While the idea of critical break rate of water distribution pipeline (defined as the break rate after which it is no longer economical to continuously repair) has been accepted in the literature and among the practicing engineers, the formula to obtain the critical break rate has remained elusive. In this dissertation, an equation for identifying the threshold break rate of a pipe is developed. The threshold break rate equation gives a rule of thumb for pipe replacement decision. Input parameters to obtain the threshold break rate of a pipe are repair and replacement costs, interest rate, and the length of the pipe. In addition, a methodology that enables the use of threshold break rate with the failure intensity and hazard functions is developed. The methodology is drawn by considering the relationships of the definitions of the threshold break rate with intensity and hazard functions in the context of a repairable system's failure process modeling. As a result, the newly developed threshold break rate equation can be coupled with any appropriate intensity and hazard function to obtain economically optimal replacement time of a pipe. Also, practical usage of the threshold break rate is demonstrated with a number of numerical examples. Design aids in the form of charts and tables are provided. The threshold break rate can be easily obtained either graphically or with the aid of the tables. The methodology that links the threshold break rate and failure rate (intensity and hazard) functions is extended to accommodate stress multiplying environmental factors in the form of the proportional intensity and hazards model. The two models consist of an age dependent failure rate function and a covariate structure. They are applied to a case study area pipe system to obtain optimal replacement times for individual pipes in the system. As a result, important hazard characteristics of water distribution pipes are drawn, and implications on the optimal replacement analysis are discussed. A pipe break prediction model is also developed in this research. The model spans the space between the linear and exponential break trends. The model is applied to the case study area pipe system with various cost options. The results from this analysis are discussed in terms of practical implementation of the replacement strategies. / Ph. D.

Water distribution system pipes span thousands of miles and form a significant part of the total infrastructure of the country. Rehabilitation of this underground infrastructure is one of the biggest challenges currently facing the water industry. Water main deterioration is twofold: the main itself loses strength over time and breaks; also, there is degradation of water quality and hydraulic capacity due to build of material within a main. The increasing repair and damage costs and degrading services demand that a deteriorating water main be replaced at an optimal time instead of continuing to repair it. In addition, expanding business districts, indirect costs, and interruptions including protected areas, waterways and roadways require examination of trenchless technologies for pipe installation. In this thesis a new threshold break rate criterion for the optimal replacement of pipes is provided. As opposed to the traditional present worth cost (PWC) criterion, the derived method uses the equivalent uniform annualized cost (EUAC). It is shown the EUAC based threshold break rate subsumes the PWC based threshold break rate. In addition, practicing engineers need a user-friendly decision support system to aid in the optimal pipeline replacement process. They also need a task-by-task cost evaluation in a project. As a part of this thesis a comprehensive decision support system that includes both technology selection knowledge base and cost evaluation spreadsheet program within a graphical user interface framework is developed. Numerical examples illustrating the theoretical derivations are also included. / Master of Science

Survival analysis is applied on mechanical components installed in gas turbines. We use field experience data collected from repair inspection reports. These data are highly censored since the exact time-to-event is unknown. We only know that it lies before or after the repair inspection time. As event we consider irreparability level of the mechanical components. The aim is to estimate survival functions that depend on the different environmental attributes of the sites where the gas turbines operate. Then, the goal is to use this information to obtain optimal time points for preventive maintenance. Optimal times are calculated with respect to the minimization of a cost function which considers expected costs of preventive and corrective maintenance. Another aim is the investigation of the effect of five different failure modes on the component lifetime. The methods used are based on the Weibull distribution, in particular we apply the Bayesian Weibull AFT model and the Bayesian Generalized Weibull model. The latter is preferable for its greater flexibility and better performance. Results reveal that components from gas turbines located in a heavy industrial environment at a higher distance from sea tend to have shorter lifetime. Then, failure mode A seems to be the most harmful for the component lifetime. The model used is capable of predicting customer-specific optimal replacement times based on the effect of environmental attributes. Predictions can be also extended for new components installed at new customer sites.

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.

<p>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.</p> <p><br></p> <p>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.</p> <p><br></p> <p>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.</p> <p><br></p> <p>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.</p> <p><br></p> <p>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.</p> <p><br></p> <p>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.</p> <p><br></p> <p>Finally, in Chapter 6, we present a summary of the dissertation with conclusions and future research potential.</p>

Pinhole leaks in copper plumbing pipes are a big concern for the homeowners. The problem is spread across the nation and remains a threat to plumbing systems of all ages. Due to the absence of a single acceptable mechanistic theory no preventive measure is available to date. Most of the present mechanistic theories are based on analysis of failed pipe samples however an objective comparison with other pipes that did not fail is seldom made. The variability in hydraulic and water quality parameters has made the problem complex and unquantifiable in terms of plumbing susceptibility to pinhole leaks. The present work determines the spatial and temporal spread of pinhole leaks across United States. The hotspot communities are identified based on repair histories and surveys. An assessment of variability in water quality is presented based on nationwide water quality data. A synthesis of causal factors is presented and a scoring system for copper pitting is developed using goal programming. A probabilistic model is presented to evaluate optimal replacement time for plumbing systems. Methodologies for mechanistic modeling based on corrosion thermodynamics and kinetics are presented. / Master of Science

Pinhole corrosion leak in home plumbing has emerged as a significant issue. In the major water distribution system managed by municipalities and water utilities the costs are distributed among all subscribers. The home plumbing repair/replacement cost and possible water damage cost must be addressed by the home owner. There are also issues of the value of home, insurance rates, health consequences, and taste and odor problems. These issues have become major concerns to home owners. Cradle to grave life cycle assessment is becoming an integral part of industrial manufacturing. In this thesis comprehensive details pertaining to life cycle assessment are presented. Copper tubing for plumbing installations is mainly obtained from recycled copper. Various stages of copper plumbing pipe manufacturing are explained. A comprehensive synthesis of various corrosion mechanisms is presented. Particular reference is given to copper plumbing pipe corrosion. A decision support tool for replacing copper plumbing pipes is presented. The deterioration process is grouped into early, normal and late stages. Because available data reflects late stage process, an optimization, neural network and curve fitting models are developed to infer early and normal stage behavior of the plumbing system. Utilizing the inferred leak rates a non-homogeneous poisson process model is developed to generate leak arrival times. An economically sustainable replacement criterion is adopted to determine optimal replacement time. / Master of Science