Joint determination of optimum variable and attribute target means

This article considers the problem of joint control of attribute and variable quality characteristics of a given product. Items are acceptable if they meet the specifications for both types of quality characteristics at the same time. Otherwise, the items are sold as scrap at reduced prices. The objective is to determine simultaneously the target values for each characteristic so as to maximize the expected profit per item. Several item-by-item quality-inspection plans are formulated on the basis of various inspection strategies. These strategies are defined in terms of whether the inspection is to be carried out simultaneously for both characteristics, or sequentially, or whether inspection for one of the characteristics is to be ignored. All these plans are shown to differ in terms of their profitability. However, they all yield equivalent quality standards. A numerical example is provided to illustrate the application of these models.     

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.     

On maximum internally stable sets of a graph

The paper makes some remarks on the paper of Hakimi and Frank and shows a simplified way of applying the concept of alternating forest. An algorithm for finding a maximum internally stable set of an undirected graph is constructed and some examples are given.     

A queue with waiting time dependent service times

Sufficient conditions are developed for the ergodicity of a single server, first-come-first-serve queue with waiting time dependent service times.     

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.     

Decision rules for attacking targets of opportunity

Frequently in warfare, a force is required to attack a perishable enemy target system - a target system where the targets are detected seemingly at random, and if not immediately attacked, will shortly escape from detection. A conflicting situation arises when an attack element detects a target of relatively low value and has to decide whether to expend his resources on that particular target or to wait for a more lucrative one, hoping one will be found. This paper provides a decision rule giving the least valued target that should be attacked as well as the resources that should be expended as a function of the attack element's remaining mission time.     

The conjugate gradient technique for certain quadratic network problems

We consider a class of network flow problems with pure quadratic costs and demonstrate that the conjugate gradient technique is highly effective for large-scale versions. It is shown that finding a saddle point for the Lagrangian of an m constraint, n variable network problem requires only the solution of an unconstrained quadratic programming problem with only m variables. It is demonstrated that the number of iterations for the conjugate gradient algorithm is substantially smaller than the number of variables or constraints in the (primal) network problem. Forty quadratic minimum-cost flow problems of various sizes up to 100 nodes are solved. Solution time for the largest problems (4,950 variables and 99 linear constraints) averaged 4 seconds on the CBC Cyber 70 Model 72 computer.     

Multichannel queueing systems with heterogeneous classes of arrivals

In an integrated telecommunications network, voice and data traffic compete for the same transmission facilities. Assuming Poisson arrivals and exponential service with different rates, analytic expressions are obtained for measures of performance such as blocking probability and average delay under the following operating rule: class 1 traffic behaves as a loss system while class 2 traffic is buffered when all channels are busy. In view of the inordinate amount of computational effort needed when the number of channels is large, simple approximations have been suggested.