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Performability of a product, a system or a service has been defined by this author (Misra in Inaugural Editorial of International Journal of Performability Engineering 1:1–3, 2005 [1] and Misra in Handbook of performability engineering, Springer, London, 2008 [2]) as an attribute of the holistic performance reckoned over its entire life cycle ensuring not only high dependability (quality, reliability, maintainability and safety) but also sustainability. Sustainability is a characteristic specific to a product, system or service. At the same time, a dependable product, system or service may not be sustainable. It may also be necessary here to point out that without dependability, sustainability is meaningless. Therefore, both dependability as well as sustainability attributes should be considered and must be evaluated in order to evaluate performability of a product. All other attributes of the definition of performability have been defined and can be computed except sustainability. In order to evaluate performability, it is therefore essential to define and compute sustainability. For developing sustainable products, systems and services in the twenty-first century, it is essential that we should be able to define precisely and quantify sustainability since one cannot improve what cannot be measured or assessed. The objective of the present chapter is to understand the implications of sustainability in order to facilitate computation of sustainability and thereby the performability. The purpose of 13 chapters in the Handbook (Misra in Handbook of performability engineering, Springer, London, 2008 [2]) by the author was to provide detailed introduction to each constituent elements of the definition of performability, namely quality, reliability, maintainability, safety and sustainability, and these chapters were received very well by the international academic community as is evident from Table 1.1. This was done with the intent to evoke interest among researchers across the world in the concept of performability leading to a way to compute or assess performability. But this did not happen in the past 12 years after the publication of the Handbook in 2008. The main impediment in this effort is the procedure to evaluate sustainability.

It is widely reported that coral reefs are suffering degradation from a combination of stresses. We have previously reported the use of genomic tools in the study of environmental impact assessment and hypothesize that monitoring the bacterial diversity associated with a coral would indicate changes in its health before visible damage occurs. This study analyzes the bacterial diversity associated with Porites coral collected from two sites in the Arabian Sea using culture independent techniques. Two clone libraries were constructed from the16S rDNA amplicons and selected individual clones were partially sequenced. Retrieved sequences were identified by BLAST analysis and indicate the presence of unidentified bacteria. Diversity index was calculated using Shannon–Wiener index. The bacterial diversity associated with coral sample 1 gives the index of species diversity, H 1 as 1.6287, divergence from eqiprobability as 45.708% and the evenness of the sample as 54.291. For coral sample 2, the values obtained were, H 1 as 1.97, divergence from eqiprobability as 15.11% and the evenness of the sample as 84.88. Sequences representing bacteria related to agricultural or industrial pollution and pathogenesis were also found. Coral samples collected near a lagoon area, showed a greater percentage of sequences representing bacteria related to human interventions, indicative of pollution.

In this paper, we propose a hybrid method to evaluate reliability of large and complex networks that incorporates the best features of earlier techniques such as KDH88 and CAREL. The present method combines CAREL’s COMpare and REDuce operators along with KDH88 and eliminates the use of the other two operators of CAREL, thus resulting in an extensive reduction in the number of exclusive and mutually disjoint terms. The procedure not only saves CPU time by an appreciable amount but also can be run even on a low‐end PC. To demonstrate the advantage of handling a large complex system on a relatively small computer, we provide a comparison of the present approach with CAREL and KDH88 and solve several problems of various complexities on a low‐end PC.

Reliability evaluation of a large and complex system is quite an involved and time-consuming process and its state-of-art is far from being called as satisfactory. This is mainly due to the fact that unionizing path sets results in large number of terms in the reliability expression. Thereafter, the process of computing numerical value of system reliability from its expression is a task not free from the build up of round-off errors. The entire process also restricts the use of a low-end PC for computing system reliability of such systems. In this paper, we propose an efficient methodology to evaluate reliability of large and complex systems based on minimal path sets; the path sets enumeration procedure used in this paper generates path sets in lexicographic and increasing order of cardinality — a condition, which is helpful in obtaining sum of disjoint products (SDP) of the system reliability expression in a compact form. Although we make use of the system connection matrix but no complicated matrix operations are performed to obtain the results. The paper further presents an improved multi-variable inversion (MVI) algorithm to evaluate system reliability in a compact form. Our approach offers an extensive reduction in the number of mutually disjoint terms and provides a minimized and compact system reliability expression. The procedure not only results in substantial saving of CPU time but also can be run on a low-end PC. To demonstrate this capability, we solve several problems of varied complexities on a low-end PC and also provide a comparison of our approach with earlier techniques available for the purpose.

In this paper a simple procedure of estimation of parameters of two widely used failure distributions (the normal and Weibull distributions) and a method of finding confidence intervals for the parameters is developed. The computational burden of estimation with fuzzy data as observed by Kruse and Meyer (1988) is easily overcome by using special properties of the estimators. It is also demonstrated that the order statistics procedure of estimation can easily be modified to tackle fuzzy data.

Weibull distribution is one of the most widely used model for failure data in reliability studies. In this paper a sequential estimation procedure for estimating the parameters of Weibull distribution is proposed, which is, in principle similar to Kalman filtering. The main advantage of this approach is that it shows the variation of parameters over a time as new failure data becomes available to the analyst for estimation. Also once an available data has been used, the method does not require that data for further processing as and when the new data becomes available for updating the estimates of parameters. Its use in Quality control asa control chart has been indicated and the procedure is illustrated with the help of examples.

A method of obtaining a minimized system reliability or unreliability expression using Demorgan's theorem is presented. Some formulae based on this theorem are provided, from which the minimized expression of system unreliability can be obtained by knowledge of pathsets. At the same time, this expression can also provide minimum cutsets of the system easily. On the other hand, one can obtain the minimum pathsets of a system without much difficulty, if the minimum cutsets are known.

It is well known that conventional reliability analysis using probabilities has been found to be inadequate to handle uncertainty of failure data and modelling. To overcome this problem, the concept of “fuzzy probability” has been used in the evaluation of reliability of a general non-series parallel network. Basically, only two operations, i.e. multiplication and complementation, need to be performed in assessing system reliability of a non-series parallel system. A procedure is developed to carry out these operations efficiently.

An efficient approach to multiple criteria redundancy optimization problem, often encountered in reliability design of engineering systems, is presented. A search technique introduced earlier (Misra 1991) in combination with multicriteria optimization methods, based on the min-max concept for finding the Pareto optimal solution of multicriteria optimization problems, provides an efficient and excellent approach for solving redundancy optimization problems. The approach is illustrated through several numerical examples. Based on this approach, a very general computer code called efficient search multi-objective programming (ESMOP) has also been developed. It is capable of considering any type of redundancy, constraint or individual cost function and thus offers a solution to many reliability design problems.

In many reliability design problems, the decision variables can only have integer values. The redundancy allocation is an example of one such problem. Besides the redundancy optimization problem, there are many other problems, such as spare pans allocation, repairmen allocation which all necessitate an integer programming formulation. In other words, integer programming plays an important role in system reliability optimization. An algorithm is presented which provides an exact, simple and economical solution to any general class of integer programming problems and thereby offers reliability designers an efficient tool for system design. The algorithm can effectively be used to solve a wide variety of reliability design problems. The scope of use of this algorithm is also indicated and the procedure is adequately illustrated through an example.

A simple and efficient technique for solving integer-programming problems that normally arise in system-reliability design is introduced. It quickly solves even a very large system problem. It consists of a systematic search near the boundary of constraints and involves functional evaluations only. It can handle system-reliability design problems of any type in which the decision variables are restricted to integer values. Several illustrative examples are given to substantiate these assertions. >

Several applications are proposed for an efficient, fast and exact technique for solving integer programming problems that normally arise in optimal reliability design problems. The computational experience of solving these problems is described and the algorithm is found to be superior to any of the earlier methods available to date in solving a wide variety of reliability design problems. The paper aims to demonstrate this capability of the algorithm; as the algorithm is based on functional evaluations only, it solves even very large system problems economically.

In many reliability design problems, the decision variables can only have integer values. The redundancy allocation is an example of one such problem; others include spare parts allocation, or repairmen allocation, which necessitate an integer programming formulation. In other words, integer programming plays an important role in system reliability optimization. In this paper, an algorithm is presented which provides an exact, simple and economical solution to any general class of integer programming problems and thereby offers reliability designers an efficient tool for system design. The algorithm can be used effectively to solve a wide variety of reliability design problems. The scope of use of this algorithm is also indicated and the procedure is illustrated by an example.

An efficient search technique is used to obtain the optimal configuration of a computer communication network. The method is based on an earlier paper and is easily programmable. An interactive computer code in FORTRAN 77 for the use on IBM-compatible PCs has also been developed. The approach has been illustrated by several examples.

The present paper provides an efficient approach to multiple criteria redundancy optimization problems, often encountered in reliability design of engineering systems. A search technique introduced earlier [10,11] in combination with the multicriteria optimization methods, based on min-max concept for finding Pareto optimal solution of multicriteria optimization problems, provides an efficient and excellent approach for solving redundancy optimization problems. The approach is illustrated through several numerical examples. Further, based on this approach, a very general computer code called ESMOP (Efficient Search Multi-Objective Programming) has also been developed. It is capable of considering any type of redundancy, constraint or individual cost function and thus offers to solve many reliability design problems.

The present paper provides a new mathematical formulation of a combined reliability and redundancy allocation involving multiple objective functions in the reliability design of a system employing mixed type of redundancy. The paper proposes an easily computerizable procedure for solving a variety of design problems. The proposed solution technique is a combination of the direct search technique [9,10] and a random search procedure for optimizing redundancy and reliability at the same time at each subsystem and uses multicriteria optimization procedure based on min-max approach [11,12] for obtaining Pareto optimal solutions. The procedure is illustrated through several examples. A general computer code, called ESMOP (Efficient Search Multi-Objective Programming), for the use on IBM compatible PCs has also been developed. The code takes into account all kinds of redundancies including multiple discrete choices for component reliabilities, and a wide variety of resource coefficients and constraint functions.

Risk is the possibility of a hazardous event occurring that will have an impact on the achievement of objectives. Risk is measured in terms of consequence (or impact) and likelihood of the event. Qualitatively, risk is considered proportional to the expected losses which can be caused by an event and to the probability of this event. Quantatively, it is the product of probability of hazardous event and the consequences. General views about risk perception and risk communication are discussed that help decision making. Risk management and risk governance along with probabilistic risk assessment and alternative approaches to risk analysis are also discussed.

This chapter is intended to introduce some of the areas of applications of performability engineering that have been presented in this handbook. Only the areas of current interest and importance have been included. It is expected that the chapters will accelerate the process of bringing about synergetic interaction between the practioners of performability engineering in several other relevant areas of applications.

The most important attribute of performance is reliability and this is defined as the probability of failure free operation over a specified duration of time under a given set of conditions, which depend on location and the kind of application the item is put to. In designing for reliability, the objective must be to maximize inherent and operational reliability such that occurrences of failures are considerably reduced. Component or system reliability goals can be achieved through design and testing. Failures and consequently accidents can be avoided if their causes of can be traced and taken care of during the design process.

Maintenance is another important aspect of system performance after reliability. There are several facets of maintenace management, and in this introductory chapter we would like to have these surveyed. Broadly speaking, maintenance is the process of maintaining equipment in its operational state either by preventing its transition to a failed state or by restoring it to an operational state following a failure. This leads to various types of maintenace activities that can be planned to realize the objective of maitenance, such as preventive, predictive, or corrective. Recent developments in maintenance engineering and management are also discussed in this chapter.

Sustainability is a characteristic of a process or state that can be maintained at a certain level indefinitely. Sustainability focuses on providing the best outcomes for both human and natural environments now, and indefinitely into the future. In recent years, academic interest and public discussion has led to the use of the word sustainability in reference to how long human ecological systems can be expected to be usefully productive. This chapter first examines the threats and then provides how the environmental threats can be assessed and mitigated.

For better system performance, attributes such as quality, reliability, maintainability, safety, and risk that are closely related and govern the dependability of the system, must be considered. It is also necessary to understand the inter-relationship between these factors so that one not only minimizes the chances of occurrence of any untoward incident at the design and fabrication stage but also minimizes the chances of occurrences and the consequences of such an event during the system operation and use phase.

Reliability is one of the most important attributes of performance in arriving at the optimal design of a system since it directly and significantly influences the system’s performance and its life cycle costs. Poor reliability would greatly increase life-cycle costs of the system, and reliability based design must be carried out if the system is to achieve its desired performance. An optimal reliability design is one in which all possible means available to a designer have been explored to enhance the reliability of the system with minimum cost under the constraints imposed on the development of a system.

All production processes employ materials, men and machines. Each of these elements has some inherent variability in addition to attributable variability, which can be controlled to an irreducible economic minimum. The subject of quality engineering and management is about reducing the variablity in products and processes, quality costs and to provide maximum satisfaction to the customers through improved product performance. The subject has grown considerably since 1930, when Shewhart first developed his statistical approach to quality. Several developments that have taken place since then are presented in this chapter along with quality planning, control, assurance and improvement, which form the backbone of any quality program.

The concept of performability is explained and the desirability of using this attribute in pursuing the design of engineering products, systems, and services is emphasized in order to meet the challenges of the 21st century. Today a new revolution is taking place where the leaders will be those nations that provide priority to the principles of sustainability in order to design, develop and use products, systems and services that are not only dependable but do not lead to disrupt the delicate ecological balance in nature. New materials, technologies and processes in consonance with environmental protection hold the key to future progress and prosperity.

The purpose of this chapter is not to deal with all the aspects of design of an engineering system, but to discuss the design process using the systems approach, which the design department or section of a manufacturing concern, particularly in the electronics, aerospace, machine tool sector and the producers of consumer goods such as automobiles, office equipment, and household appliances and in many other areas, can use. For a manufacturer, the research function helps develop new products or useful design modifications to an existing product range and development activity, which is basically an engineering function aimed at converting the research concept into a viable product, is known as an R&D activity and sometimes it may be associated with design engineering as a project design and development function.

The performance of a product, a system or a service is usually judged in terms of dependability (which can be defined as an aggregate of quality, reliability, and maintainability etc.) and safety, not overlooking the cost of achieving these attributes. As of now, dependability and cost effectiveness are primarily seen as instruments for conducting the international trade in the free market environment and thereby deciding the economic prosperity of a nation. However, the internalization of the hidden costs of environment preservation will have to be accounted for, sooner or later, in order to be able to produce sustainable products in the long run. These factors cannot be considered in isolation of each other. The Handbook of Performability Engineering considers all aspects of performability engineering, providing a holistic view of the entire life cycle of activities of the product, along with the associated cost of environmental preservation at each stage, while maximizing the performance.

At a post-Chernobyl conference on Probabilistic Safety Assessment and Risk management (PSA '87) held in September 1987, the inadequacies of the current Probabilistic Risk Assessment (PSA) came into sharp focus. Highlighting the importance of improvements in the current PSA, Professor Rasmussen - a pioneer in the PSA methodology - made a strong plea for reduction of rather large uncertainties in the results of current PSA. Obviously, amongst the ways to achieve this, one of the approaches would be to encourage collection and use of accurate failure data. However as the state of affairs is, a better alternative would be to develop a methodology which could handle imprecision of data and uncertainties of models which are existence in the current PSA. Fuzzy Set Theory (FST) provides a natural framework to achieve the above goal and therefore the present paper is intended to emphasize and explore the possibility of the use of such a theory to develop a methodology which is computationally simple and easy to use in the quantitative assessment of failure probability of catastrophic events in PSA, particularly, in level-I studies. Some illustrative examples are provided to demonstrate the feasibility and effectiveness of such an approach. It is demonstrated that a general purpose computer code can be developed without much difficulty to recast the PRA studies to incorporate fuzzy probabilities.

The present study gives a computerizable exact method to obtain the optimal design of a repairable computer communication system, assuming that a given amount of resources is available for linking the centres. The method is based on the Lawler-Bell algorithm. The objective is to obtain a design that maximizes the global availability of the system. This paper also provides several heuristics for the same problem, when the system under consideration is very large.

The 15 papers in this special section present new tools, techniques, applications, approaches, and surveys related to various aspects of reliability, and risk analysis and management.

The present paper applies a least square method to estimate parameters of a Weibull distribution, with the shape parameter lying in the range 0–3, where other methods like the maximum likelihood method are generally not applicable. Further, Fisher's F-test is employed to find the goodness of fit of a straight line. Two approximate methods have also been developed for the remaining range of the shape parameter. Illustrations are provided wherever necessary.

Cleaner production can’t be viewed in isolation and sustained without improving product performance as better product performance would imply less environmental pollution on account of product longevity and optimum utilization of material and energy for given resources. It is also naturally an economic proposition. Therefore the objective of this chapter is to invite the attention of environmental scientists, engineers and economists to incorporate the strategy of performance in future cleaner production planning and designs. Some of these concepts, such as an environmental risk presented in this chapter may not be new to them but the effort here has been to present a holistic view of the problem for effective implementation of performance improvement programme. Performance should be viewed together with environment and economy. Then only we will be able to realize the goal of sustainable development for prosperity in the 21st century.

In this paper, we propose a method of estimating top event fuzzy probability of a fault tree in case of a system consisting of multistate elements. To the best of our knowledge, no such attempt has ever been made in this direction in the past. Beta fuzzy probability vectors, as proposed by Stein [9], are used to model the joint-possibility distribution of multistate elements. The use of resolution identity keeps the computational requirement at its minimum. However, the estimation procedure is based on Zadeh’s extension principle.

In this chapter, we discuss an entirely new development in the area of system reliability evaluation. This development promises to provide an analyst a handy tool for carrying out various reliability analyses and make system reliability assessment a routine job, which need not be confined to highly qualified analysts only. This desk-top facility is considered preferable and economical over the sophisticated softwares on a PC, or on a mini or microcomputer keeping in view the several iterative trials that are required during the reliability design of a system. Besides, using this gadget, a reliability analyst or designer can observe the consequences of his ramifications of the designed system configuration, interactively. This gadget can also help in the learning process of system reliability designers.

There was a serious discussion on Reliability Engineering for the Future during the European Conference on Safety and Reliability held at Copenhagen, in June 1992. The panellists discussed the current state-of-art and critically examined the shortcomings of present models, practices, methodologies and approaches in the context of dependability engineering. The editor's motivation to put these thoughts into a detailed logical and meaningful presentation of involved problems in the form of a book came as a consequence of this event. This stocktaking will guide and channelize the on-going efforts and the future developments in the area of system reliability evaluation.

Fuzzy sets being relatively a new concepts, a brief summary of important definitions and relevant mathematical background are essential for understanding the fuzzy set theory (FST) and its applications. Our objective, in this chapter, is to restrict our discussion to such topics in FST which will have direct bearing on their applications to system reliability or performance evaluation and other related areas like fault tree analysis and risk assessment. The applications of FST are being presented in Part-II of this chapter, separately.

Since FST is necessary to deal with subjectivity and fuzziness which are inherent in the system reliability analysis, we introduce some of the important applications of FST to system reliability evaluation in this chapter. The first is fuzzy performance which is represented by a fuzzy set. The fuzzy performance is based on the consideration that the system performance can't be necessarily classified into crisp categories and that the transition from one state to the other is not sharp. The second application consists of fault tree analysis by a fuzzy probability, which is a fuzzy set defined on a probability space and by a failure possibility concept, which is a subjective unreliability measure. This approach allows the use of natural language in the system reliability analysis. Lastly, we discuss dependency considerations, environmental considerations and common cause failures in the failure possibility approach.

A large number of research articles have appeared in the literature during the last two decades on the subject of system reliability optimisation, each with a view to providing simple, exact and efficient techniques. Here, an efficient, fast and exact technique is proposed for solving integer‐programming problems that normally arise in optimal reliability design problems. The algorithm presented is superior to any of the earlier methods available so far, being based on functional evaluations and a limited systematic search close to the boundary of resources. Thus it can quickly solve even very large system problems. It can also be effectively used with other operations research problems involving integer‐programming formulations.

A geometric programming formulation of tolerance assignment problem in circuit is presented. The expressions for optimum component tolerances in circuit are derived. A method is also suggested for the tolerance assignment problem having multiple constraints. The advantage of the method is that it involves only hand calculations.

It is well-known that the conventional fault tree analysis using probabilities has been found to be inadequate to handle the imprecision of input failure data and the uncertainties associated with the modelling particularly in relation to dependency of failures. Therefore, to overcome these problems, a Fuzzy Fault Tree Analysis (FFTA) based on possibility distributions associated with the basic events and a fuzzy algebra for combining these events, has been presented in this paper. The authors propose an algorithm based on a discretization procedure which permits consideration of any arbitrary possiblity distribution for the events and provides a higher precision than that could be obtained in a graphical approach, as is presented here. The method described in this paper can be used for any coherent system. Further, an approximate representation for conditional possibility distributions has also been provided which can be used in conjunction with AND and OR-gates of the fault tree to consider the dependency of failures.

This paper presents a simple heuristic technique to arrive at the optimal redundancy allocation. There is a drastic reduction in the number of steps because of the criterion evolved, which allows for the addition of one or more units, simultaneously, at more than one stage. Examples have been provided to demonstrate the effectiveness of the technique.

Reliability evaluation of complex systems is of interest to engineers of all disciplines. The techniques for reliability evaluation depend upon the logic diagram of the system. System reliability evaluation is straight forward in case of series-parallel systems; while this is not so in general nonseries parallel systems. In this paper, many different techniques for reliability evaluation of general systems have been presented. Merits and demerits of every method are discussed. An example is solved by all the methods to have a comparison of computational labour involved and the size of final derived reliability expression.

This paper presents a systematic methodology to evaluate usual system effectiveness indexes of large and complex systems using network reduction and transformation techniques. This approach, allows some or all nodes to be imperfect, is efficient and simple, and uses less computer time and memory than existing techniques. Situations where it may not be feasible to use either star-delta or delta-star transformations in its usual form, to reduce a complex network are identified. Five subnetwork configurations are suggested to facilitate simplifying the network. search and subnetwork selection scheme which is adequate for the above purpose, and an efficient array-form representation requiring minimum memory to store the information about the network are offered.

Very few techniques exist for reliability evaluation of communication systems where links as well as nodes have certain probability of failure. This correspondence describes a technique by which the reliability expression for such a system can be conveniently derived. It is also shown that using the concept of this correspondence, it is possible to extend all the existing reliability-evaluation algorithms to communication systems with little effort.