On The Maintenance Modeling and Optimization of Repairable Systems: Two Different Scenarios

The use of mathematical modeling for the purpose of analyzing and optimizing the performance of repairable systems is widely studied in the literature. In this dissertation, we study two different scenarios on the maintenance modeling and optimization of repairable systems. First, we study the long-run availability of a traditional repairable system that is subjected to imperfect corrective maintenance. We use Kijima\u27s second virtual age model to describe the imperfect repair process. Because of the complexity of the underlying probability models, we use simulation modeling to estimate availability performance and meta-modeling to convert the reliability and maintainability parameters of the repairable system into an availability estimate without the simulation effort. As a last step, we add age-based, perfect preventive maintenance to our analysis. Second, we optimize a preventive maintenance policy for a two-component repairable system. When either component fails, instantaneous, minimal, and costly corrective maintenance is performed on the component. At equally-spaced, discrete points during the system\u27s useful life, the decision-maker has the option to perform instantaneous, imperfect, and costly preventive maintenance on one or both of the components, to instantaneously replace one or both of the components, or to do nothing. We use a Genetic Algorithm in an attempt to find a cost-optimal set of preventive maintenance and replacement decisions

A hybrid load flow and event driven simulation approach to multi-state system reliability evaluation

Structural complexity of systems, coupled with their multi-state characteristics, renders their reliability and availability evaluation difficult. Notwithstanding the emergence of various techniques dedicated to complex multi-state system analysis, simulation remains the only approach applicable to realistic systems. However, most simulation algorithms are either system specific or limited to simple systems since they require enumerating all possible system states, defining the cut-sets associated with each state and monitoring their occurrence. In addition to being extremely tedious for large complex systems, state enumeration and cut-set definition require a detailed understanding of the system׳s failure mechanism. In this paper, a simple and generally applicable simulation approach, enhanced for multi-state systems of any topology is presented. Here, each component is defined as a Semi-Markov stochastic process and via discrete-event simulation, the operation of the system is mimicked. The principles of flow conservation are invoked to determine flow across the system for every performance level change of its components using the interior-point algorithm. This eliminates the need for cut-set definition and overcomes the limitations of existing techniques. The methodology can also be exploited to account for effects of transmission efficiency and loading restrictions of components on system reliability and performance. The principles and algorithms developed are applied to two numerical examples to demonstrate their applicability

Data-driven extraction and analysis of repairable fault trees from time series data

Fault tree analysis is a probability-based technique for estimating the risk of an undesired top event, typically a system failure. Traditionally, building a fault tree requires involvement of knowledgeable experts from different fields, relevant for the system under study. Nowadays’ systems, however, integrate numerous Internet of Things (IoT) devices and are able to generate large amounts of data that can be utilized to extract fault trees that reflect the true fault-related behavior of the corresponding systems. This is especially relevant as systems typically change their behaviors during their lifetimes, rendering initial fault trees obsolete. For this reason, we are interested in extracting fault trees from data that is generated from systems during their lifetimes. We present DDFTAnb algorithm for learning fault trees of systems using time series data from observed faults, enhanced with Naïve Bayes classifiers for estimating the future fault-related behavior of the system for unobserved combinations of basic events, where the state of the top event is unknown. Our proposed algorithm extracts repairable fault trees from multinomial time series data, classifies the top event for the unseen combinations of basic events, and then uses proxel-based simulation to estimate the system’s reliability. We, furthermore, assess the sensitivity of our algorithm to different percentages of data availabilities. Results indicate DDFTAnb’s high performance for low levels of data availability, however, when there are sufficient or high amounts of data, there is no need for classifying the top event

Systems reliability for phased missions

The concept of a phased mission has been introduced as a sequential set of objectives that operate over different time intervals. During each phase of the mission, the system may alter such that the logic model, system configuration, or system failure characteristics may change to accomplish a required objective. A new fault tree method has been proposed to enable the probability of failure in each phase to be determined in addition to the whole mission unreliability. Phase changes are assumed to be instantaneous, and component failure rates are assumed to be constant through the mission. For any phase, the method combines the causes of success of previous phases with the causes of failure for the phase being considered to allow both qualitative and quantitative analysis of both phase and mission failure. A new set of Boolean laws is introduced to combine component success and failure events through multiple phases so that the expression for each phase failure can be reduced into minimal form. [Continues.

Integrating modelling of maintenance policies within a stochastic hybrid automaton framework of dynamic reliability

The dependability assessment is a crucial activity for determining the availability, safety and maintainability of a system and establishing the best mitigation measures to prevent serious flaws and process interruptions. One of the most promising methodologies for the analysis of complex systems is Dynamic Reliability (also known as DPRA) with models that define explicitly the interactions between components and variables. Among the mathematical techniques of DPRA, Stochastic Hybrid Automaton (SHA) has been used to model systems characterized by continuous and discrete variables. Recently, a DPRA-oriented SHA modelling formalism, known as Stochastic Hybrid Fault Tree Automaton (SHyFTA), has been formalized together with a software library (SHyFTOO) that simplifies the resolution of complex models. At the state of the art, SHyFTOO allows analyzing the dependability of multistate repairable systems characterized by a reactive maintenance policy. Exploiting the flexibility of SHyFTA, this paper aims to extend the tools’ functionalities to other well-known maintenance policies. To achieve this goal, the main features of the preventive, risk-based and condition-based maintenance policies will be analyzed and used to design a software model to integrate into the SHyFTOO. Finally, a case study to test and compare the results of the different maintenance policies will be illustrated