Estimating reliability of components with increasing failure rate using series system data

The maximum likelihood estimator (MLE) for a distribution function with increasing failure rate is derived, based on a collection of series system data. Applications can arise in industries where operating environments make available only such system-level data, due to system configuration or type-II censoring. The estimator can be solved using isotonic regression. For the special case in which systems contain one component, the estimator is equivalent to the restricted maximum likelihood estimator of Marshall and Proschan [9]. The MLE is illustrated using emergency diesel generator failure data from the nuclear industry. © 1998 John Wiley & Sons, Inc. Naval Research Logistics 45: 115–123, 1998     

A squared-euclidean distance location-allocation problem

This article is concerned with the analysis of a squared-Euclidean distance location-allocation problem with balanced transportation constraints, where the costs are directly proportional to distances and the amount shipped. The problem is shown to be equivalent to maximizing a convex quadratic function subject to transportation constraints. A branch-and-bound algorithm is developed that utilizes a specialized, tight, linear programming representation to compute strong upper bounds via a Lagrangian relaxation scheme. These bounds are shown to substantially dominate several other upper bounds that are derived using standard techniques as problem size increases. The special structure of the transportation constraints is used to derive a partitioning scheme, and this structure is further exploited to devise suitable logical tests that tighten the bounds implied by the branching restrictions on the transportation flows. The transportation structure is also used to generate additional cut-set inequalities based on a cycle prevention method which preserves a forest graph for any partial solution. Results of the computational experiments, and a discussion on possible extensions, are also presented.     

Waiting times for M/G/1 queues with service-time or delay-dependent server vacations

This article shows how to determine the stationary distribution of the virtual wait in M/G/1 queues with either one-at-a-time or exhaustive server vacations, depending on either service times or accrued workload. For the first type of dependence, each vacation time is a function of the immediately preceding service time or of whether the server finds the system empty after returning from vacation. In this way, it is possible to model situations such as long service times followed by short vacations, and vice versa. For the second type of dependence, the vacation time assigned to an arrival to follow its service is a function of the level of virtual wait reached. By this device, we can model situations in which vacations may be shortened whenever virtual delays have gotten excessive. The method of analysis employs level-crossing theory, and examples are given for various cases of service and vacation-time distributions. A closing discussion relates the new model class to standard M/G/1 queues where the service time is a sum of variables having complex dependencies. © 1992 John Wiley & Sons, Inc.     

The reporting time problem: Integration of intelligence with verification

This article is a theoretic study of the following problem in verification: Mobile units under control of an agent, whom we call the HIDER, travel on a known transportation network and must at the conclusion of their itinerary report locations at fixed time intervals to a monitoring authority, whom we call the SEEKER. The purpose of this reporting requirement is to verify that illegal units do not infiltrate the network from sources under the control of the HIDER. We assume that the SEEKER has an independent intelligence-gathering capability which gives sightings of both legal and illegal units. The purpose of this article is to quantify the advantage of frequent over infrequent reporting. © 1992 John Wiley & Sons, Inc.     

Evaluation of an integrated supplier-buyer quality-control system

In this article, a quality-control design framework that employs information for the supplier-buyer system is modeled. Significant operational savings may be obtained by using the integrated plans developed under this framework. This is especially true when the cost of a defective is high, and the variable sampling and rework costs are low. Analysis of the interaction of defective, rework, and variable sampling costs reveals that the savings are the result of a shift of control effort from the process-control to the lot-acceptance stage, which is the consequence of tradeoffs involving both stages. The managerial impact of adopting integrated plans is discussed.     

Some two-on-two homogeneous stochastic combats

In this article we consider two versions of two-on-two homogeneous stochastic combat and develop expressions, in each case, for the state probabilities. The models are natural generalizations of the exponential Lanchester square law model. In the first version, a marksman whose target is killed resumes afresh the killing process on a surviving target; in the second version, the marksman whose target is killed merely uses up his remaining time to a kill on a surviving target. Using the state probabilities we then compute such important combat measures as (1) the mean and variance of the number of survivors as they vary with time for each of the sides, (2) the win probabilities for each of the sides, and (3) the mean and variance of the battle duration time. As an application, computations were made for the specific case of a gamma (2) interfiring time random variable for each side and the above combat measures were compared with the appropriate exponential and deterministic Lanchester square law approximations. The latter two are shown to be very poor approximations in this case.     

The shortest queue model with jockeying

In this article we deal with the shortest queue model with jockeying. We assume that the arrivals are Poisson, each of the exponential servers has his own queue, and jockeying among the queues is permitted. Explicit solutions of the equilibrium probabilities, the expected customers, and the expected waiting time of a customer in the system are given, which only depend on the traffic intensity. Numerical results can be easily obtained from our solutions. Several examples are provided in the article.     

A network reformulation of an electric utility expansion planning model

We reformulate a multiperiod capacity expansion model of electric utilities as a network model. We show how to reconstruct the dual solution of the original mathematical program from the network model solution. To formulate the network model, we use information about the properties of the optimal solution of the mathematical program to reduce the number of constraints. The remaining constraints are then readily converted into network constraints. © 1993 John Wiley & Sons. Inc.     

A game with distorted information

This article considers a two-person game in which the first player has access to certain information that is valuable but unknown to the second player. The first player can distort the information before it is passed on to the second player. The purpose in distorting the information is to render it as useless as possible to the second player. Based on the distorted information received, the second player then maximizes some given objective. In certain cases he may still be able to use the distorted information, but sometimes the information has been so badly distorted that it becomes completely useless to him. © 1993 John Wiley & Sons, Inc.