Statistical Inference for a Virtual Age Reliability Model

During the lifetime of a system, repairs may be performed when the system fails. It is most common to assume either perfect repair or minimal repair. However, a repair actually will sometimes be between minimal repair and perfect repair, which is called imperfect repair. The Kijima type I virtual age model can be used to model these types of repairable systems. This model contains a parameter which reflects the restoration level after each repair. This thesis considers statistical inference for the Kijima type I model, which deals with repairable systems that can be restored to the operating state through system replacement or repair after the system fails. We present Bayesian analysis for the Kijima type I virtual age model, including consideration of the system's overall time to failure if a given number of repairs is possible. We use both Bayesian analysis, which specifies a single prior distribution, and a robust Bayesian analysis approach. A set of prior distributions is used in robust Bayesian analysis in order to deal with uncertainty regarding prior knowledge of the Kijima type I model parameters in a flexible way and to enhance the objectivity of the analysis in an imprecise Bayesian framework by computing predictive posterior distribution bounds for the reliability function of the system. Finally, we discuss the use of the developed methods to decide about optimal replacement. Optimal replacement is the methodology of replacing a system component at the most advantageous or efficient moment to increase its performance and minimize overall expected costs. Two policies are introduced with cost functions based on time and number of failures to make a decision on optimal replacement time or optimal number of failures of the system under the Kijima type I model using the Weibull distribution. These policies illustrate how the Bayesian and robust Bayesian analysis can be used for inferences about the optimal replacement and the expected total cost

Ferramenta Automática para Avaliação da Fiabilidade e Disponibilidade de Sistemas Reparáveis

Nesta dissertação apresentam-se as contribuições de um trabalho de investigação que tem como objetivo o desenvolvimento e implementação de uma ferramenta automática que disponibiliza, quase em tempo real, indicadores de fiabilidade e de disponibilidade para um qualquer sistema reparável. A ferramenta recebe dados recolhidos no equipamento em estudo, modela o processo gerador das avarias por recurso a vários modelos matemáticos/estatísticos, seleciona o modelo mais adequado aos dados recolhidos e, como base nesse modelo, apresenta um conjunto de indicadores úteis. Estes indicadores podem ser usados, tanto para prever o comportamento do sistema, como para avaliar como é que este responde a ações externas, como, por exemplo, à respetiva manutenção. Os trabalhos são iniciados com uma revisão dos conceitos e instrumentos fundamentais que suportam, grosso modo, o trabalho desenvolvido, seguindo-se o desenho, implementação e validação da ferramenta. A ferramenta é desenvolvida em ambiente Python e de forma automática. Este automatismo facilita a obtenção de resultados em tempo quase real e permite que o perito do processo tenha acesso a um conjunto de indicadores do estado do sistema sem que tenha conhecimentos específicos sobre modelação de processo geradores de avarias. O resumo dos dados recolhidos, assim como a informação produzida pela ferramenta desenvolvida são apresentados de forma organizada através de um dashboard, também desenvolvido em ambiente Python, de forma que a interpretação dos resultados seja mais rápida e eficiente.This dissertation presents the contributions of a research work that aims to develop and implement an automatic tool that provides, almost in real time, reliability, and availability indicators for any repairable system. The tool receives data collected from the equipment, models the process that generates the faults using various mathematical/statistical models, selects the most appropriate model for the data collected and based on that model, presents a set of useful indicators. These indicators can be used both to predict the behavior of the system and to assess how it responds to external actions, such as, for example, its maintenance. The work begins with a review of the fundamental concepts and instruments that roughly support the work developed, followed by the design, implementation, and validation of the tool. The tool is developed in a Python environment and automatically. This automatism facilitates obtaining results in near real time and allows the process expert to have access to a set of system status indicators without having specific knowledge about modeling fault-generating processes. The summary of the collected data, as well as the information produced by the developed tool, are presented in an organized way through a dashboard, also developed in a Python environment, so that the interpretation of the results is faster and more efficient

A review on maintenance optimization

To this day, continuous developments of technical systems and increasing reliance on equipment have resulted in a growing importance of effective maintenance activities. During the last couple of decades, a substantial amount of research has been carried out on this topic. In this study we review more than two hundred papers on maintenance modeling and optimization that have appeared in the period 2001 to 2018. We begin by describing terms commonly used in the modeling process. Then, in our classification, we first distinguish single-unit and multi-unit systems. Further sub-classification follows, based on the state space of the deterioration process modeled. Other features that we discuss in this review are discrete and continuous condition monitoring, inspection, replacement, repair, and the various types of dependencies that may exist between units within systems. We end with the main developments during the review period and with potential future research directions