Advances in Reliability Analysis and its Applications

In recent times, there has been a tremendous research interests and growth in the direction of time varying communication networks (TVCNs) due to their widespread applications. The examples of such networks include, but not limited to, the networks like mobile ad hoc networks (MANETs), delay tolerant networks (DTNs), vehicular ad hoc networks (VANETs) and opportunistic mobile networks (OMNs). Some formidable challenges posed by such networks are long propagation delay, frequent disruption of communication between any two nodes, high error rates, asymmetric link rates, lack of end-to-end connectivity, routing, etc. Thus, it is vital for TVCN design, modelling and performance evaluation and/or comparison to assess their performance through some quantifiable metrics like packet delivery ratio (PDR), average number of link failures during the routing process, routing requests ratio, average end-to-end (E2E) delay, route lifetime and network reliability. Although a plethora of tools and techniques are available that deal with the design, modelling, analysis and assessment of reliability and other performance metrics of static networks yet the same is not true for the present days’ TVCNs. This Chapter describes extension of the reliability assessment techniques and performance metrics used for static networks to the TVCNs. More specifically, the aspects dealt in this chapter are: (i) TVCN models for representing features like mobility, links and topology, (ii) description of the notion of time-stamped-minimal path sets (TS-MPS) and time-stamped-minimal cut sets (TS-MCS) for TVCNs as an extension of MPS and MCS, respectively that are widely used in static networks, (iii) techniques for enumerating TS-MPS and TS-MCS, and evaluating reliability measure(s)-particularly two-terminal reliability, expected hop and slot counts along with some other related metrics, and (iv) discussion on several recent optimization problems in TVCNs.

The probability that an energy system will successfully enter into operation and perform the required function of the criteria within the allowed tolerances for a given period of time and given environmental conditions (working temperature, pressure, humidity, permissible vibrations, noise and shock, changes in operating parameters of labor, etc.) represents its effectiveness. The effectiveness indicator is characterized by a unit (unit parameter) or several effectiveness properties (complex parameter), such as: reliability (the ability of system to maintain continuous working ability within the limits of allowed deviations during the calendar period of time, quantified through indicators: probability of operation without cancellation, medium time in work, intensity of cancellation and cancellation rate), maintenance convenience (ability to prevent and detect cancellation and damage, to restore working ability and correctness through technical service and technical repairs, quantified through: probability of renewal for the given calendar period of time, medium recovery time and the intensity of renewal), durability (the system’s ability to maintain its working ability from the very beginning of its application or exploitation until the transition to limit states in which certain stop is possible in the realization of certain activities for technical service maintenance and repairs, defined through indicators: medium resource, gamma-percentage resource, medium expiration date, gamma-percentage life), stability (the system’s ability to continuously maintain hot reserves, storage and/or transport). Optimal management of complex technical systems must be based on the assessment and complex optimization of the reliability indicators, depending on how they are provided and the hierarchical level of detailing, as well as the current phase of the life cycle. For these reasons, the optimization process includes the basic structural, parametric and constructive solutions related to the technical system itself through the change of its most important characteristics: efficiency (mostly energy), maneuverability, reliability and economic effectiveness in general. The set of goals of optimization is concluded in the overall choice of reliability indicators and possible ways to secure them, and given the already established rules regarding the higher hierarchical level of the system. Creating effectiveness is closely related to the concrete energy system, its behavior at a certain time and the environment in which it works (the power system as a higher hierarchical system). For this realization, it is necessary to provide the appropriate backgrounds, first of all the database, then to define based on the function of the goal and the available database of the interconnection and the relationship between the individual elements of the system. Within this chapter, appropriate methods will be provided for prognosis and optimizing the effectiveness based on the quality of design, production and testing, assembly and trial release, exploitation, development of procedures for prognosis of the complex systems behavior based on the characteristics of certain constituent elements of the system and the possible impact of human factors and environment itself on the system. Starting from the initial stage of development, design and conquering the production of certain types of thermal energy equipment in the goal of fulfilling all requirements without limitations, if it is based on its purpose, a multivariate assembly is set up before the designer, with the need to optimize according to certain already adopted algorithms. The goal is to create such a facility that has a satisfactory structure in terms of reliability indicators, with minimal costs of maintenance during the projected working life. Defining the plant that best meets the set requirements related to reliability and the process of exploitation and maintenance itself must be the result of the implemented optimization process (in this case, on the basis of the selected minimum investment criterion). The sum consumption of all devices that ensure the normal operation of the thermal power plant is called own consumption. General consumption consists of all other devices that do not have a direct impact on the technological process at the plant. Preserving the continuity in supplying of own power consumption is essential for safe operation under normal operating conditions, in the case of short-term transitions, as well as in starting and normal stopping, it is particularly important in case of stopping in case of disorder or failure of the system. With the growing unit block strength, there is also the growth of unit power of electric motors with their own consumption, and therefore requirements related to the power supply. The basic problem is to achieve safe power supply in a variety of drive operation situations, with fewer short-circuit currents and the voltage drop when starting large synchronous motors. The solution is achieved by the proper choice of the transformer of own consumption and voltage level.

Economic development of a country requires the consumption of appropriate energy resources. Any deviation from the timing as a result may have the appearance of development restrictions in the other economic activities, so the development of energy consumption should be continuously monitored. On the other hand, energy consumption itself is linked to certain influential factors (population growth, science and technology development, economic development, standard, etc.), which intensity of activity changes over time. Choosing the optimal structure for covering consumption is very important for the development of energy. Planning of development in the field of energy is important as for the dependence of the development of the society on safe, sufficient and appropriate quantities of necessary forms of energy, as well as for the engagement of large financial resources in this field. When planning the development of energy, the following criteria should be followed: the security of consumer supply with minimal costs, the rational use of domestic sources, with proper evaluation of imported energy forms, maximum prevention of monopolistic and single forms of energy, and achieving acceptable conditions for environmental protection and sustainable development. Planning of the development of the electric power system includes all activities from the first assumptions about the possibility of building an object until its entry into operation. But in terms of terminology, the term planning refers primarily to the planning of power generation plants (hydro, nuclear and thermal power plants). When planning the development of the electro-energy system (EES), the goal and criteria are uniquely determined: the settlement of the predicted consumption of electricity at a minimum cost and assuming that the specified limitations are met, such as, financial, technical, ecological, limitations on the availability of primary forms of energy, etc. Satisfying the limitations is imposed as a primary task, regardless of the method of planning, which is the reason that a particular limitation is often the decisive factor in deciding on the final strategies of development. Although long-term plans bear a great deal of uncertainty, such planning is necessary primarily for two reasons: the first is the basic and extended lifetime of the production plants (e.g., 25–30 basic plus 15–20 years of extended service life after revitalization, reconstruction and modernization of thermal power plant), while the second is the time necessary for the preparation of the construction and the construction itself (3–6 years, not counting the possibility of a delay in the project). Planning of the construction of production plants should be determined by the necessary construction to meet the future consumption (volume and capacity), the time of entry of a particular production plant into operation and the possibility and improvement of technologies for production of electricity (improved and cleaner technologies, cogeneration and trigeneration systems, hybrid systems, …). Only the making of development studies can be divided into two parts, which include simulation of the legality of work in the system (system operation), as well as the economic evaluation of production facilities or entire development plans. The first part requires the development of a system model, i.e. it is necessary to describe the system in mathematical equations and to approximate it with the inevitable neglect and simplification. In the second part, the energy contribution of each plant should be evaluated and by economic methods to do its valorization. The methods used in planning the development of the electric power system differ with respect to: optimization technique (linear programming, nonlinear programming, etc.), type of approximation (linear, nonlinear) and economic valorization (with inflation, without inflation). None of these methods has proven to be absolutely acceptable for all problems so far, so a large number of methods are being developed that are intended to solve partial problems, i.e. or they serve to optimize the self-production facilities, or optimize only the transmission/distribution network, or the process of optimization refers to the whole energy (with very simplified relationships in the given system). The basic assumption of applying optimization models is the high reliability of the parameters on which the budget is based. Namely, if the parameters are not reliable enough, the question arises of the need for optimization. Sometimes, even the sensitivity analysis, usually used in the final phase of any optimization model, cannot eliminate effective reliability and input data. Furthermore, it is never possible to include all the limitations within the model, so that only an approximately objective picture of the condition in the system is obtained. However, today, it is impossible to rely solely on the intuition of planners in selecting the most favorable development option, so the application of the model is inevitable (more criterion evaluation methods). Energy development planning is based on the security of consumer supply with minimal costs, with the accompanying rational use of domestic resources, which implies correct evaluation of imported energy forms, maximum prevention of monopolistic behavior (the only form of energy available) and achieving satisfactory environmental protection conditions. When planning the development of the electricity sector of any country, the goal and criteria are uniquely determined through the settlement of the estimated electricity consumption, with minimum costs and assuming that certain financial, technical and environmental limitations on the availability of primary forms of energy are met. The new value of own consumption of a thermal power plant, which can be achieved by applying the proposed measures, is still above reference values in relation to similar systems in the world, which means that there is still a serious work on analyzing possible savings and reducing losses as a whole. It should be noted that it is expected that in the first period of implementation of the energy management system, several short-term measures will be identified, which do not require financial investments and are more of an organizational nature. After the introduction of the BAS ISO 50001 standard and the application of appropriate standardized procedures in practice, the number of short-term measures will be reduced, which also indicates an organized monitoring of the implementation of energy efficiency measures.

Effective management of Hazardous Production Facilities (HPF), forecasting of deviations from nominal modes, prevention of failures, incidents and accidents is possible only on the basis of collecting and analysis of continuous flow of information on condition of HPF and also knowledge of processes complex happening at it (technological, organizational, behavioural and so forth). In the article problems of creation of integrated index within development of control methods of HPF industrial safety condition are designated and the problem of such objects management modelling because of precedents, based on classes of states is solved (there is an event/there is no event). The indicators describing conditions of industrial safety (in fact—risks factors) are offered to consider as signs of assessed situation. Assessments of analyzed states values of integrated index deviations are used. The offered approach to integration of methods of “data mining”, conclusion based on precedents and adaptive management in consistent self-training advising system allows providing management of HPF safety and similar objects with weak formalizable behaviour. Based on a certain measure of proximity in capacity of which it is offered to use Hamming distance, one of similar precedents is chosen. The offered approach, using a method of support vectors, solves this problem according to precedents in the past. A solver (auditor, qualifier, or recognizer) always keeps the found order until essential key signs on which partial order is formed are rejected. Examples of integrated index creation are presented.

This chapter describes an assessment methodology for various sustainability indicators of technical systems, such as reliability, availability, fault tolerance, and reliability associated cost of technical safety-critical systems, based on Multi-Level Hierarchical Reliability Model (MLHRM). As an application case of the proposed methodology, the various sustainability indicators of electric vehicle propulsion systems are considered and evaluated on the different levels of the hierarchical model. Taking into account that vehicle traction drive systems are safety-critical systems, the strict requirements on reliability indices are imposed to each of their components. The practical application of the proposed technique for reliability oriented development of electric propulsion system for the search-and-rescue helicopter and icebreaker LNG tanker and the results of computation are presented. The opportunities of improvement regarding reliability and fault tolerance of such technical systems are investigated. The results of the study, allowing creating highly reliable technical systems for the specified operating conditions and choosing the most appropriate system design, are discussed in detail.

Reliability is a conceptual term that means endurance, dependability, and good performance. However, in system engineering, it is more than a conceptual term; it can be measured and evaluated. Reliability means the ability of a system to perform the required task under the normal conditions during its age. A complexity in system reliability may be commonly arisen due to the interconnection of various elements in the form of a network that can be represented by graphs. The graph theory and computer programs are essential tools for analyzing large and complex systems. This chapter presents how a complexity of system reliability can be reduced through the use of computer programs based on a graph theory. The software program has been developed for reliability assessment of complex systems such as aircraft. It can handle any statistical distributions. It uses the inclusion-exclusion method for finding the minimal paths for directed acyclic graph using reliability block diagram (RBD). A system may be considered to operate if there exists a set of functioning components from source to target. So, at least one minimal path must function for the system operation. The probability of the union of all minimal paths can be used to find the reliability of the whole system.

Predicting and understanding the machining system performance is a constant challenge in the process industries like manufacturing and production systems, computer and communication systems, just-in-time (JIT) service systems. The reliability modeling supports the decision-making process from early to the optimal state-of-the-art design of the machining system. Reliability measures account the performance of different preventive, predictive, corrective, zero-hours, and periodic maintenance strategies. For all strategies, the most anterior arrangement is the availability of the service facility as and when required to maintain the high grade or efficient quality of service (QoS). The permanent service facility may increase cost, idleness, deterioration in quality. To reduce the wastage of valuable resources like time, money, quality, etc., vacation is a prominent idea for the service facility. The vacation time is a period of time of not doing the usual service or activities. In this time, the server may take rest to rejuvenate, to reduce idle time at the station, to diminish the expected cost incurred in service. The long vacation time also wastes the valuable resources substantially due to the long waiting queue of failed machines. The vacation time period is a critical issue and needs to analyze judgementally. In this chapter, a comparative study of different vacation policies on the reliability characteristics of the machining system is presented. For that purpose, the queueing-theoretic approach is employed, and the Markovian models are developed for various types of vacation policy namely N-policy, single vacation, multiple vacations, Bernoulli vacation, working vacation, vacation interruption, etc. For all vacation policies, the reliability and mean-time-to-failure (MTTF) of the system are compared, and results are depicted in the graphs for quick insights. From this study, readers get a glance to understand about vacation, researchers get a concrete platform to choose appropriate assumptions for their research in machining/service system or system analyst may opt suitable vacation policy as per limitation of the system.

Last decade has seen several multi up-gradation models and related software release policies. The unified modeling framework for developing multi-release software systems has gained tremendous lime light for prediction of software reliability. Various models have been developed to cater the diversified scenarios like those of imperfect debugging, stochasticity and testing effort related modeling. In the present work, using the unified modeling approach, it has been checked out which release performs best for a particular type of real life scenario. The data for Tandem computers has been utilized for validation purpose.

In this chapter we introduce an original approach to predict a day-ahead energy demand, based on machine learning and pattern recognition. Our Hidden Markov Model (HMM) is a simple and explainable model that uses integer sequences to define emission probability distributions attached to states. We develop a Mathematica code which relies on the maximum likelihood principle in HMM environment. Based on these exploratory results, we conclude that the HMM approach is an efficient way in modeling short-term/day-ahead energy demand prediction, especially during peak period(s) and in accounting for the inherent stochastic nature of demand conditions. The model can be easily extended to predict energy demand values for more than one day in the future. However, the accuracy of such predictions would decrease as we expect.

One of important classical reliability problems can be formulated as follows. Given a k-component system (k = 2, 3, …) with series reliability structure where the life-times X₁, …, X_k of the components are nonnegative stochastically dependent random variables. In order to determine the system’s (as a whole) reliability function as well as for some system maintenance analysis, one needs to find or construct a proper joint probability distribution of the random vector (X₁, …,X_k) which may be expressed in terms of the joint reliability (survival) function. Numerous particular solutions for this problem are present in the literature, to mention only [Freund in J Am Stat Assoc 56:971–77, 1961 1, Gumbel in J Am Stat Assoc 55:698–707, 1960 2, Marshall and Olkin in J Appl Probab 4:291–303, 1967 3]. Many other, not directly associated with reliability, k-variate probability distributions were invented [Kotz et al. in Continuous Multivariate Distributions, Wiley, New York, 2000 4]. Some of them later turned out to be applicable to the above considered reliability problem. However, the need for proper models still highly exceeds the existing supply. In this chapter we present not only particular bivariate and k-variate new models, but, first of all, a general method for their construction competitive to the copula methodology [Sklar A in Fonctions de repartition a n dimensions et leurs marges, Publications de l’Institut de Statistique de l’Universite de Paris, pp. 229–231, 1959 5]. The method follows the invented universal representation of any bivariate and k-variate survival function different from the corresponding copula representation. A comparison of our representation with the one given by copulas is provided. Also, some new bivariate models for 2-component series systems are presented. Possible applications of our models and methods may go far beyond the reliability context, especially toward bio-medical and econometric areas.

The chapter focuses on treating a particular problem of intelligent threats. We consider a least cost attack in a network-interdiction framework with a single source and a single destination. We suppose that a network is disabled if all links of a full cut set fail. That is, no flow can reach its destination node. We propose an exact solution under a budget constraint accounting for a threshold of success probability of the attack on targeted cut sets. We investigate the efficiency of the suggested solution through some illustrations. We extend the results to the case of networks with multiple sources/destinations.

The aim of this work is to study the performance issues of cooling tower unit of a coal fired thermal power plant. The complex series- parallel arrangement of repairable system has been modeled with Petri-Net (PN) approach. Reliability parameters of the considered system have been tabulated using fuzzy Lambda-Tau approach. Triangular Membership Function (TFN) has been used for considering the vagueness in the collected operational failure rate and repair time data. Failure dynamics of the considered system was studied on the basis of increasing and decreasing trend of reliability parameters. The analysis result has been supplied to the maintenance engineer of the plant to fix the optimum maintenance interval for the considered unit.

This paper addresses the overflowing issue of a suspension bridge in context of system’s reliability measures. Suspension Bridges have proved to be the most stable structure in the never-ending list of bridge constructions. Unfortunately, various effects of operational and environmental variability (factors) have posed several challenges to the reliability of the whole structure. History has encountered various failures of the suspension bridges with no early prediction and aftermath analysis. This paper investigates the ability to use Markov process for degradation modelling of suspension bridges by taking some of its important section namely Tower Foundation, Tower, Anchor, Cable, Deck along with human error. Here we identify various factors responsible for deterioration of the major components of bridge, which further affects the working of the mainframe structure.