Frank A. Van der Duyn Schouten

A Review of Multi-Component Maintenance Models with Economic Dependence

In this paper we review the literature on multi-component maintenance models with economic dependence. The emphasis is on papers that appeared after 1991, but there is an overlap with Section 2 of the most recent review paper by Cho and Parlar (1991). We distinguish between stationary models, where a long-term stable situation is assumed, and dynamic models, which can take information into account that becomes available only on the short term. Within the stationary models we choose a classification scheme that is primarily based on the various options of grouping maintenance activities: grouping either corrective or preventive maintenance, or combining preventive-maintenance actions with corrective actions. As such, this classification links up with the possibilities for grouped maintenance activities that exist in practice.

Two Simple Control Policies for a Multicomponent Maintenance System

Optimal group maintenance policies for a set of M identical machines subject to stochastic failures are considered. The control of the system is not based on the complete age configuration of all components, nor on the number of failed components only. We compromise between these two extreme cases by introducing four possible states for each component: good, doubtful, preventive maintenance is due, and failed. Two types of control policies are considered, both based on the number of doubtful components at component failure epochs. Starting from a general model with general but identical lifetime distributions for the individual components, we introduce an approximate model in which the four possible states are identified with certain age intervals for each individual component. The sojourn times in the good and the doubtful state are supposed to be exponentially distributed. For this resulting approximate model, explicit expressions are derived for various performance measures, like the time to system replacement and the average costs per unit time. By making use of the results obtained for the approximate model several approximations for the performance measures of the original model are presented. Validation of these approximations is performed by simulation.

Two-stage queueing network models for quality control and testing

We study sojourn times in a two-node open queueing network with a processor sharing node and a delay node, with Poisson arrivals at the PS node. Motivated by quality control and blood testing applications, we consider a feedback mechanism in which customers may either leave the system after service at the PS node or move to the delay node; from the delay node, they always return to the PS node for new quality controls or blood tests. We propose various approximations for the distribution of the total sojourn time in the network; each of these approximations yields the exact mean sojourn time, and very accurate results for the variance. The best of the three approximations is used to tackle an optimization problem that is mainly inspired by a blood testing application.

Maintenance Management and Availability Assessment during the Last Decade

One of the most important developments in the area of maintenance mangement and availability assessment during the last ten years is undoubtedly the increasing interest in industry for a scientific approach of these management areas. Apart from economic reasons also the shifting attention in the scientific world towards more realistic and applicable models contributed to this development to a large extent. In this lecture the major achievements of the last ten years will be reviewed.

Calculation of the Availability of a Two-Unit Parallel System With Cold Standby

A two-unit parallel system with cold standby, Markovian degradation of the working unit and one repair facility is considered. The calculation of the availability of this system under a control-limit repair policy is discussed. Iterative schemes for computing the availability in case of Erlangian repair-time distributions are presented along with numerical results.