On systems with shared resources and optimal switching strategies

Simple series systems of identical components with spare parts are considered. It is shown that the cumulative distribution function of a system failure time tends to a step function as the number of components increases and resources can be shared. An example of ‘continuous resources’ is also described. The time-sharing strategy for standby systems is investigated. It is proved that an optimal rule for a system of standby components with increasing failure rates is the single switching performed at t/2 , where t is a mission time.

Modeling Spare Parts Demands Forecast under Two-Dimensional Preventive Maintenance Policy

In maintenance practice, there is such a situation where the spare parts replacement should be carried out at the scheduling time of calendar or usage for whichever comes first. The issue of two-dimensional preventive maintenance usually was not addressed by traditional methods, and at present, few studies were focused on this very topic. Based on these considerations, this paper presented the two-dimensional preventive policy where replacements of spare parts are based on both calendar time and usage time. A novel model was developed to forecast spare parts demands under two-dimensional preventive maintenance policy, and a discrete algorithm was presented for solving the mathematical model. A case study was given to demonstrate its applicability and validity, and it was showed that the presented model can be used to forecast spare parts demands as well as to optimize spare parts and preventive maintenance jointly

A load sharing system reliability model with managed component degradation

Motivated by an industrial problem affecting a water utility, we develop a model for a load sharing system where an operator dispatches work load to components in a manner that manages their degradation. We assume degradation is the dominant failure type, and that the system will not be subject to sudden failure due to a shock. By deriving the time to degradation failure of the system, estimates of system probability of failure are generated, and optimal designs can be obtained to minimize the long run average cost of a future system. The model can be used to support asset maintenance and design decisions. Our model is developed under a common set of core assumptions. That is, the operator allocates work to balance the level of the degradation condition of all components to achieve system performance. A system is assumed to be replaced when the cumulative work load reaches some random threshold. We adopt cumulative work load as the measure of total usage because it represents the primary cause of component degradation. We model the cumulative work load of the system as a monotone increasing and stationary stochastic process. The cumulative work load to degradation failure of a component is assumed to be inverse Gaussian distributed. An example, informed by an industry problem, is presented to illustrate the application of the model under different operating scenarios

Architecting Fail-Safe Supply Chains / Networks

Disruptions are large-scale stochastic events that rarely happen but have a major effect on supply networks’ topology. Some examples include: air traffic being suspended due to weather or terrorism, labor unions strike, sanctions imposed or lifted, company mergers, etc. Variations are small-scale stochastic events that frequently happen but only have a trivial effect on the efficiency of flow planning in supply networks. Some examples include: fluctuations in market demands (e.g. demand is always stochastic in competitive markets) and performance of production facilities (e.g. there is not any perfect production system in reality). A fail-safe supply network is one that mitigates the impact of variations and disruptions and provides an acceptable level of service. This is achieved by keeping connectivity in its topology against disruptions (structurally fail-safe) and coordinating the flow through the facilities against variations (operationally fail-safe). In this talk, I will show that to have a structurally fail-safe supply network, its topology should be robust against disruptions by positioning mitigation strategies and be resilient in executing these strategies. Considering “Flexibility” as a risk mitigation strategy, I answer the question “What are the best flexibility levels and flexibility speeds for facilities in structurally fail-safe supply networks?” Also, I will show that to have an operationally fail-safe supply network, its flow dynamics should be reliable against demand- and supply-side variations. In the presence of these variations, I answer the question “What is the most profitable flow dynamics throughout a supply network that is reliable against variations?” The method is verified using data from an engine maker. Findings include: i) there is a tradeoff between robustness and resilience in profit-based supply networks; ii) this tradeoff is more stable in larger supply networks with higher product supply quantities; and iii) supply networks with higher reliability in their flow planning require more flexibilities to be robust. Finally, I will touch upon possible extensions of the work into non-profit relief networks for disaster management

Maintenance Centered Service Parts Inventory Control

High-tech capital goods enable the production of many services and articles that have become a part of our daily lives. Examples include the refineries that produce the gasoline we put in our cars, the photolithography systems that enable the production of the chips in our cell phones and laptops, the trains and railway infrastructure that facilitate public transport and the aircraft that permit us to travel long distances. To prevent costly production disruptions of such systems when failures occur, it is crucial that service parts are readily available to replace any failed parts. However, service parts represent significant investments and failures are unpredictable, so it is unclear which parts should be stocked and in what quantity. In this thesis, analytical models and solution methods are developed to aid companies in making this decision. Amongst other things, we analyze systems in which multiple parts need replacement after a failure, a situation that is frequently encountered in practice. This affects the ability to complete repairs in a timely fashion. We develop new modeling techniques in order to successfully apply scalable deterministic approaches, such as column generation techniques and sample average approximation methods, to this stochastic problem. This leads to solution techniques that, unlike traditional methods, can ensure that all parts needed to complete maintenance are readily available. The approach is capable of meeting the challenging requirements of a real-life repair shop