F.A. van der Duyn Schouten

Maintenance optimization of a production system with buffer capacity

Abstract We consider a deteriorating installation, which supplies input to a subsequent production system. The installation is provided with a buffer to cope with unexpected failures of the installation, which may cause interruptions of the production process. By preventive maintenance on the installation a further improvement of the production process can be obtained. In this paper we consider a preventive maintenance policy, which is based not only on the information about the age of the installation but also on the content of the subsequent buffer. For this integrated maintenance-production problem, we analyse a class of control limit policies which are nearly optimal and easy to implement. The analysis is based on the embedding technique from Markov decision theory. In addition, we provide a characterization of the overall optimal policy and report on numerical comparisons of the best control limit policy with the overall optimal policy and other reference policies.

Reliability and Maintenance of Complex Systems

Stochastic Models of Reliability and Maintenance: An Overview.- Fatigue Crack Growth.- Predictive Modeling for Fatigue Crack Propagation via Linearizing Time Transformations.- The Case for Probabilistic Physics of Failure.- Dynamic Modelling of Discrete Time Reliability Systems.- Reliability Analysis via Corrections.- Towards Rational Age-Based Failure Modelling.- Maintenance Policies for Multicomponent Systems: An Overview.- Complex Systems in Random Environments.- Optimal Replacement of Complex Devices.- A Framework for Single-Parameter Maintenance Activities and Its Use in Optimisation, Priority Setting and Combining.- Economics Oriented Maintenance Analysis and the Marginal Cost Approach.- Availability Analysis of Monotone Systems.- Optimal Replacement of Monotone Repairable Systems.- How to Determine Maintenance Frequencies for Multi-Component Systems? A General Approach.- A Probabilistic Model for Heterogeneous Populations and Related Burn-in Design Problems.- An Overview of Software Reliability Engineering.- The Operational Profile.- Assessing the Reliability of Software: An Overview.- The Role of Decision Analysis in Software Engineering.- Analysis of Software Failure Data.- Simulation: Runlength Selection and Variance Reduction Techniques.- Simulation: Sensitivity Analysis and Optimization Through Regression Analysis and Experimental Design.- Markov Dependability Models of Complex Systems: Analysis Techniques.- Bounded Relative Error in Estimating Transient Measures of Highly Dependable Non-Markovian Systems.- Maintenance Management System: Structure, Interfaces and Implementation.- PROMPT, A Decision Support System for Opportunity-Based Preventive Maintenance.- Maintenance Optimisation with the Delay Time Model.- List of Contributors.

Analysis and computation of (n, N)-strategies for maintenance of a two-component system

Abstract In this paper ( n , N )-strategies are investigated for the maintenance of a two component series system. Vergin and Scriabin [8] provided some numerical evidence on the near-optimality of this type of policies. In a recent paper, Ozekici [5] gave a characterization of the structure of the optimal policy and its possible deviations from the ( n , N )-structure for the discounted cost criterion. The same kind of structure is shown to hold for the average cost criterion. In view of the complicated form of the optimal policy and the near-optimality of the ( n , N )-policies we present a fast computational method to compute the average costs under a given ( n , N )-policy. This method is based on a well-known embedding technique. Moreover, a heuristic based on this computational method, is presented by which the optimal values of n and N can be determined.

A Markov decision algorithm for optimal inspections and revisions in a maintenance system with partial information

Abstract This paper deals with a gradually deteriorating equipment whose actual degree of deterioration can be revealed by inspections only. An inspection can be succeeded by a revision depending on the systems degree of deterioration. In the absence of inspections and revisions, the working condition of the system evolves according to a Markov chain whose changes of state are not observable with the possible exception of a breakdown. Examples of this model include production machines subject to stochastic breakdowns, and maintenance of communication systems. The cost structure of the model consists of inspection, revision and operating costs. It is intuitively reasonable that in many applications a simple control-limit rule will be optimal. Such a rule prescribes a revision only when inspection reveals that the degree of deterioration has exceeded some critical level. A special-purpose Markov decision algorithm operating on the class of control-limit rules is developed for the computation of an average cost optimal schedule of inspections and revisions.

Inventory control with two switch-over levels for a class of M/G/1 queueing systems with variable arrival and service rate

This paper deals with inventory control in a class of M/G/1 queueing systems. At each point of time the system can be switched from one of two possible stages to another. The rate of arrival process and the service rate depend on the stage of the system. The cost structure imposed on the model includes both fixed switch-over costs and a holding cost at a general rate depending on the stage of the system. The rule for controlling the inventory is specified by two switch-over levels. Using an embedding approach, we will derive a formula for the long-run average expected costs per unit time of this policy. By an appropriate choice of the cost parameters, we may obtain various operating characteristics for the system amongst which the stationary distribution of the inventory and the average number of switch-overs per unit time.

Group Testing Models with Processing Times and Incomplete Identification

We consider the group testing problem for a finite population of possibly defective items with the objective of sampling a prespecified demanded number of nondefective items at minimum cost. Group testing means that items can be pooled and tested together; if the group comes out clean, all items in it are nondefective, while a “contaminated” group is scrapped. Every test takes a random amount of time and a given deadline has to be met. If the prescribed number of nondefective items is not reached, the demand has to be satisfied at a higher (penalty) cost. We derive explicit formulas for the distributions underlying the cost functionals of this model. It is shown in numerical examples that these results can be used to determine the optimal group size.

Approximate analysis of the delivery splitting model

The concept of order splitting has been proposed primarily to enable buyers to obtain substantial inventory savings. In this paper we investigate the order splitting concept from the suppliers point of view, referred to as delivery splitting. We will show that for the supplier considerable cost savings can be obtained by using the concept of delivery splitting, although the motivation and the practical implementation can be different for buyer and supplier. Also we will show that an analytical (although approximative) treatment of the delivery splitting concept is feasible, which brings the concept within reach of practical implementation.

Coordinated replenishment systems with discount opportunities

Abstract In many practical situations, coordination of replenishment orders for a family of items can lead to considerable cost savings. A well-known class of strategies for the case where cost savings are due to reduced joint ordering costs is the class of can-order strategies. However, these strategies, which are simple to implement in practice, do not take discount possibilities into account. We propose a method to incorporate discounts in the framework of can-order strategies. A continuous review multi-item inventory system is considered with independent compound Poisson demand processes for each of the individual items. Discounts are offered by the supplier as a percentage of the total dollar value whenever this value exceeds a given threshold. Starting from the can-order strategy as a basic decision rule, we develop a simple heuristic to evaluate these discount opportunities. The performance of the can-order strategy with discount evaluation is compared with that of another class of discount evaluat...

Operator-based intensity functions for the nonhomogeneous Poisson process

A nonhomogeneous Poisson process (NHPP) plays an important role in a variety of applications as reliability of repairable systems, software reliability and actuarial studies. An NHPP is characterized by its intensity function m(t), which provides information on the time-dependent nature of the reliability of the system. Various intensity functions, which describe different behavior (from reliability decay to reliability growth along with monotonicity, convexity or concavity), have been suggested for NHPP’s for modeling repairable systems. Perhaps one of the most frequently utilized NHPP is the power lawprocess (PLP) in which m(t) is a power function of t. Inthis studywe present a general method for constructing new intensity functions for NHPP’s yielding new classes of NHPP’s. This method utilizes certain operators Ln, n ∈ N0, acting on some suitable functions L0 = f (termed base functions). We call these classesOBIF’s (operator-based intensity functions). These classes are represented in terms of three parameters of which one is an indexing parameter n ∈ N0 and two others are scale and shape parameters. The fact that n ∈ N0 is also a parameter provides a flexibility in the choice of the appropriate statistical model for NHPP’s data. In particular, we consider the exponential operator acting on the PLP intensity function f and realize that Ln’s, n ≥ 2, inherit properties similar to those of L1 (convexity and concavity) and thus are suitable for modelling bathtub data. We also consider a more comprehensive treatment of OBIF classes where both, the operator and base functions, are general. All of the introduced operators are demonstrated with illustrative examples.