Optimal Policies in Reliability Modelling of Systems Subject to Sporadic Shocks and Continuous Healing

Indiana University-Purdue University Indianapolis (IUPUI)Recent years have seen a growth in research on system reliability and maintenance. Various studies in the scientific fields of reliability engineering, quality and productivity analyses, risk assessment, software reliability, and probabilistic machine learning are being undertaken in the present era. The dependency of human life on technology has made it more important to maintain such systems and maximize their potential. In this dissertation, some methodologies are presented that maximize certain measures of system reliability, explain the underlying stochastic behavior of certain systems, and prevent the risk of system failure. An overview of the dissertation is provided in Chapter 1, where we briefly discuss some useful definitions and concepts in probability theory and stochastic processes and present some mathematical results required in later chapters. Thereafter, we present the motivation and outline of each subsequent chapter. In Chapter 2, we compute the limiting average availability of a one-unit repairable system subject to repair facilities and spare units. Formulas for finding the limiting average availability of a repairable system exist only for some special cases: (1) either the lifetime or the repair-time is exponential; or (2) there is one spare unit and one repair facility. In contrast, we consider a more general setting involving several spare units and several repair facilities; and we allow arbitrary life- and repair-time distributions. Under periodic monitoring, which essentially discretizes the time variable, we compute the limiting average availability. The discretization approach closely approximates the existing results in the special cases; and demonstrates as anticipated that the limiting average availability increases with additional spare unit and/or repair facility. In Chapter 3, the system experiences two types of sporadic impact: valid shocks that cause damage instantaneously and positive interventions that induce partial healing. Whereas each shock inflicts a fixed magnitude of damage, the accumulated effect of k positive interventions nullifies the damaging effect of one shock. The system is said to be in Stage 1, when it can possibly heal, until the net count of impacts (valid shocks registered minus valid shocks nullified) reaches a threshold $m_1$. The system then enters Stage 2, where no further healing is possible. The system fails when the net count of valid shocks reaches another threshold $m_2 (> m_1)$. The inter-arrival times between successive valid shocks and those between successive positive interventions are independent and follow arbitrary distributions. Thus, we remove the restrictive assumption of an exponential distribution, often found in the literature. We find the distributions of the sojourn time in Stage 1 and the failure time of the system. Finally, we find the optimal values of the choice variables that minimize the expected maintenance cost per unit time for three different maintenance policies. In Chapter 4, the above defined Stage 1 is further subdivided into two parts: In the early part, called Stage 1A, healing happens faster than in the later stage, called Stage 1B. The system stays in Stage 1A until the net count of impacts reaches a predetermined threshold $m_A$; then the system enters Stage 1B and stays there until the net count reaches another predetermined threshold $m_1 (>m_A)$. Subsequently, the system enters Stage 2 where it can no longer heal. The system fails when the net count of valid shocks reaches another predetermined higher threshold $m_2 (> m_1)$. All other assumptions are the same as those in Chapter 3. We calculate the percentage improvement in the lifetime of the system due to the subdivision of Stage 1. Finally, we make optimal choices to minimize the expected maintenance cost per unit time for two maintenance policies. Next, we eliminate the restrictive assumption that all valid shocks and all positive interventions have equal magnitude, and the boundary threshold is a preset constant value. In Chapter 5, we study a system that experiences damaging external shocks of random magnitude at stochastic intervals, continuous degradation, and self-healing. The system fails if cumulative damage exceeds a time-dependent threshold. We develop a preventive maintenance policy to replace the system such that its lifetime is utilized prudently. Further, we consider three variations on the healing pattern: (1) shocks heal for a fixed finite duration $\tau$; (2) a fixed proportion of shocks are non-healable (that is, $\tau=0$); (3) there are two types of shocks---self healable shocks heal for a finite duration, and non-healable shocks. We implement a proposed preventive maintenance policy and compare the optimal replacement times in these new cases with those in the original case, where all shocks heal indefinitely. Finally, in Chapter 6, we present a summary of the dissertation with conclusions and future research potential

The latent state hazard model, with application to wind turbine reliability

We present a new model for reliability analysis that is able to distinguish the latent internal vulnerability state of the equipment from the vulnerability caused by temporary external sources. Consider a wind farm where each turbine is running under the external effects of temperature, wind speed and direction, etc. The turbine might fail because of the external effects of a spike in temperature. If it does not fail during the temperature spike, it could still fail due to internal degradation, and the spike could cause (or be an indication of) this degradation. The ability to identify the underlying latent state can help better understand the effects of external sources and thus lead to more robust decision-making. We present an experimental study using SCADA sensor measurements from wind turbines in Italy.Comment: Published at http://dx.doi.org/10.1214/15-AOAS859 in the Annals of Applied Statistics (http://www.imstat.org/aoas/) by the Institute of Mathematical Statistics (http://www.imstat.org

Merging Data Sources to Predict Remaining Useful Life – An Automated Method to Identify Prognostic Parameters

The ultimate goal of most prognostic systems is accurate prediction of the remaining useful life (RUL) of individual systems or components based on their use and performance. This class of prognostic algorithms is termed Degradation-Based, or Type III Prognostics. As equipment degrades, measured parameters of the system tend to change; these sensed measurements, or appropriate transformations thereof, may be used to characterize degradation. Traditionally, individual-based prognostic methods use a measure of degradation to make RUL estimates. Degradation measures may include sensed measurements, such as temperature or vibration level, or inferred measurements, such as model residuals or physics-based model predictions. Often, it is beneficial to combine several measures of degradation into a single parameter. Selection of an appropriate parameter is key for making useful individual-based RUL estimates, but methods to aid in this selection are absent in the literature. This dissertation introduces a set of metrics which characterize the suitability of a prognostic parameter. Parameter features such as trendability, monotonicity, and prognosability can be used to compare candidate prognostic parameters to determine which is most useful for individual-based prognosis. Trendability indicates the degree to which the parameters of a population of systems have the same underlying shape. Monotonicity characterizes the underlying positive or negative trend of the parameter. Finally, prognosability gives a measure of the variance in the critical failure value of a population of systems. By quantifying these features for a given parameter, the metrics can be used with any traditional optimization technique, such as Genetic Algorithms, to identify the optimal parameter for a given system. An appropriate parameter may be used with a General Path Model (GPM) approach to make RUL estimates for specific systems or components. A dynamic Bayesian updating methodology is introduced to incorporate prior information in the GPM methodology. The proposed methods are illustrated with two applications: first, to the simulated turbofan engine data provided in the 2008 Prognostics and Health Management Conference Prognostics Challenge and, second, to data collected in a laboratory milling equipment wear experiment. The automated system was shown to identify appropriate parameters in both situations and facilitate Type III prognostic model development

Part 3: Systemic risk in ecology and engineering

The Federal Reserve Bank of New York released a report -- New Directions for Understanding Systemic Risk -- that presents key findings from a cross-disciplinary conference that it cosponsored in May 2006 with the National Academy of Sciences' Board on Mathematical Sciences and Their Applications. ; The pace of financial innovation over the past decade has increased the complexity and interconnectedness of the financial system. This development is important to central banks, such as the Federal Reserve, because of their traditional role in addressing systemic risks to the financial system. ; To encourage innovative thinking about systemic issues, the New York Fed partnered with the National Academy of Sciences to bring together more than 100 experts on systemic risk from 22 countries to compare cross-disciplinary perspectives on monitoring, addressing and preventing this type of risk. ; This report, released as part of the Bank's Economic Policy Review series, outlines some of the key points concerning systemic risk made by the various disciplines represented - including economic research, ecology, physics and engineering - as well as presentations on market-oriented models of financial crises, and systemic risk in the payments system and the interbank funds market. The report concludes with observations gathered from the sessions and a discussion of potential applications to policy. ; The three papers presented in this conference session highlighted the positive feedback effects that produce herdlike behavior in markets, and the subsequent discussion focused in part on means of encouraging heterogeneous investment strategies to counter such behavior. Participants in the session also discussed the types of models used to study systemic risk and commented on the challenges and trade-offs researchers face in developing their models.Financial risk management ; Financial markets ; Financial stability ; Financial crises

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

Numerical modeling of thermal fracture development in unconventional reservoirs

Rapid depletion of hydrocarbons in conventional reservoirs and the availability of abundant oil and gas resources in unconventional forms demand new technology to economically produce these energy resources. From exploration to consumption of hydrocarbons, a great number of complex physical, chemical, mechanical, electrical, and thermal phenomena occurs in reservoir from reservoir rock to surface facilities. In addition to good rock samples and cores which could represent the reservoir rock for laboratory experiments, numerical tools should always be used to provide predictive capability of reservoir rock and fluid behavior. A great number of numerical methods have been developed and used over the past decades for rock mechanics problems. In this research the main focus is on thermal fracturing, heat transfer in rock, flow in porous media and stress-deformation analysis. We use three numerical methods for thermal fracturing of reservoir rock and investigate their capabilities in providing a solution for fracture propagation in rock. We finally propose the best numerical method among the ones we used in this work. We finally show two applications of thermal rock fracturing for improvement of hydrocarbon recovery in tight formations.Petroleum and Geosystems Engineerin

Prognostics and Health Management of Industrial Equipment

ISBN13: 9781466620957Prognostics and health management (PHM) is a field of research and application which aims at making use of past, present and future information on the environmental, operational and usage conditions of an equipment in order to detect its degradation, diagnose its faults, predict and proactively manage its failures. The present paper reviews the state of knowledge on the methods for PHM, placing these in context with the different information and data which may be available for performing the task and identifying the current challenges and open issues which must be addressed for achieving reliable deployment in practice. The focus is predominantly on the prognostic part of PHM, which addresses the prediction of equipment failure occurrence and associated residual useful life (RUL)