model for critical crack size estimation in fatigue failure of gun barrels

With repeated firing, fatigue cracks are produced in a gun barrel, and the barrel is no longer useful when a crack reaches a critical size. The initial crack size and the critical crack size, as well as the number of firings producing the critical crack size, may be considered as random variables. Assuming a proportional damage model for crack growth, a method for estimating the critical crack size distribution is presented. From these results, an estimate of the barrel life, or the residual barrel life once a crack of a given size is measured, can be obtained.     

Incorporating redundancy considerations into stockage models

This article is concerned with evaluating the impact on weapon system availability of component and assembly redundancy. The evaluation must be efficient, and it must be possible to integrate the evaluation into multiechelon stockage models whose objective is to find the least cost mix of stockage consistent with the availability goals for weapon (or other type) systems. The mathematics to be discussed here provides a rigorous solution to the evaluation problem when there is only a single supply echelon; there can be upper-echelon repair, but not supply, unless the supply is from a “perfect” supplier, always in stock. For the more general multiechelon case, approximate approaches are presented.     

Facility location on a grid with a diagonal line

This article extends the traditional median problem on a grid to include a diagonal line (e.g., a street). In contrast to the traditional median problem, this generalized problem is nonconvex and nonseparable, invalidating some of the properties on which well-known median-seeking algorithms are based. This work presents an algorithm for finding the median on this generalized grid and discusses the relationship between it and the traditional median.     

Assemble to order and assemble in advance in a single-period stochastic environment

Faced with stochastic demand, a firm may decide to assemble its products in advance or assemble them once actual demand is realized. In general, the production cost for items assembled in advance (AIA) is lower than for items assembled to order (ATO), because there is no need to expedite, and the production process can be planned and executed well in advance. On the other hand, items assembled in advance (AIA) for which there is no demand incur excessive and unnecessary assembly costs. The two policies, AIA and ATO, as well as a composite one, are compared and analyzed in light of these trade-offs. The composite model, which is shown as the dominating policy, is also extended to deal with the following two scenarios. The first assumes a loss of a fraction of the demand when demand cannot be satisfied from the shelf but rather through ATO. The second considers the effects of budget constraints on the total inventory cost. © 1995 John Wiley & Sons, Inc.     

Single-machine scheduling with early and tardy completion costs

We address a single-machine scheduling problem in which penalties are assigned for early and tardy completion of jobs. These penalties are common in industrial settings where early job completion can cause the cash commitment to resources in a time frame earlier than needed, giving rise to early completion penalties. Tardiness penalties arise from a variety of sources, such as loss of customer goodwill, opportunity costs of lost sales, and direct cash penalties. Accounting for earliness cost makes the performance measure nonregular, and this nonregularity has apparently discouraged researchers from seeking solutions to this problem. We found that it is not much more difficult to design an enumerative search for this problem than it would be if the performance measure were regular. We present and demonstrate an efficient timetabling procedure which can be embedded in an enumerative algorithm allowing the search to be conducted over the domain of job permutations.© 1993 John Wiley & Sons, Inc.     

Discrete repairable reliability systems

Consider a reliability system consisting of n components. The failures and the repair completions of the components can occur only at positive integer-valued times k ϵ N₊₊ ϵ (1, 2, …). At any time k ϵ N₊₊ each component can be in one of two states: up (i.e., working) or down (i.e., failed and in repair). The system state is also either up or down and it depends on the states of the components through a coherent structure function τ. In this article we formulate mathematically the above model and we derive some of its properties. In particular, we identify conditions under which the first failure times of two such systems can be stochastically ordered. A variety of special cases is used in order to illustrate the applications of the derived properties of the model. Some instances in which the times of first failure have the NBU (new better than used) property are pointed out. © 1993 John Wiley & Sons, Inc.