Robin P. Nicolai

A comparison of models for measurable deterioration: An application to coatings on steel structures

Steel structures like bridges, tanks and pylons are exposed to outdoor weathering conditions. In order to prevent them from corrosion they are protected by organic coating systems. This paper focuses on modelling the deterioration of the organic coating layer that protects steel structures from corrosion. Only if there is sufficient knowledge of the condition of the coating on these structures, maintenance actions can be done in the most efficient way. Therefore the course of the deterioration of the coating system and its lifetime, which is also of importance for doing maintenance, have to be assessed accurately. In this paper three different stochastic processes, viz. Brownian motion with non-linear drift, the non-stationary gamma process and a two-stage hit-and-grow physical process, are fitted to two real data sets. In this way we are the first who compare the three stochastic processes empirically on criteria such as goodness-of-fit, computational convenience and ease of implementation. The first data set is based on expert judgement; the second consists of inspection results. In the first case the model parameters are obtained by a least squares approach, in the second case by the method of maximum likelihood. A meta-analysis is performed on the two-stage hit-and-grow model by means of fitting Brownian motion and gamma process to the outcomes of this model.

Maintenance and Production: A Review of Planning Models

Maintenance is the set of activities carried out to keep a system into a condition where it can perform its function. Quite often these systems are production systems where the outputs are products and/or services. Some maintenance can be done during production and some can be done during regular production stops in evenings, weekends and on holidays. However, in many cases production units need to be shut down for maintenance. This may lead to tension between the production and maintenance department of a company. On one hand the production department needs maintenance for the long-term well-being of its equipment, on the other hand it leads to shutting down the operations and loss of production. It will be clear that both can benefit from decision support based on mathematical models.

Modelling and optimizing imperfect maintenance of coatings on steel structures

Steel structures such as bridges, tanks and pylons are exposed to outdoor weathering conditions. In order to prevent them from corrosion they are protected by an organic coating system. Unfortunately, the coating system itself is also subject to deterioration. Imperfect maintenance actions such as spot repair and repainting can be done to extend the lifetime of the coating. In this paper we consider the problem of finding the set of actions that minimizes the expected maintenance costs over a bounded horizon. To this end we model the size of the area affected by corrosion by a non-stationary gamma process. An imperfect maintenance action is to be done as soon as a fixed threshold is exceeded. The direct effect of such an action on the condition of the coating is assumed to be random. On the other hand, maintenance may also change the parameters of the gamma deterioration process. It is shown that the optimal maintenance decisions related to this problem are a solution of a continuous-time renewal-type dynamic programming equation. To solve this equation time is discretized and it is verified theoretically that this discretization induces only a small error. Finally, the model is illustrated with a numerical example.

Automated response surface methodology for stochastic optimization models with unknown variance

Response surface methodology (RSM) is an optimization tool that was introduced in the early 50s by Box and Wilson (1951). In this paper we are interested in finding the best settings for an automated RSM procedure when there is very little information about the objective function. We present a framework of the RSM procedures that is founded in recognizing local optima in the presence of noise. We emphasize both stopping rules and restart procedures. The results show that considerable improvement is possible over the proposed settings in the existing literature.

Modeling the deterioration of the coating on steel structures: a comparison of methods

Steel structures like bridges, tanks and pylons are exposed to outdoor weathering conditions. In order to prevent them from corrosion they are protected by organic coating systems. This paper focuses on the deterioration process of the organic coating layer that protects steel structures from corrosion. Only if there is sufficient knowledge of the condition of the coating on these structures, maintenance actions can be done in the most efficient way. Therefore the deterioration of the coating in course of time has to be estimated accurately. To this end the Brownian motion with non-linear drift, the Gamma process with non-linear shape function and the simulation of a physical process are compared. Expert judgment is used to obtain parameter estimates.

Automated Response Surface Methodology for Simulation Optimization Models with Unknown Variance

Abstract Response Surface Methodology (RSM) is a collection of mathematical and statistical techniques useful for developing, improving, and optimizing processes. Applications of RSM can be found in e.g. chemical, engineering and clinical sciences. Still, there does not seem to be an established code of practice for the automated application of RSM in the field of simulation optimization. In this paper our aim is to find the best settings for an automated RSM procedure when there is very little information about the objective function. We present a framework of the RSM procedures for finding optimal solutions and emphasize the use of both stopping rules and restart procedures. Various versions of the RSM algorithms are compared on a number of test functions, including a simulation model for cancer screening. The results show that considerable improvement is possible over the proposed settings in the existing literature. Accordingly, we give general recommendations on the application of automated RSM algorithms in simulation optimization.

Maintenance and Markov Decision Models

In this chapter we first give an introduction to Markov decision theory. We state the main optimality criteria and solution approaches. Next we sketch how it can be applied in maintenance theory. In particular, we deal with the civil infrastructure sector and show what kind of results it brings. Finally we also indicate which problems arise in applications. Keywords: Markov decision process; maintenance; replacement; policy optimization; aging; civil structures